Save the Dates:
On Fri Feb 13th, 2021 – 11.00 am via zoom
Maximilian Buser will give an ExQM talk on
`Probing Quantum Phases and the Hall Response in Bosonic Flux Ladders’
The focus of this talk is on bosonic flux ladders. First, we touch on a model which is envisioned to be realized in a future quantum gas experiment exploiting the internal states of potassium atoms as a synthetic dimension. Considering specifics of the future experiment, we map out the ground-state phase diagram and report on Meissner and biased-ladder phases. We show that quantum quenches of suitably chosen initial states can be used to probe the equilibrium properties of the dominant ground-state phases.
The 24th QIP is hosted and chaired by Profs. Michael Wolf and Robert König.
On Fri Jan 15th, 2021 – 11.00 am via zoom
Till Klostermann will give an ExQM talk on
`Fast, Long Distance Optical Transport of Cs’
As experimental setups for quantum gas experiments become more complicated, access around the experimental chamber for lasers, microscopes or magnetic field coils becomes a limiting factor. One way to address this issue is optical transport, to spacially separate the pre-cooling stages from the place of the final experiment.
On Fri Dec 11th, 2020 – 10.30 am via zoom
Max Bramberger (group Prof. Schollwöck) will give his inaugural ExQM talk on
`Dynamical Mean Field Theory with Matrix Product States’
When electrons become strongly correlated there is no straightforward way of treating macroscopic systems, as the local interaction between electrons competes with the non-local band structure effects.
In the last decades Dynamical Mean Field Theory (DMFT) has proven to be an appropriate method to treat both these effects. It approximates the problem by embedding an interacting impurity in a bath of non-interacting fermions.
The first part of this talk aims at explaining DMFT from a theoretical
point of view, as well as at introducing the algorithmic implementation using Matrix Product States (MPS) as an impurity solver. The second part gives an introduction to a recent application of the method to BaOsO3, a transition metal oxide in which Hund’s coupling and spin-orbit coupling as well as the van Hove singularity play a fundamental role.
On Fri Dec 4th, 2020 – 10.30 am via zoom
Adomas Baliuka (group Prof. Weinfurter) will give his inaugural ExQM talk on
`Post-Processing for Discrete Variable Quantum Key Distribution’
Two communicating parties can use quantum key distribution (QKD) to establish a shared secret key: First, they exchange quantum signals and measure them. Second, they perform post-processing, during which the secret key is extracted from the measurement results by making use of classical communication.
Key tasks of post-processing are authentication of the communication, error reconciliation and privacy amplification.
One solution to the error reconciliation problem is distributed source coding using low-density parity-check codes. Their decoding via iterative message passing algorithms is an example of inference on probabilistic graphical models. In our work, we further develop such code constructions and decoding algorithms suited for application-oriented QKD systems.
On Fri Nov 27th, 2020 – 10.30 am via zoom
Dr Frederik vom Ende will give an extended version of his PhD-defense talk on
`Reachability in Controlled Markovian Quantum Systems: An Operator-Theoretic Approach‘
On Fri Nov 20th, 2020 – 10.30 am via zoom
Prof. Dariusz Chruściński will give a distinguished-speaker ExQM lecture on
`On the Universal Constraints for Relaxation Rates for Quantum Dynamical Semigroups’
A conjecture for the universal constraints for relaxation rates of a quantum dynamical semigroup is proposed. It is shown that it holds for several interesting classes of semigroups, e.g., unital semigroups and semigroups derived in the weak coupling limit from the proper microscopic model.
Moreover, the conjecture proposed is supported by numerical analysis. This conjecture has further interesting implications: it allows to provide universal constraints for spectra of quantum channels and it provides a necessary condition to decide whether a given channel is consistent with Markovian evolution.
On Fri Nov 13th, 2020 – 10.30 am via zoom
Emanuel Malvetti will give his inaugural ExQM seminar on
`Optimal Cooling of Markovian Quantum Systems with Unitary Control’
We consider quantum systems described by Lindblad dynamics with unitary control. First we derive a master equation describing the evolution of the spectrum of the state, and give some polyhedral bounds on the achievable derivatives, leading to speed limits for the eigenvalues of the state. We characterize the Lindblad operators of systems that can always be asymptotically cooled to a pure state using unitary control, and systems for which any state can be reached from a pure state.
On Fri July 17th, 2020 at 10.30 am via zoom
Bo Wang will give an ExQM seminar on
`Continuous Quantum Light from a Dark Atom’
Single photons can be generated from a single atom strongly coupled to a optical cavity via a stimulated Raman adiabatic passage between two atomic ground states [1]. During the generation of the photon, the atom stays within the dark state of electromagnetically induced transparency (EIT) avoiding spontaneous decay from the excited state.
In contrast to this well-know scenario, here we present the result to generate quantum light continuously from an atom in the dark state. A coherent coupling is added between the atomic ground states to allow the coherent generation of multiple photons. This would usually result in the destruction of the dark state and the reappearance of spontaneous decay.
However, the dark states of the strongly coupled cavity EIT result from the interference between two atomic ground states entangled with different photonic states [2]. Such dark states are preserved from the local coupling that is applied only within the atomic Hilbert space. Additionally, the nonlinearity of the system allows us to control the quantum fluctuations of the generated light via a quantum Zeno effect.
[1] Kuhn, A. et al., Phys. Rev. Lett. 89, 067901 (2002)
[2] Souza, J.A. et al., Phys. Rev. Lett. 111, 113602 (2013).
On Fri July 10th, 2020 at 10.30 am via zoom
Dr Bálint Koczor will give an ExQM seminar on
`Measurement Cost of Metric-Aware Variational Quantum Algorithms’
Variational quantum algorithms are promising tools for near-term quantum computers as their shallow circuits are robust to experimental imperfections. Their practical applicability, however, strongly depends on how many times their circuits need to be executed for sufficiently reducing shot-noise.
In my talk I will introduce metric-aware quantum algorithms which are variational algorithms that use a quantum computer to efficiently estimate both a matrix and a vector object. I will discuss in detail the recently introduced quantum natural gradient approach which uses the quantum Fisher information matrix as a metric tensor to correct the gradient vector for the co-dependence of the circuit parameters.
I will finally present our rigorous characterisation of the number of measurements required to determine an iteration step to a fixed precision, and propose a general approach for optimally distributing samples between matrix and vector entries. In particular, we establish that the number of circuit repetitions needed for estimating the quantum Fisher information matrix is asymptotically negligible for an increasing number of iterations and qubits.
MCQST Virtual-Conference Programme
Held via meetanyway due to covid-19.
On Fri July 3rd, 2020 at 10.30 am via zoom
Lukas Knips will give an ExQM seminar on
`How Random Measurements Can Reveal Entanglement‘
In my talk, I’d like to present a method to use measurements in
arbitrary – and possibly even unknown – directions for detecting
entanglement.
Usually, quantum entanglement is revealed via a well aligned, carefully chosen set of measurements. Yet, under a number of experimental conditions, for example in communication within multiparty quantum networks, noise along the channels or fluctuating orientations of reference frames may ruin the quality of the distributed states.
In this talk and the corresponding paper [1] it is shown that even for strong fluctuations one can still gain detailed information about the state and its entanglement using random measurements. Correlations between all or subsets of the measurement outcomes and especially their distributions provide information about the entanglement structure of a state. We analytically derive an entanglement criterion for two-qubit states and provide strong numerical evidence for witnessing genuine multipartite entanglement of three and four qubits. Our methods take the purity of the states into account and are based on only the second moments of measured correlations.
Extended features of this theory are demonstrated experimentally with four photonic qubits. As long as the rate of entanglement generation is sufficiently high compared to the speed of the fluctuations, this method overcomes any type and strength of localized unitary noise.
[1] Knips, L., Dziewior, J., Kłobus, W. et al. Multipartite
entanglement analysis from random correlations. npj Quantum Inf 6, 51 (2020).
On Fri June 26th, 2020 at 10.30 am via zoom
Zoltán Zimborás will give an ExQM seminar on
`Fermionic Superselection Rules and the Concept of Orbital Entanglement and Correlation in Quantum Chemistry’
A recent development in quantum chemistry has established the quantum mutual information between orbitals as a major descriptor of electronic structure. This has already facilitated remarkable improvements of numerical methods and may lead to a more comprehensive foundation for chemical bonding theory.
Building on this promising development, our work provides a refined discussion of quantum information theoretical concepts by introducing the physical correlation and its separation into classical and quantum parts as distinctive quantifiers of electronic structure. In particular, we succeed in quantifying the entanglement. Intriguingly, our results for different molecules reveal that the total correlation between orbitals is mainly classical, raising questions about the general significance of entanglement in chemical bonding.
Our work also shows that implementing the fundamental particle number superselection rule, so far not accounted for in quantum chemistry, removes a major part of correlation and entanglement previously seen. In that respect, realizing quantum information processing tasks with molecular systems might be more challenging than anticipated.
Based on joint work including the Schollwöck group, see arXiv:2006.00961 .
On Fri June 5th, 2020 at 10.30 am via zoom
Frederik Bopp will give an ExQM seminar on
`Towards Singlet-Triplet Qubits in Quantum-Dot Molecules‘
Coherence, ease of control and scalability lie at the heart of all hardware for distributed quantum information technologies. This is particularly true for spin-photon interfaces based on III-V semiconductor quantum dots (QDs) since they combine properties such as strong interaction with light, robust spin-photon selection rules, nearly pure transform limited emission into the zero-phonon line and ease of integration into opto-electronic devices. However, the comparably short spin coherence times of single electrons and holes in QDs (T2* ~ 10-100ns) [1], could limit their applicability for distributed quantum technologies.
Unlike single electron and hole spins which are sensitive to the fluctuating nuclear spin environment in III-V materials, singlet-triplet (S-T) qubits in pairs of coupled dots – quantum dot molecules (QDMs) – have extended spin coherence times when operated at a sweet spot for which the S-T splitting is independent of electric and magnetic field fluctuations. Such optically addressable S-T spin qubits promise to extend the obtainable T2* times by several orders of magnitude whilst retaining the advantages outlined above. Previously, experiments using Schottky gated samples have provided important insights into orbital structure, exchange couplings, phonon couplings and spin-dephasing [2, 3]. However, these studies have also shown it is very challenging to simultaneously maintain the electric field needed to reach the sweet spot condition whilst simultaneously operating in the required charge stability condition, where the QDM is populated by two spins (electron or hole), one in each of the dots forming the QDM.
We present a different approach where the charge status of the QDM is controlled optically, whilst the coupling between the two spins can be tuned to the sweet spot electrically. To achieve this, an AlGaAs tunneling barrier is inserted immediately adjacent to the QDM layer, allowing for sequential optical control of the charge status via tunneling ionization [2] while the tunnel coupling between the two dots can be electrically controlled via a gate voltage. We will present first studies of the dynamics of the optical charging of QD molecules as well as first results on the electric field dependent coupling control.
On Fri May 29th, 2020 at 10.30 am via zoom
David Castells Graells will give his inaugural ExQM seminar on
`Tunable Enhanced Atom-Light Interaction Using Atomic Subwavelength Arrays’
A central challenge in quantum optics is the realization of controlled efficient interactions between atoms and photons. One promising approach consists on coupling one or more atoms to an optical medium such as photonic crystal waveguides [1]. The use of these structures not only improves the free-space approaches, but their tailored dispersion relations offer prospects of new paradigms for atom-light interactions. Imperfections and optical losses inside the medium can, however, hinder the observation and use of some its features.
In this project we investigate as an alternative subwavelength arrays of atoms, which are known to contain collective states with suppressed – compared to single emitters – emission to free space [2]. These states can be understood as guided modes of the atomic chain in the 1D case. To describe the dynamics of the system, we use a quantization scheme based on the classical electromagnetic Green’s tensor, and the master equation that results of tracing out the electromagnetic modes.
We, then, engineer the “impurity” atoms that interact with the subwavelength array to achieve an efficient coupling to the subradiant states only. In the Markovian regime, we obtain effective expressions for the dynamics of the impurity atoms, which show many of the interesting features predicted with photonic crystal waveguides.
[1] D. E. Chang, et al., Rev. Mod. Phys. 90.3 (2018): 031002
[2] A. Asenjo-Garcia, et al., Phys Rev. X 7.3 (2017): 031024
On Fri May 15th, 2020 at 10.30 am via zoom
Frederik vom Ende will give an ExQM seminar on
`The Role of Strict Positivity in Quantum Dynamics’
Motivated by quantum thermodynamics we investigate the notion of strict positivity, that is, linear maps which map positive definite states to something positive definite again.
We show that strict positivity is decided by the action on any full-rank state, and that the image of not-strictly positive channels—up to something unitary—lives inside a lower-dimensional block. This implies that such channels have maximal distance from the identity channel.
We use this to conclude that Markovian dynamics are strictly positive and investigate connections between strict positivity and other notions of divisibility.
On Fri May 8th, 2020 at 10.30 am via zoom
Julian Roos will give an ExQM seminar on
`Markovian Regimes in Quantum Many-Body Systems’
Long time evolution of the full state of quantum many body systems is generally out of reach due to build-up of entanglement. However, the computation of local observables only requires knowledge of the state of (small) subsystems. Is it possible to obtain a description of the reduced dynamics similarly to what is done in the fields of Quantum Optics and Open Quantum Systems (OQS)?
We expect that such an endeavour is most promising in the simplest case, i.e. when the dynamics are Markovian (memoryless), and we thus study if such regimes do also exist in a many body setup. Here, the conditions that allow for the derivation of a Markovian master equation in the theory of OQS (Born-Markov) are not satisfied.
You may wish to install www.zoom.us for preparation. Stay healthy!
On Fri Mar. 20th, 2020 in the Mathematics Building, 3rd floor Seminar Room 03.10.011 (Wolf group) at 10.30 am [note room shift due to MPQ Corona-virus policy!]
Julian Roos would have given an ExQM seminar on
`Markovian Regimes in Quantum Many-Body Systems’
Long time evolution of the full state of quantum many body systems is generally out of reach due to build-up of entanglement. However, the computation of local observables only requires knowledge of the state of (small) subsystems. Is it possible to obtain a description of the reduced dynamics similarly to what is done in the fields of Quantum Optics and Open Quantum Systems (OQS)?
We expect that such an endeavour is most promising in the simplest case, i.e. when the dynamics are Markovian (memoryless), and we thus study if such regimes do also exist in a many body setup. Here, the conditions that allow for the derivation of a Markovian master equation in the theory of OQS (Born-Markov) are not satisfied.
On Tue Mar. 10th, 2020 in Chemistry Dept. (6th level in yellow section) Lecture Room CH 63.214 at 1.15 pm
Emanuel Malvetti (ETH Zurich, Renner group) will give an ExQM seminar on
`Quantum Circuits for Sparse Isometries’
We consider the task of breaking down a quantum computation given as an isometry into C-Nots and single-qubit gates, while keeping the number of C-Not gates small. Although several decompositions are known for general isometries, here we focus on a method based on Householder reflections that adapts well in the case of sparse isometries.
On Fri Mar. 6th, 2020 in the Mathematics Building, 3rd floor Seminar Room 03.10.011 (Wolf group) at 10.30 am [note room shift due to MPQ Corona-virus policy!]
Nicola Pancotti will give an ExQM seminar on
`Quantum East Model: Localization, Non-Thermal Eigenstates
and Slow Dynamics’
We study in detail the properties of the quantum East model, an interacting quantum spin chain inspired by simple kinetically constrained models of classical glasses.
Through a combination of analytics, exact diagonalization and tensor network methods we show the existence of a fast-to-slow transition throughout the spectrum that follows from a localization transition in the ground state.
On the slow side, we explicitly construct a large (exponential in size) number of non-thermal states which become exact finite-energy-density eigenstates in the large size limit, as expected for a true phase transition.
A “super-spin” generalization allows us to find a further large class of area-law states proved to display very slow relaxation.
Under slow conditions, many eigenstates have a large overlap with product states and can be approximated well by matrix product states at arbitrary energy densities.
We discuss implications of our results for slow thermalization and non-ergodicity more generally for quantum East-type Hamiltonians and their extension in two or higher dimensions.
On Wed Feb. 19th in Chemistry Dept. (6th level in yellow section) Lecture Room CH 63.214 at 10.30 am
Nicolas Augier (CNRS, Paris) will give a special ExQM seminar on
`Results for the Ensemble Controllability of Quantum Systems´
The principal issue that will be developed in this talk is how to control a parameter-dependent family of quantum systems with a common control input, that is, the ensemble controllability problem. Thanks to the study one-parametric families of Hamiltonians and their generic singularities when the system is driven by two real inputs, we will give an explicit adiabatic control strategy for the ensemble controllability problem when geometric conditions on the spectrum of the Hamiltonian are satisfied, in particular, the existence of conical or semi-conical intersections of eigenvalues.
Then, in order to understand which controllability properties can be extended to the case where the system is driven by a single real input, we will study the compatibility of the adiabatic approximation with the rotating wave approximation.
On Wed Feb. 5th in MPQ Lecture Hall at 2.00 pm
Prof. Ugo Boscain (CNRS, Paris) will give a special ExQM seminar on
`Ensemble Control of Spin Systems´
On Thu Jan. 16th in the LMU Centre for Advanced Studies (CAS), Seestr. 13, 80802 Munich at 6.30 pm
Prof. Immanuel Bloch will be giving a show-case lecture on the state-of-the-art of quantum simulation in optical lattices. Registration is recommended under info@cas.lmu.de .
On Fri Jan. 10th in MPQ Lecture Hall at 10.30 am
Qiming Chen will give his inaugural ExQM seminar on
`Quantum Fourier Transform in Oscillating Modes´
Quantum Fourier transform (QFT) is a key ingredient for many quantum algorithms. In typical applications such as phase estimation, a considerable number of ancilla qubits and gates are used to form a Hilbert space large enough for high-precision results. Qubit recycling reduces the number of ancilla qubits to one, but it is only applicable to semi-classical QFT and requires repeated measurements and feedforward within the coherence time of the qubits.
In this work, we explore a novel approach that uses two ancilla resonators to form a large dimensional Hilbert space for the realization of QFT. By employing the perfect state-transfer method, we map an unknown multi-qubit state to one resonator, and generate the QFT state in the second oscillator through cross-Kerr interaction and projective measurement. Quantitative analyses show that our method enables relatively high-dimensional and fully-quantum QFT in the state-of-the-art superconducting quantum circuits, which paves the way for implementing various QFT related quantum algorithms in the near future.
Moritz August, Anna-Lena Hashagen, Bálint Koczor, Lukas Knips, David Leiner, Stephan Welte, Jakob Wierzbowski receive their honours documents during the ceremony.
On Mon Dec. 9th in MPQ Lecture Hall B0.32 at 10.30 am
Dr Bálint Koczor (now Oxford University) will talk on
`Variational-State Quantum Metrology´
Quantum metrology aims to increase the precision of a measured quantity that is estimated in the presence of statistical errors using entangled quantum states.
We present a novel approach for finding (near) optimal states for metrology in the presence of noise, using variational techniques as a tool for efficiently searching the classically intractable high-dimensional space of quantum states. We comprehensively explore systems consisting of up to 9 qubits and find new highly entangled states that are surprisingly not symmetric under permutations and non-trivially outperform previously known states up to a constant factor 2. We consider a range of environmental noise models; while passive quantum states cannot achieve a fundamentally superior scaling (as established by prior asymptotic results) we do observe a significant absolute quantum advantage.
We finally outline a possible experimental setup for variational quantum metrology which can be implemented in near-term hardware.
This talk is based on a joint work (arXiv:1908.08904) with Suguru Endo, Tyson Jones, Yuichiro Matsuzaki and Simon C. Benjamin.
On Fri Nov. 29th in MPQ Lecture Hall at 10.30 am
Maximilian Buser will talk on
`’Ground-State Phases and Quench Dynamics in Interacting Bosonic Flux-Ladders´
Furthermore, we demonstrate that quantum quenches from suitably chosen initial states can be used to probe the equilibrium properties in the transient dynamics. Concretely, we consider the instantaneous turning on of hopping matrix elements along the rungs or legs in the synthetic flux-ladder model, with different initial particle distributions.
On Fri Oct. 25th in MPQ Lecture Hall at 10.30 am
Markus Hasenöhrl (Group Michael Wolf) will talk on
`’Interaction-Free’ Channel Discrimination´
On Tue Oct. 8th in MPQ Lecture Hall at 2.30 pm
John Preskill will talk on
`Quantum Computing in the NISQ Era and beyond´
Noisy Intermediate-Scale Quantum (NISQ) technology will be available in the near future. Quantum computers with 50-100 qubits may be able to perform tasks which surpass the capabilities of today’s classical digital computers, but noise in quantum gates will limit the size of quantum circuits that can be executed reliably.
NISQ devices will be useful tools for exploring many-body quantum physics, and may have other useful applications, but the 100-qubit quantum computer will not change the world right away – we should regard it as a significant step toward the more powerful quantum technologies of the future.
Quantum technologists should continue to strive for more accurate quantum gates and, eventually, fully fault-tolerant quantum computing.
On Wed. 25th Sept. at 10.00am in MPQ Lecture Hall
Stephan Welte will give his PhD defense talk on
`Generation of Optical Cat States Entangled with an Atom´
Schrödinger’s cat is a famous gedanken experiment on the existence of quantum mechanical superposition states of macroscopic objects [1]. Experimental implementations in quantum optics employ the superposition of two coherent states with an opposite phase, so-called cat states. These continuous-variable states can be tuned to vary the degree of macroscopicity and to study decoherence effects.
Our experiment implements a strong interaction of a coherent light pulse with a single trapped Rubidium atom, provided by an optical cavity [2]. We deterministically produce a hybrid entangled state between the atomic spin and the phase of the propagating light pulse. A projective measurement of the atomic spin projects the optical state and prepares it in an optical cat state. We study the non-classical properties of the produced states and demonstrate control over all relevant degrees of freedom, using coherent control of the atomic qubit. In the future, cat states may find applications in fiber-based optical quantum networks.
Joint work with Bastian Hacker, Severin Daiss, Lin Li, Lukas Hartung, Emanuele Distante, and Gerhard Rempe.
NB: will be held in Bad Aibling, see Conference Schedule.
MPQ, Lecture Hall at 10.30 am.
We will plan activities in 2019/20 including
Please all attend.
In MPQ Lecture Hall at 10.30 am
Margret Heinze will talk on
`Universal Uhrig Dynamical Decoupling for Bosonic Systems´
We construct efficient deterministic dynamical decoupling schemes protecting continuous variable degrees of freedom from decoherence.Our schemes target decoherence induced by quadratic system-bath interactions with analytic time dependence. We show how to suppress such interactions to ?-th order using only ? pulses. Furthermore, we show to homogenize a 2m-mode bosonic system using only (? + 1)^(2?+1) pulses, yielding – up to ?-th order – an effective evolution described by non-interacting harmonic oscillators with identical frequencies.
The decoupled and homogenized system provides natural decoherence-free subspaces for encoding quantum information. Our schemes only require pulses which are tensor products of single-mode passive Gaussian unitaries and SWAP gates between pairs of modes.
PRL_123 (2019), 010501 (also https://arxiv.org/abs/1810.07117v2)
Held at Deutsches Museum, Centre for New Technologies (ZNT), Museumsinsel 1, see map.
In MPQ Lecture Hall at 10.30 am
Frederik vom Ende will talk on
`Reachability in Infinite-Dimensional Unital Open Quantum Systems with Switchable GKS-Lindblad Generators´
In quantum systems theory one of the fundamental problems boils down to: given an initial state, which final states can be reached by the dynamic system in question?
Here we consider infinite-dimensional open quantum dynamical systems following a unital Kossakowski-Lindblad master equation extended by controls. More precisely, their time evolution shall be governed by an inevitable (potentially unbounded) Hamiltonian drift term, finitely many bounded control Hamiltonians allowing for (at least) piecewise constant control amplitudes plus a bang-bang switchable noise term in GKS form (generated by some compact V).
Generalizing standard majorization results from finite to infinite dimensions, we show that such bilinear quantum control systems allow to approximately reach any target state majorized by the initial one — as up to now only has been known in finite-dimensional analogues.
In MPQ Lecture Hall (back again to left of entrance) at 10.30 am
Stephan Welte will talk on
`Generation of Optical Cat States Entangled with an Atom´
Schrödinger’s cat is a famous gedanken experiment on the existence of quantum mechanical superposition states of macroscopic objects [1]. Experimental implementations in quantum optics employ the superposition of two coherent states with an opposite phase, so-called cat states. These continuous-variable states can be tuned to vary the degree of macroscopicity and to study decoherence effects.
Our experiment implements a strong interaction of a coherent light pulse with a single trapped Rubidium atom, provided by an optical cavity [2]. We deterministically produce a hybrid entangled state between the atomic spin and the phase of the propagating light pulse. A projective measurement of the atomic spin projects the optical state and prepares it in an optical cat state. We study the non-classical properties of the produced states and demonstrate control over all relevant degrees of freedom, using coherent control of the atomic qubit. In the future, cat states may find applications in fiber-based optical quantum networks.
Joint work with Bastian Hacker, Severin Daiss, Lin Li, Lukas Hartung, Emanuele Distante, and Gerhard Rempe.
In MPQ Lecture Hall (back again to left of entrance) at 10.30 am
Prof. Michael Keyl will talk on
‘Unitary Control of Quantum Systems in Finite and Infinite Dimensions’
In finite dimensions this question can be completely answered in a Lie-algebraic framework. Infinite dimensions, on the other hand, trigger more challenging mathematics and require methods from operator analysis and (extensions of) infinite dimensional Lie theory.
This talk will provide an introduction into this topic, and an overview on some of its central questions and results. In finite dimensions we show in particular how a system Lie algebra can be associated to a quantum control system, which leads to an easy condition for deciding controllabiliy: the celebrated Lie algebra rank conditon.
In MPQ Lecture Hall (back again to left of entrance) at 10.30 am
Dr Claudius Hubig will talk on
‘Recent Developments in Tensor Networks’
In the first half of the talk, I will report on recent progress made in the description of finite-dimensional quantum systems with non-local interactions using tensor network approaches. Such systems include molecular systems of interest in quantum chemistry as well as effective systems arising as the to-be-solved inner problems of the dynamical mean-field theory or the density matrix embedding theory. In all cases, using loop-free MPS or tree tensor networks, sufficient progress can be made over standard solvers using exact diagonalisation.
In the second half of the talk, we will summarise the relatively novel application of real-time evolution to infinite two-dimensional tensors networks to obtain time-dependent observables. The evolution is applied to the 2D S=1/2 Néel state on the square lattice in a disorder averaged Hamiltonian, where we find hints towards many-body localisation in the spin dynamics as the disorder strength is increased.
Refs.: arXiv:1811.00048, arXiv:1901.05824 and arXiv:1812.03801.
Note Location: MPI for Astrophysics, MPA, Lecture Hall E.0.11 at 10.30 am (MPA is next door to MPQ, Karl-Schwarzschild-Str. 1, see room finder here.)
Prof. Rédei will talk on
‘On the Tension between Mathematics and Physics’
Because of the complex interdependence of physics and mathematics their relation is not free of tensions. The talk looks at how the tension has been perceived and articulated by some physicists, mathematicians and mathematical physicists.
Some sources of the tension are identified and it is claimed that the tension is both natural and fruitful for both physics and mathematics. An attempt is made to explain why mathematical precision is typically not welcome in physics.
MPQ Lecture Hall B0.32 at 10.30 am
Till Klostermann will talk on
‘Building a New Caesium Quantum Gas Microscope’
I will present my PhD-thesis project, setting up a new experiment utilizing Caesium for investigating artificial gauge fields. The new experiment will use Raman assisted tunneling in a state-dependent lattice instead of shaking to engineer these gauge fields. A single-site resolution objective will give access to the individual particles position.
Due to Caesium’s large and accessible Feshbach resonance, it is a good candidate to investigate interactions in systems influenced by artifical gauge fields. I will also talk about the current status of the setup.
IAS, Lichtenbergstr. 2a, Wed Jan. 16th at 1.00 pm.
Prof. Robert König will talk on
‘Quantum Advantage with Shallow Circuits’
Prof. Robert König (Theory of Complex Quantum Systems) will talk about the advantage of quantum computers as compared to conventional computers.
Quantum computers can perform operations on many values in one fell swoop whereas a single conventional computer typically must execute these operations sequentially. The promise of quantum computing lies in the ability to solve certain problems significantly faster (TUM press release).
Relevant Publication:
S. Bravyi, D. Gosset, R. König, “Quantum advantage with shallow circuits”, Science, 19. October 2018. DOI: 10.1126/science.aar3106
MPQ Lecture Hall B0.32, Tue Jan. 15th at 10.30 am.
Prof. Maurice de Gosson (Univ. Vienna) will talk on
‘Symplectic Coarse-Grained Dynamics: Chalkboard Motion in
Classical and Quantum Mechanics’
In the usual approaches to mechanics (classical or quantum) the primary object of interest is the Hamiltonian, from which one tries to deduce the solutions of the equations of motion (Hamilton or Schrödinger).
In the present talk, we reverse this paradigm and view the motions themselves as being the primary objects. This is made possible by studying arbitrary phase space motions, not of points, but of ellipsoids with the requirement that the symplectic capacity of these ellipsoids is preserved. This allows us to pilot and control these motions as we like. In the classical case these ellipsoids correspond to a symplectic coarse-graining of phase space, and in the quantum case they correspond to the “quantum blobs” we have defined in previous work, and which can be viewed as minimum uncertainty phase-space cells which are in a one-to-one correspondence with Gaussian pure states.
Mathematics Building MI, Boltzmann Str. 3, Room 00.10.011 at 12.30 noon.
Anna-Lena Hashagen will talk on
‘Symmetry Methods in Quantum Information Theory’
Conference Centre, Gögginger Str. 10, Augsburg
Michael Lohse and Christian Sames (QCCC) receive their honours documents during the ceremony.
MPQ Seminar Room Cirac Group in Third Floor at 10.30am
Bálint Koczor will talk on
‘On Phase-Space Representations of Spin Systems and their Relations to Infinite-Dimensional Quantum States’
For more detail see also arXiv:1808.02697 and arXiv:1811.05872 .
'Tensor Networks and Machine Learning for Approximating and Optimizing Functions in Quantum Physics'
Mathematics Building MI, Boltzmann Str. 3, Room 03.09.012 at 3.00 pm.
Moritz August will talk on
‘Tensor Networks and Machine Learning for Approximating and Optimizing Functions in Quantum Physics’
We explore the intersection of computer science and mathematics to address challenging problems in numerical quantum physics. We introduce, analyze and evaluate novel methods for the approximation of physical quantities of interest as well as the optimization of performance criteria in quantum control. These methods are based on techniques from the fields of tensor networks, numerical analysis and machine learning. Furthermore, we present work on the relation between machine learning and tensor network methods for the representation of quantum states.
We introduce a general algorithm which for the first time allows to approximate global functions Trf (A) of matrix product operators A which represent Hermitian matrices of very high dimensionality. Following this, we present an analytical analysis of the partial results computed by the procedure. This analysis leads us to the discovery of a more efficient variant of the algorithm and we subsequently show that it can be applied to a large class of spin Hamiltonians in quantum physics. We finally demonstrate how our method yields a novel strategy to approximate properties of thermal equilibrium states, some of which were so far inaccessible for numerical methods.
In the second part, we present a novel and broadly applicable method for solving quantum control scenarios. The method employs a particular class of recurrent neural networks, the long short-term memory network, to probabilistically model control sequences and optimize these models with tools from supervised and reinforcement learning. In a first version, we use an optimization procedure inspired by evolutionary algorithms to train the networks. We demonstrate in a quantum memory setting that the method can produce better results than certain analytical solutions. We then improve on these results by introducing a different optimization strategy based on insights from reinforcement learning known as policy gradient algorithms. The combination of long short-term memory networks and policy gradient optimization schemes allows us to tackle a wide variety of control problems, which we demonstrate numerically.
Finally, we show results on the relation between tensor networks and a particular class of machine learning models, the restricted Boltzmann machine. We find that restricted Boltzmann machines can be generalized in the tensor network framework and gain insight about their efficiency in representing states of many-body quantum systems.
MPQ Lecture Hall B0.32 at 10.30 am.
Nicola Pancotti (back from Harvard) will talk on
‘Machine Learning and Tensor Networks for Quantum Many Body Physics’
In this talk, I will give a simple introduction to Machine Learning and Tensor Network techniques for the ground state search problem in Quantum Many Body physics. I will show how one can use Neural Network States as a powerful ansatz for the description of many body quantum spin systems and how to map a sub class of them to some well known Tensor Network families. I will show applications to classical pattern recognition and how to combined those families to existing Machine Learning techniques in order to improve their performances.
Finally I will discuss possible directions to extend these methods to fermionic systems and, in particular, to the framework of Gaussian states.
MPQ Lecture Hall B0.32 at 10.30 am.
Frederik Bopp (who has just joined the Finley group as ExQM student) will talk on
‘Hybrid Photonic-Plasmonic Biosensing’
Cavity-enhanced optical and plasmonic sensing are two commonly utilised techniques to analyse nanoparticle. Combining them into a hybrid system potentially allows to achieve high finesses and sub diffraction limited mode volumes simultaneously, leading to enhanced detection sensitivities and an increased range of detectable biomolecules. On the long term, these biosensors could form a new set of medical tools for the discovery, the study and the detection of biomarkers. My Master research aims at studying the coupling of an open microcavity to a gold plasmonic nanorod and to establish their potential for single molecule detection.
In my presentation I will provide a theoretical and experimental description of the coupling mechanism, linking these results to the potential sensitivity limit of this system.
MPQ Lecture Hall B0.32 at 2 pm.
Dr. Enno Aufderheide (Secretary General of Humboldt-Foundation) will talk on
‘Postdoc Opportunities in the Humboldt-Foundation`s Global Network’
Dr. Enno Aufderheide
On 1 July 2010, Enno Aufderheide became the new Secretary General of the Humboldt Foundation. From 2006 to 2010, he was head of the Research Policy and External Relations Department at the Max Planck Society in Munich where he played a key role in the Society’s internationalisation strategy. From December 2008 onwards, he also took on responsibility for managing the Minerva Foundation for the promotion of German-Israeli academic cooperation.
The 14th International Workshop on Numerical Ranges and Radii (WONRA) is co-hosed by ExQM (and organised by Th. Schulte-Herbrüggen) under the motto
The numerical range, i.e. the set W(A):={<x|Ax> | <x|x> =1} plays a crucial role in spectral theory and, e.g., in the search of ground-state energies (Rayleigh quotient). In 1918/1919, by the celebrated Toeplitz-Hausdorff Theorem, it was shown to form a convex set. Clearly, the numerical range W(A) comprises the spectrum spec(A). In quantum-many-body systems, the important question arises, whether the spectrum of the underlying Hamiltonian is gapped — this decision problem was addressed in a seminal paper by Cubitt, Perez-Garcia, and Wolf, Nature 528, 207 (2015). Michael Wolf will talk on Undecidebility of the Spectral Gap in a special ExQM Lecture on Fri Jun 15th at 3pm in MPQ Lecture Hall B0.32 as one highlight in this conference.
Schedule in Overview,
June 14 (Thursday), MPQ, Lecture Hall B0.32
9:30 to 16:30 talks by Choi, Spitkovsky, Tam, Farenick, Nakazato, Chien, Osaka, Taheri
June 15 (Friday) MPQ, Lecture Hall B0.32
9:30 to 17:30 talks by Życzkowski, Schulte-Herbrüggen, Gross, Psarrakos, Schuch, Wolf, Weis, Huckle
June 16 (Saturday)
Social event and discussion
Afternoon: Visit in Munich downtown museums, e.g., Blue Rider in Lenbachhaus
18:30 optional dinner in a Munich beergarden downtown
June 17 (Sunday), IAS, Lichtenbergstr. 2a, Auditorium on ground floor
10:00 to 16:30 talks by Bebiano, Badea, vom Ende, Diogo, Crouzeix, Sze, Bračic
18:00 to 20:30 conference dinner at IAS faculty club
June 18 (Monday), IAS, Lichtenbergstr. 2a, Auditorium on ground floor
9:45 to 12:00 talks by Kressner, Lau, Li
12:00 to 14:00 Lunch on campus at IPP mensa
TUM Campus, Walther-Meissner Institute, Walther-Meissner-Straße 8, 2nd floor, Seminar Room 143 (or, if too noisy, 128) at 1.30 pm.
Dr. Shai Machnes (University of Saarbrücken) will talk on
‘Control of Quantum Devices: Merging Pulse Calibration and System Characterization using Optimal Control’
The current methodology for designing control pulses for quantum devices circuits often results in a somewhat absurd situation: pulses are designed using simplified models, resulting in initially poor fidelities. The pulses are then calibrated in-situ, achieving high-fidelities, but without a corresponding model. We are therefore left with a model we know is inaccurate, working pulses for which we do not have a matching model, and a calibration process from which we learned nothing about the system.
Here, we propose a novel procedure to rectify the situation, by merging pulse design, calibration and system characterization: Calibration is recast as a closed-loop search for the best-fit model parameters, starting with a detailed, but only partially characterized model of the system. Fit is evaluated by fidelity of a complete set of gates, which are optimized to fit the current system characterization. The end result is a best-fit characterization of the system model, and a full set of high-fidelity gates for that model.
We believe the new approach will greatly improve both gate fidelities and our understanding of the systems they drive.
MPQ, Lecture Hall (moved to B0.32) at 10.30 am
Bo Wang (Rempe group) will talk on
‘Strong Coupling between Photons via a Four-Level N-type Atom’
Four-level N-type atomic systems have been investigated for effects like the electromagnetically induced absorption (EIA) and cross-phase modulation (XPM) when interacting with classical light fields. Despite the giant non linearity, the interaction strengths are negligible at the level of individual quanta. However with the strong light matter coupling provided by cavity quantum electrodynamics, a significant interaction between single photons can be reached.
Here I will give a brief introduction on our experimental setup and the experiment where the photons of two light fields are strongly coupled via a single four-level N-type atom. The fields drive two modes of an optical cavity, which are strongly coupled to two separate transitions. A control laser drives one transition’s ground state to the other transition’s excited state, the inner transition of the N-type atom. It induces a tunable coupling between the modes and results in a doubly nonlinear energy-level structure of the photon-photon-atom system. The strong correlation between the light fields is observed via photon-photon blocking and photon-photon tunneling. With this system, nondestructive counting of photons and heralded n-photon sources might be within reach.
TUM Mathematics Building, Boltzmannstr. 8, Lecture Hall 3 at 4.00 pm.
Prof. Stefan Weltge will give his inaugural lecture on
‘A Barrier to P=NP Proofs’
The P-vs-NP problem describes one of the most famous open questions in mathematics and theoretical computer science. The media are reporting regularly about proof attempts, all of them being later shown to contain flaws. Some of these approaches where based on small-size linear programs that were designed to solve problems such as the traveling salesman problem efficiently.
Fortunately, a few years ago, in a breakthrough result researchers were able to show that no such linear programs can exist and hence that all such attempts must fail, answering a 20-year old conjecture.
In this lecture, I would like to present a quite simple approach to obtain such a strong result. Besides an elementary proof, we will hear about (i) the review of all reviews, (ii) why having kids can boost your career, and (iii) a nice interplay of theoretical computer science, geometry, and combinatorics.
von-Neumann Lecture Series by Prof. Marius Junge (University of Illinois, USA) held at TUM Mathematics, Boltzmannstr. 3.
TUM Campus, Chemistry Building, Lichtenbergstrasse 4, 6th floor (yellow section), Seminar Room CH63.214 at 4.15 pm.
Prof. Martin Plenio (University of Ulm) will talk on
‘Diamond Quantum Devices: From Quantum Simulation to Medical Imaging’
Perfect diamond is transparent for visible light but there are famous diamonds, such as the famous Oppenheim Blue or the Pink Panther worth tens of millions of dollar, which have intense colour. An important source of colour in diamond are lattice defects which emit and absorb light at optical frequencies and may indeed possess a non-vanishing ground state electronic spin.
I will explore the physics of one of these defects, the nitrogen vacancy center, and show how we can manipulate its electronic spin and make use of this capability to create quantum simulators, quantum sensors and perhaps surprisingly applications in medical imaging that may, we hope, find applications for example in cancer research and treatment.
MPQ, Seminar Room B0.41 in Library at 10.30 am.
Julian Roos will talk on
‘Non-Markovianity Measures in the Many-Body Context’
The ability to coherently control the dynamics of an ever-increasing number of particles pushed development of quantum technologies during the past decade. In order to achieve scalability, environment-induced decoherence effects need to be identified, understood and minimised such that the required thresholds for error correction are achieved. Also, people now control and modify the environment itself to design noise. All of this triggered renewed interest in fundamental studies of open quantum systems (OQS) amongst which are multiple studies on the existence of two different dynamical regimes: Markovian dynamics, underlying, e.g., the well known Lindblad master equations and non-Markovian dynamics, which are usually associated with recoherence and information backflow from the environment to the system.
I will introduce you to several measures that are widely used in the field to quantify the ‘amount’ of non-Markovianity that is present in the reduced dynamics of an OQS and provide some examples of their use in the context of time evolution of matrix product states. Here, the OQS consists, e.g., of two spins in the center of a spin chain and thus any system-bath weak-coupling assumptions (used in the derivation of the Lindblad form) are clearly invalid. Still there seem to exist special cases where the underlying dynamics are Markovian.
MPQ, Seminar Room B0.41 in Library at 10.30 am.
Maximilian Buser will talk on two topics
‘Open Quantum Systems with Initial System-Environment Correlations’
Open quantum systems exhibiting initial system-environment correlations are notoriously difficult to simulate. — We point out that given a sufficiently long sample of the exact short-time evolution of the open system dynamics, one may employ transfer tensors for the further propagation of the
reduced open system state. This approach is numerically advantageous and allows for the simulation of quantum correlation functions in hardly accessible regimes.
We benchmark this approach against analytically exact solutions and exemplify it with the calculation of emission spectra of multichromophoric systems as well as for the reverse-temperature estimation from simulated spectroscopic data.
‘Quasi-One-Dimensional Systems with Artificial Gauge Fields: Interactions and Finite Temperatures’
Artificial, highly tunable gauge (or ”magnetic”) fields have been successfully implemented in a number of optical lattice experiments with ultracold neutral Bose gases. In this context,
quasi-one-dimensional ladder-like lattices are of significant interest. They are the most simple geometries allowing the exploration of intriguing physical effects related to quantum Hall physics, exotic topological states and superconductivity. While experimental research mainly focused on non-interacting particles, recent results encourage the prospect of future experiments with strongly interacting bosons.
Analytical, mean-field and DMRG-based studies provided extensive theoretical results regarding the ground state properties of such strongly interacting, ladder-like systems. The presence of gauge fields clearly enriches the corresponding phase diagrams. For instance, it gives rise to so-called Meissner and vortex lattice phases as well as to intriguing effects such as chiral current reversals.
The aim of this work (in progress) is to provide theoretical predictions in experimentally much more feasible regimes. Therefore, we plan to investigate the effects of finite temperature states and intend to employ DMRG-based simulation techniques.
von-Neumann Lecture Series in Computer Science by Prof. Daniel Kressner (EPFL Lausanne, CH) held at TUM Computer Science (Host Prof. Huckle), Boltzmannstr. 3.
Low-rank compression is an ubiquitous tool in scientific computing and data analysis. There have been numerous exciting developments in this area during the last decade and the goal of this course is to give an overview of these developments, covering theory, algorithms, and applications of low-rank matrix and tensor compression.
Specifically, the following topics will be covered:
1. Theory
2. Algorithms
3. Applications
Depending on how the course progresses and the interest of the participants, hierarchical low-rank formats (HODLR, HSS, H matrices) may be covered as well.
Hands-on examples using publicly available software (in Matlab, Python, and Julia) will be provided throughout the course.
MPQ, Lecture Hall (moved to B0.32) at 10.30 am.
Nicola Pancotti and Moritz August will talk on
‘Neural Networks Quantum States, String-Bond States and Chiral Topological States’
Neural Networks Quantum States have been recently introduced as an ansatz for describing the wave function of quantum many-body systems. In this talk we will give an overview of recent works on Neural Networks Quantum States taking the form of Boltzmann machines. We will explain the motivation for considering Boltzmann machines in machine learning and explain how they can be used to study quantum systems. We will then focus on the expressive power of this class of states and discuss their relationship to Tensor Networks.
In particular we will show that restricted Boltzmann machines are String-Bond States with a non-local geometry and low bond dimension and explain how it enables us to define generalizations of restricted Boltzmann machines that combine the entanglement structure of tensor networks with the efficiency of Neural Networks Quantum States. We will then provide evidence that these techniques are able to describe chiral topological states both analytically and numerically.
Finally we will discuss how String-Bond States can also be used in traditional machine-learning applications.
based on: I. Glasser, N. Pancotti, M. August, I. Rodriguez, and I. Cirac, Phys. Rev. X. 8, 011006 (2018)
MPQ, Lecture Hall (moved to B0.32) at 10.30 am.
Stephan Welte will talk on
‘Processing of Two Matter Qubits Using Cavity QED’
In a quantum network, optical resonators provide an ideal platform for the creation of interactions between matter qubits. This is achieved by exchange of photons between the resonator-based network nodes, and in this way enables the distribution of quantum states and the generation of remote entanglement [1].
Here we will show how single photons can also be used to generate local entanglement between matter qubits in the same network node [2]. Such entangled states are indispensable as a resource in a plethora of quantum communication protocols.
We will give an overview of the necessary experimental toolbox for an implementation with neutral atoms. Several entanglement protocols showing the generation of all the Bell states for two atoms will be presented. We will also detail how we experimentally exploit the employed method for quantum computation and quantum communication applications.
[1] S. Ritter et al., Nature 484, 195 (2012)
[2] A. Sørensen and K. Mølmer, Phys. Rev. Lett. 90, 127903 (2003)
MPQ, Lecture Hall (moved to B0.32) at 10.30 am.
Anna-Lena Hashagen and Lukas Knips will give a double-feature on
Information-Disturbance Tradeoffs
In the first part of our double feature, we investigate the tradeoff between the quality of an approximate version of a given measurement and the disturbance it induces in the measured quantum system. We prove that if the target measurement is a non-degenerate von Neumann measurement, then the optimal tradeoff can always be achieved within a two-parameter family of quantum devices that is independent of the chosen distance measures.
This form of almost universal optimality holds under mild assumptions on the distance measures such as convexity and basis-independence, which are satisfied for all the usual cases that are based on norms, transport cost functions, relative entropies, fidelities, etc. for both worst-case and average-case analysis. We analyze the case of the cb-norm (or diamond norm) more generally for which we show dimension-independence of the derived optimal tradeoff for general von Neumann measurements.
A SDP solution is provided for general POVMs and shown to exist for arbitrary convex semialgebraic distance measures.
In the second part, we evaluate the information-disturbance tradeoff experimentally for the observation of a qubit by implementing the full range of possible measurements and determining the measurement error for a given disturbance. The special case of the worst-case total variational distance and the 1-1 norm distance is considered.
The various measurements are realized by a tunable Mach-Zehnder-Interferometer, which supplies the ancillary degrees of freedom necessary to implement arbitrary POVMs and quantum channels for the measurement of a polarization qubit. We demonstrate the tightness of the bound by saturating it with high significance. Furthermore, we show that the optimal procedure outperforms the optimal cloning protocol, not only on a theoretical level, but clearly resolvable in the laboratory.
MPQ, Lecture Hall (moved to B0.32) at 10.30 am.
Michael Fischer will talk on
Chains of Nonlinear and Tunable Superconducting Resonators
In this talk I will first give a brief introduction and overview of superconducting quantum circuits as a basis for quantum simulation. I will then present a quantum simulation system of the Bose-Hubbard-Hamiltonian in the driven dissipative regime in the realm of circuit QED in more detail.
The system consists of series-connected, capacitively coupled, nonlinear and tunable superconducting resonators. The nonlinearity is achieved by galvanically coupled SQUIDs, placed in the current anti-node of each resonator and can be tuned by external coils and on-chip antennas.
Theoretical models of the Bose-Hubbard system predict bunching and antibunching behavior both in the second order auto- and cross-correlation function of the bosonic modes in the lattice sites. Characterization measurements of our sample show that we can reach the parameter space of interest for these quantum simulation experiments.
MPQ, Lecture Hall (moved to B0.32) at 10.30 am.
Jakob Wierzbowski will talk on
‘Long-Lived Quantum Emitters in hBN-WSe2 van-der-Waals Heterostructures’
We present a significant linewidth narrowing (12.5 %) of free excitons in hBN encapsulated TMDs and localized (< 350 nm) single-photon emitters with long lifetimes of ~18 ns in hBN/WSe2 heterostructures.
Block Course by Prof. Michael Keyl (FU Berlin) on Mathematical Aspects of Quantum Field Theory (Part 2) together with TMP and IMPRS-QST. Held at LMU Physics, Theresienstr. 39, Room A449, Mon through Fri: 10-12 am plus 2-4 pm.
In the beginning of the semester, we studied QFT in the Wightman framework. This included in particular scalar and operator valued distributions, Wightman axioms, Wightman functions and the reconstruction theorem, and the Borchers-Uhlmann algebra with its representations. As an explicit example we studied the free scalar field, its Wick-ordered products, and self-interacting models in 1+1 dimensions. In the latter context questions of renormalization were discussed.
Now, the second series will be devoted to perturbation theory: After a short look at the S-matrix, we will use the Epstein-Glaser formalism to construct the perturbation series term by term as a formal power series. This will be carried out in detail with \Phi^4 self interactions as an explicit example. In this context perturbative renormalizability will also be discussed.
For the complete script (parts 1 and 2) follow this link.
3 ECTS points can be acquired by writing an at least 10 page essay on a topic related to the course.
MPQ, Lecture Hall (moved to B0.32) at 10.30 am.
Prof. Maurice de Gosson will talk on
‘Properties of Phase Space Distributions in the Cohen Class’
Non-standard phase space distributions play an increasingly important role in quantum mechanics, to witness recent work by Koczor, Zeier, and Glaser who highlight the relation of these distributions with tomography.
In this talk we will discuss the properties (marginal conditions, Moyal identity) for a large class of phase space distributions obtained from the usual Wigner distribution by convolution with a Cohen kernel. We will examine in detail two particular cases from this perspective. the Husimi distribution, and the Born-Jordan distribution. The latter arises naturally when one uses the Born and Jordan quantization scheme instead of the traditional Weyl correspondence.
MPQ, Lecture Hall (moved to B0.32) at 10.30 am.
Michael Lohse will talk on
Generalizing the quantum Hall effect to four-dimensional systems leads to the appearance of an additional quantized Hall response, but one that is nonlinear and described by a 4D topological invariant—the second Chern number.
MPQ, Lecture Hall (moved to B0.32) at 10.30 am.
We will plan activities in 2018 including
Please all attend.
The Max-Planck Harvard Research Centre for Quantum Optics (MPHQ) will be opened with a two-day symposion on Jan. 11th at IAS Garching and on Jan. 12th at Deutsches Museum. It is a joint venture with the Harvard Quantum Optics Center.
See the programmes here:
The event is open to the public and the participation of students is highly encouraged! The Max Planck Research Center for Quantum Optics aims for becoming one of the major internationally recognized scientific collaborations of its kind in the field of Quantum Optics.
MPQ, Lecture Hall (moved to B0.32) at 10.30 am.
David Leiner will talk on
‘Wigner Tomography of Multi-Spin Operators’
We study the tomography of operators for multi-spin systems in the context of finite-dimensional Wigner representations. An arbitrary operator can be completely characterized and visualized using multiple shapes assembled from linear combinations of spherical harmonics. We develop a general methodology to experimentally recover these shapes by measuring expectation values of rotated axial spherical tensor operators.
Our approach is experimentally demonstrated for quantum systems consisting of up to three spins using nuclear magnetic resonance spectroscopy.
[Joint work with Robert Zeier and Steffen J. Glaser: arXiv: 1707.08465 ]
MPQ, Seminar Room, Theory Group in 3rd floor at 10.30 am.
Bálint Koczor
Continuous Phase-Space Representations for Finite-Dimensional Quantum States and Their Tomography
Continuous phase spaces have become a powerful tool for describing, analyzing, and tomographically reconstructing quantum states in quantum optics and beyond. A plethora of these phase-space techniques are known, however a thorough understanding of their relations was still lacking for finite-dimensional quantum states. We present a unified approach to continuous phase-space representations which highlights their relations and tomography. The quantum-optics case is then recovered in the large-spin limit. Our results will guide practitioners to design robust innovative tomography schemes.
[Joint work with Robert Zeier and Steffen J. Glaser: arXiv:1711.07994v1 ]
with an intro by Margret Heinze on 'The Lindblad-Kossakowski Theorem in Infinite Dimensions'
MPQ, Lecture Hall (moved to B0.32) at 10.30 am.
After Margret Heinze (IMPRS-QST, group Michael Wolf) has given a short tutorial proving the Lindblad-Kossakowski Theorem in infinite dimensions,
Frederik vom Ende will talk on
‘Discrete Open Dynamical Systems and Unitary Dilations’
Arbitrary quantum maps, in particular the time evolution of open dynamical quantum systems, are described by so-called quantum channels (which simply are linear, trace-preserving and completely positive maps) acting on trace-class operators.
Every quantum channel has a Kraus decomposition, so it can be built from the basic operations of tensoring with an environment, a unitary transformation or the larger system, and finally the return to the original (sub)system via tracing out. This idea can be extended to the whole dynamical semigroup induced by a quantum channel (where the environment now is way larger than in the Kraus decomposition); it is the unitary dilation of the semigroup in question. Analogously, one can mathematically structure (a) the solution of discrete quantum dynamical systems and (b) certain types of discrete quantum dynamical control systems.
MPQ Large Lecture Hall (moved to B0.32) at 12.30 noon.
Dr. Volkher Scholz, ETH Zurich
Analytic Approaches to Tensor Networks for Critical Systems and Field Theories
I will discuss analytic approaches to construct tensor network representations of quantum field theories, more specifically critical systems and conformal field theories in 1+1 dimensions. A key insight is that we should understand how well the tensor network can reproduce the correlation functions of the quantum field theory. Based on this measure of closeness, I will present rigorous results allowing for explicit error bounds which show that the multiscale renormalization Ansatz (MERA) does approximate conformal field theories.
In particular, I will discuss the case of free fermions, both on the lattice and in the continuum, as well as Wess-Zumino-Witten models.
[Based on joint work with Jutho Haegeman, Glen Evenbly, Jordan Cotler (lattice) and Brian Swingle and Michael Walter (lattice & continuum)]
MPQ Large Lecture Hall (now moved to B0.32) at 11.00 am.
Prof. Michael Keyl, FU Berlin
Controlling a d-Level Atom in a Cavity
We study controllability of a d-level atom interacting with the electromagnetic field in a cavity. The system is modelled by an ordered graph Γ. The vertices of Γ describe the energy levels and the edges allowed transitions. To each edge of Γ we associate a harmonic oscillator representing one mode of the electromagnetic eld. The dynamics of the system (drift) is given by a natural generalization of the Jaynes-Cummings Hamiltonian.
If we add suffcient control over the atom, the overall system (atom and electromagnetic field) becomes strongly controllable, i.e. each unitary on the system Hilbert space can be approximated with arbitrary precision in the strong topology by control unitaries. A key role in the proof is played by a topological *-algebra A(Γ) which is generated (roughly speaking) by the path of Γ. For that reason A(Γ) is called path algebra. It contains crucial structural information about the control problem, and it is therefore an important tool for the implementation of control tasks like preparing a particular state from the ground state.
This is demonstrated by a detailed discussion of different versions of 3-level systems.
[Based on joint work with Thomas Hofmann]
Symposion by Munich Quantum Centre (MQC)
Held at TUM ZNN, Campus Garching, Am Coulombwall 4a.
Block Course by Prof. Michael Keyl (FU Berlin) on Mathematical Aspects of Quantum Field Theory (Part 1) together with TMP and IMPRS-QST. Held at LMU Physics, Theresienstr. 39, Room B101, Mon: 2-4pm; Tue, Wed, Thu 10-12am plus 2-4pm.
In the beginning of the semester, we will study QFT in the Wightman framework. This includes in particular scalar and operator valued distributions, Wightman axioms, Wightman functions and the reconstruction theorem, and the Borchers-Uhlmann algebra with its representations. As an explicit example we will study the free scalar field, its Wick-ordered products, and self-interacting models in 1+1 dimensions. In the latter context questions of renormalization are also discussed.
The second week at the end of the semester will be devoted to perturbation theory. After a short look at the S-matrix, we will use the Epstein-Glaser formalism to construct the perturbation series term by term as a formal power series. This will be carried out in detail with \Phi^4 self interactions as an explicit example. In this context perturbative renormalizability will also be discussed.
For the complete script (parts 1 and 2) follow this link.
3 ECTS points can be acquired by writing an at least 10 page essay on a topic related to the course.
MPQ Small Lecture Hall at 11.00am.
Frederik vom Ende
Unitary Dilations of Discrete Quantum-Dynamical Semigroups
The time evolution of physical systems is a main factor in order to understand their nature and properties. Operations and therefore time evolutions of open quantum systems are described by quantum maps which are linear, trace-preserving and completely positive.
Also for the discrete case, we want to understand why the condition of complete positivity is necessary and which structure it provides. Again we will see that every quantum channel has a Kraus decomposition and that it can be built from the basic operations of tensoring with a second system in a specified state, a unitary transformation, and the reduction to a subsystem.
Thus one can mathematically structure the solution of discrete quantum dynamical systems and even certain types of discrete quantum dynamical control systems.
[Work based on a masters thesis in maths at U Wuerzburg.]
MPQ Small Lecture Hall at 11.00am.
Lukas Knips
How to Detect Entanglement – a Summary of Methods
Entanglement is a fascinating feature of quantum systems and one of the key resources for quantum information processing. In order to detect and quantify entanglement, and thus to attest the prepared system to be a useful resource, sophisticated methods are required.
I will review and compare some specialized and efficient entanglement criteria for multiqubit systems with standard tools such as the PPT criterion [1], which is easily applicable, but limited to small systems, and linear fidelity witnesses [2], which are helpful if prior knowledge about the state is present, but already need several measurements.
The toolbox, I will present, encompasses methods which, for example, detect entanglement after only two measurements [3], work without any prior knowledge about the state [4] or can be applied when one cannot even know the local reference frames [5].
[1] A. Peres, Phys. Rev. Lett. 77, 1413 (1996); M. Horodecki, P.
Horodecki, R. Horodecki, Phys. Lett. A 223, 1 (1996)
[2] O. Gühne, G. Tóth, Physics Reports 474, 1 (2009)
[3] L. Knips, C. Schwemmer, N. Klein, M. Wiesniak, H. Weinfurter, Phys. Rev. Lett. 117, 210504 (2016)
[4] W. Laskowski, D. Richart, C. Schwemmer, T. Paterek, H. Weinfurter, Phys. Rev. Lett. 108, 240501 (2012); W. Laskowski, C. Schwemmer, D. Richart, L. Knips, T. Paterek, H. Weinfurter, Phys. Rev. A 88, 022327 (2013)
[5] in preparation
MPQ Seminar Room of Theory Group in 2nd floor at 10.00am.
Nicola Pancotti
Long-time dynamics of non-integrable systems hold the key to fundamental questions (thermalization). Analytical tools can only apply to particular cases (integrable models, perturbative regimes). Numerical simulations, limited in time, have found evidence of different time scales.
A new numerical technique for constructing slowly evolving local operators was introduced by Kim et al. in Phys. Rev. E 92, 012128 (2015). Those operators have a small commutator with the Hamiltonian and they might give rise to long time scales.
In this work, we apply this technique to the many body localization problem. We show that this method can not only signal the difference between the ergodic and localized phases, but it is also sensitive to the presence of a subdiffusive phase between both.
Symposion by Munich Quantum Centre (MQC)
Held at LMU Physics, Theresienstr. 37 Room A348/349:
12.05am: Viatcheslav Mukhanov: “Quantum Mechanics in the Sky”
12.35am: Frank Pollmann: “Dynamical Signatures of Spin Liquids”
1:10pm: Poster session with coffee and snacks
MPQ Herbert Walther Lecture Hall at 5.00pm.
Dr. Susanne Pielawa
(Google, Munich)
During their undergraduate and graduate studies, physicists acquire a broad set of transferable skills which make many career paths available, also outside of academia.
Dr. Susanne Pielawa studied Physics at the University of Ulm, did her PhD in Condensed Matter Theory at Harvard and then went on to a postdoc position, also in Condensed Matter Theory, at the Weizmann Institute of Science. Afterwards, she joined the Start-Up Yowza (in Tel Aviv) and developed algorithms for a 3D-model search engine. She is now a software engineer at Google Munich.
She will talk about what it is like to be a software engineer, and share impressions of her transition from theoretical physics to algorithm development and software engineering. She will also present career opportunities at Google, and talk about the company’s work culture.
MPQ Herbert Walther Lecture Hall at 10.30am.
Prof. Witlef Wieczorek
(formerly QCCC, then U Vienna, now at U Gothenburg)
Impressive results have recently been achieved in controlling micro- and nanomechanical devices in the quantum regime. These achievements pave the way for exploring novel applications and tests of quantum mechanics employing mechanical devices. In my talk I will describe progress towards quantum control of optomechanical states. In particular, I will address the question on how does one optimally estimate the state of an optomechanical system.
Further, I will talk about a completely different approach of controlling mechanical systems that has been recently proposed by employing superconducting levitation. This experimental platform offers unrivaled low mechanical dissipation and coupling capability to superconducting circuits. Its envisioned applications range from studying of fundamental questions to novel sensing prospects. I will describe first ideas and experimental steps in this direction.
MPQ Herbert Walther Lecture Hall at 10.30am.
Anna-Lena Hashagen
(returning from Prof. Stephen Bartlett, U Sydney)
Randomised benchmarking is a widely used experimental technique to characterise the average error of quantum operations. Its robustness regarding state preparation and measurement errors as well as its efficient scaling has made it a standard and reliable choice.
I will give an overview and a short introduction to the randomised benchmarking protocol for characterising the average error of Clifford gates.
MPQ Seminar Room B0.22 at 10.30am.
Umut Kaya (formerly with Renato Renner at ETH Zurich)
Catalyst systems are just additional systems you include to your setup to widen the range of your allowable transformations on the main state. But if you naively use this ancillary system in an approximate manner, you come across a well-known phenomenon called thermal embezzling, which says you can reach any output state without any restrictions–thus no 2nd Law.
I will present some analytical and computational results showing that the Catalytic Coherence setup is limited by certain second-law like relations, therefore it does not suffer from this embezzling problem.
Symposion: Quantum Control Theory: Mathematical Aspects and Physical Applications
Mon-Wed/April 3rd-5th 2017 at TUM Institute of Advanced Study, IAS Garching, Lecture Hall
Symposion: Macroscopic Limits of Quantum Systems
Thu/Fri (March 30th/31st), 2pm: TUM, IMETUM, Garching, Lecture Hall E.127
Sat (April 1st), 2pm: LMU Mathematics Department, Centre, Lecture Hall A027
MPQ Theory Group Seminar Room 2nd floor at 2.00pm.
Claudius Hubig
The Density Matrix Renormalisation Group when applied to matrix- product states is the method of choice for ground-state search on one-dimensional systems and still highly competitive even in unfavourable circumstances, such as critical systems and higher dimensions.
In this talk, I will discuss two separate methods which can be used to
improve the computational efficiency of DMRG and related methods on matrix-product states and beyond. The first component is the
implementation of both abelian and non-abelian symmetries in an entirely general way suitable also for higher-rank tensors as encountered in, e.g., tree tensor network states. The second ingredient, the subspace expansion, allows for a fully single-site DMRG algorithm with favourable linear scaling in the local dimension of the tensor network. Even for common problems, this results in a considerable speed-up over the traditional two-site DMRG method or the density matrix perturbation approach for ground-state search at reduced algorithmic complexity.
Additionally, the subspace expansion can potentially be used in a large
set of other algorithms, such as the TDVP or the variational application
of a matrix-product operator onto a matrix-product state.
MPQ Seminar Room B0.22 at 10.30am.
Dr. Manfred Liebmann (U Graz, formerly Maths. Dept. TUM)
In the lecture I will discuss several striking consequences of the following generalization that will give rise to a new perspective on structures in the standard model of particle physics:
The Hurwitz theorem states that a bilinear product on $R^n$ with the property x◦y = ||x|| . ||y|| can only exist in dimensions n = 1, 2, 4, 8. The associated algebras are the division algebras of the real numbers R, the complex numbers C, the quaternions H, and the non-associative algebra of the octonions O, also known as Cayley algebra.
It turns out that the structure of the Dirac equation is deeply related to the non-assoziative multiplication law of the Cayley algebra. The Dirac matrices can be identified with complex versions of the left action maps Lx(y) := x◦y. However not all left actions can be complex represented and this leads to a generalization of the Dirac equation that transcends the traditional complex Hilbert space framework of quantum physics.
11am, Prof. Cirac, MPQ
Tensor Networks:
A Quantum Information Perspective to Many-Body Physics
Abstract: The theory of entanglement offers a new perspective to view many-body quantum systems. In particular, systems in thermal equilibrium and with local interactions contain very little entanglement, which allows us to describe them efficiently, circumventing the exponential growth of parameters with the system size. Tensor Networks offer such a description, where few simple tensors contain all the information about all physical properties. In this talk I will review some of the latest results on entanglement and tensor networks, and explain some of their connections to quantum computing, condensed matter, and high-energy physics.
See programme, in particular for Mon afternoon and Tue morning.
19.12.2016 at 16:00
4pm, Dr. Thomas Schulte-Herbrüggen
Season’s Applications of Knot Theory
Abstract: Surprise.
Dr. Juan Bermejo-Vega (FU Berlin)
A central question in quantum computation is to identify the resources that are responsible for quantum speed-up. Quantum contextuality has been recently shown to be a resource for quantum computation with magic states for odd-prime dimensional qudits and two-dimensional systems with real wavefunctions.The phenomenon of state-independent contextuality poses a priori an obstruction to characterizing the case of regular qubits, the fundamental building block of quantum computation. Here, we establish contextuality of magic states as a necessary resource for a large class of quantum computation schemes on qubits. Our proof exploits novel simple arguments and, for the first time, does not rely on Wigner functions. Our new methods can be extended to a family of magic-state protocols on qudits of any local dimension and lead to a new most-general proof in the odd dimensional case.
Based on:
https://arxiv.org/abs/1610.08529
https://arxiv.org/abs/1610.07093
The IMPRS “Quantum Science and Technology” is inaugurated. ExQM has an e-poster session on Fri, Oct. 28th at 1:30 pm in WSI.
Prof. Michael Keyl
The toric code introduced by Kitaev is one of the most simple models of topological order and therefore a good candidate to discuss some mathematical topics related to the last Nobel Prize in Physics. Apart from topological phases this includes in particular the emergence of quasi particles with exotic statistics in low dimensions.The latter relates to the representation theory of the braid group and the algebraic theory of superselection sectors, which we will briefly discuss.
05.07.2016 at 17:15
Public Lecture: Quantum Computing and the Entanglement Frontier
Professor John Preskill, California Institute of Technology, USA more
Room B052 – Faculty of Physics – LMU – Theresienstr. 39 – 80333 München
06.07.2016 at 16:15
Theory Colloquium: Quantum Information and Spacetime
Professor John Preskill, California Institute of Technology, USA more
Room A348/349 – Faculty of Physics – LMU – Theresienstr. 37, 80333 München
07.07.2016 at 16:15
Fields and Strings Seminar: Holographic Quantum Codes
Professor John Preskill, California Institute of Technology, USA more
Room A348/349 – Faculty of Physics – LMU – Theresienstr. 37, 80333 München
Details on: http://www.asc.physik.lmu.de/activities/lectures/
June 29th 2016 at 2.30pm in Lecture Hall 3 in the TUM Maths Dept. (Hörsaal 3 (MI 00.06.011)).
Classical information theory provides quantitative answers to basic questions about communication and computation. In the presence of quantum effects, its basic tenets need to be reassessed as fundamentally novel information-processing primitives become possible. Their potential appears promising, but their realization hinges on our ability to construct mechanisms protecting information against unwanted noise.
In this talk, I will consider two problems associated with communication and computation. First, I will discuss the additivity problem for classical capacities. I will review some of the more recent results in this direction: for continuous-variable channels, quantum generalizations of certain geometric inequalities yield operationally relevant statements. Second, I will discuss the problem of performing gates on information encoded in an error-correcting code, and explain how this relates to automorphisms of the latter.
overall programme: see ProgrammExQM2016rev.pdf
detailed programme: see BookletWorkshop2016new.pdf
Wednesday June 1st 2016 at 11.30am at MPQ lecture hall.
I will give a pedagogical non-formal introduction to the notion of topology. The idea is to outline an intuitive pathway from geometrical to topological concepts by increasing the number of allowed transformations within the congruence classes of Euclidean geometry. I will then pick one or the other basic system from the class of topological phases of matter and discuss why the word topological is used to describe it.
Here is a little teaser by Martin Gardner :
Draw a continuous line across the closed network shown so that the line crosses each of the 16 segments of the network only once. The curved line shown in the attached image does not solve it, because it leaves one segment uncrossed. It is not difficult to prove that the puzzle cannot be solved on a plane surface. Can it be solved on the surface of a sphere? On the surface of a torus?
Stephan Welte on “A cavity-mediated photon-photon gate”.
Photons are promising candidates for applications in quantum information processing and quantum communication. However, the direct interaction between two photons is negligible in free space, which is a drawback when it comes to the implementation of quantum logic gates between them. A solution to this problem was offered by Duan and Kimble [1] who proposed that a strongly coupled atom in an optical cavity [2] could mediate an effective interaction between two photons. We experimentally demonstrate that an implementation of this proposal is indeed possible. To this end, the universal CNOT operation of the gate as well as its capability to entangle two separable input photons are characterized. We will discuss details of our experimental implementation and present intriguing implications of our gate for photonic quantum information processing.
[1] L.-M. Duan, H.J.Kimble, Phys. Rev. Lett. 92, 127902 (2004)
[2] A.Reiserer, G.Rempe, Rev. Mod. Phys. 87, 1379 (2015)
Follow-up on last week’s talk on “Symmetry control of layered 2D semiconducting materials in novel nanodevices”.
Jakob Wierzbowski gives a short lab tour showing related experiments… also welcoming those who could not come last Fri, of course.
Jakob Wierzbowski on “Symmetry control of layered 2D semiconducting materials in novel nanodevices”.
The emergence of truly two-dimensional materials like graphene [1] extends the range of commercially available material systems for future electronic and optoelectronic devices. Especially, semiconducting transition metal dichalcogenides (STMDs) MoS2, MoSe2, WS2 and WSe2 play a key role in bridging the gap between bandgap-less graphene and insulating hBN. Importantly, TMDs exhibit a direct bandgap in the monolayer limit with optical transitions in the visible and near-infrared wavelength range [2]. Here, intrinsic electronic and optical signatures in few-layer crystals strongly depend on crystallographic symmetry properties.
Specifically, the inherently broken inversion symmetry in monolayer crystals naturally facilitates valleytronic applications [3]. Here, we present the electrical control of symmetry properties of few-layer MoS2 crystals embedded within electrically tunable Si-SiO2-STMD-Al2O3-metal microcapacitors with optical access as presented in Figure 1. By tuning the electric field, we induce strong static electric fields exceeding ±3.5 MV/cm resulting in significant DC Stark shifts of the interband emission (>15 meV) for mono- to pentalayer crystals. We extract an effective exciton polarizability of β=(0.58±0.25)×10−8 DmV−1; independent of the number of layers probed [4].
In polarization resolved photoluminescence measurements performed on mono- to trilayer MoS2, we observe pronounced electric field control of valley optical dichroism for bilayer crystals. Importantly, we are able to continuously tune the degree of circular polarization of the emission from η=20 % up to 58 % [5]. Selected data are presented in Figure 2. Moreover, for the bilayer crystal, we demonstrate intense electrical control of second-harmonic generation (SHG) originating in naturally inversion symmetric 2H stacked MoS2. Using ultrashort pulses of ~ 70 fs within a spectral window 840 – 1000 nm (1.24 – 1.47 eV), we observe broadband tunability of the SHG signal throughout the probed region with a ~ 60 fold conversion amplification at its optimum [6]. Our results demonstrate the potential for emergent spin- and valleytronic devices based on two-dimensional atomically thin crystals and efficient electrically driven broadband frequency doubling by external control of the symmetry properties of 2H MoS2.
[1] A. K. Geim, I. V. Grigorieva, Nature 499, 419-425 (2013)
[2] Mak et al., Phys. Rev. Lett. 105, 136805 (2010)
[3] Zeng et al., Nature Nano. 7, 490-493 (2012)
[4] J. Klein and J. Wierzbowski et al., Nano Lett. DOI: 10.1021/acs.nanolett.5b03954 (2016)
[5] J. Wierzbowski and J. Klein et al., in preparation (2016)
[6] J. Wierzbowski and J. Klein et al., in preparation (2016)
Double feature of two short DPG talks:
Prof Michael Keyl will dwell on”Controlling a d-level atom in a cavity”
In this talk we discuss quantum control theory for a d-level atom in a cavity. The atom is described by a Graph Γ with energy levels as vertices and edges e as allowed transitions. For each such e the atom interacts (via a Jaynes-Cummings like interaction term) with a different mode of the cavity. We consider controllability of the overall system (i.e. atom and cavity) under the assumption that all atom-cavity interactions can be switched on and off individually and that the atom itself is fully controllable. Our main tools are symmetry based arguments recently introduced for the discussion of the two-level case [M. Keyl, R. Zeier, T. Schulte-Herbrüggen, NJP 16 (2014) 065010]. The basic idea is to divide the control Hamiltonians into two sets. One which is invariant under the action of an Abelian symmetry group G and a second set which breaks this symmetry. We will discuss how the group G and its action are related to the graph Γ and its fundamental groupoid, and how these structure can be used to prove full controllability – at least if Γ is acyclic. For Graphs containing cycles the situation is more difficult and the universal covering graph has to be used. We demonstrate this, using the fully connected graph on three vertices as an example.
and Mrs Margret Heinze continues on “Quantum control for a Jaynes-Cummings-Hubbard model “.
We examine the control of a quantum system consisting of several two-level atoms with each atom interacting with a different mode of an electromagnetic field.
More precisely, the system is a Jaynes-Cummings-Hubbard model where each cavity contains an atom and a bosonic excitation that can tunnel to the neighbouring cavities. The interaction strengths can be time dependently tuned in order to achieve controllability.
We discuss if it is possible that every pure state can be reached from a given reference state (pure-state controllability). This analysis is lifted to the level of operators where each unitary has to be approximated with arbitrarily small error by a time evolution operator for appropriate control functions and finite time (strong controllability).
The challenge of this infinite dimensional control problem is met, by firstly examining the symmetries of the system. A finite dimensional block diagonal decomposition is obtained for the control Hamiltonians that obey an abelian symmetry and due to a cut-off finite dimensional Lie analysis can be applied. By then adding a Hamiltonian that breaks the symmetry pure state and strong controllability are examined, c.f. [New Journal of Physics 16 (2014): 065010].
ExQM Miniworkshop:
“Mathematical Aspects of Quantum Systems and Control Engineering”
Feb. 25-26th 2016 at Math. Inst. TUM Campus Garching and MPQ.
Thu 25. Feb. Motto: “Mostly Finite-Dimensional Systems”
(all in Sem. Room Maths Dept. MI 03.08.011 on floor 3)
13:30h Dr Gunther Dirr (Uni Würzburg) “Some New Results on Ensemble Control”
To begin with, we present necessary and sufficient accessibility/controllability criteria for finitely many parallel connected bilinear systems.
Then, extending these ideas to infinitely many systems, we arrive at so-called bilinear ensembles and discuss first results on ensemble controllability.
14:30h Dr Thomas Schulte-Herbrüggen (TUM) “Systems Theory and Control of Closed & Open Markovian Quantum Systems: A Unified Lie Symmetry Approach”
We give necessary and sufficient symmetry conditions for controllability and simulability in closed systems. For open Markovian systems, we discuss accessibility in terms of Lie semigroups and their Lindblad-Kossakowski generators. We elucidate the Lie-algebraic structure of the Lie wedges and their embedding system algebras.
15:30h Coffee and extensive discussion
ca. 18:30h Dinner in Garching
Fri 26.Feb: Motto: “Infinite-Dimensional Systems”
10:30h Prof. Ugo Boscain (CNRS Paris Saclay) “Controlling the Schrödinger Equation via Adiabatic Methods Using Conical Intersection of Eigenvalues” (ExQM Seminar at MPQ Room B0.21)
In this talk I will discuss how to obtain a population transfer in a quantum mechanical system using adiabatic methods and the presence of conical intersections in the space of controls. The method is powerful. In the finite dimensional case it permits to prove that if the system is “conically connected” then it is Lie bracket generated. Also it permits to control systems presenting a dispersion of parameters (ensamble controllability). Conical eigenvalue intersections are not rare. For systems with a real Hamiltoniana and two controls they are structurally stable.
12:00h Lunch at IPP
13:30h Dr Mario Sigalotti (INRIA Paris Saclay) “Control of the Discrete-Spectrum Schroedinger Equation” (Sem. Room Maths Dept. MI 03.08.011 on floor 3)
We show how to deduce approximate controllability of the control-affine Schroedinger equation from the controllability properties of its Galerkin approximations, in the case in which the uncontrolled Hamiltonian has discrete spectrum.
14:30h Prof. Michael Keyl (TUM) “Controlling Atoms in a Cavity” (Sem. Room Maths Dept. MI 03.08.011 on floor 3)
We treat control of several two-level atoms interacting with one mode of the electromagnetic field in a cavity. This provides a useful model to study pertinent aspects of quantum control in infinite dimensions via the emergence of infinite-dimensional system algebras.
15:30h Coffee and extensive final discussion panel
Dr Christian Schwemmer will be so kind as to give his fare-well talk on “Efficient Tomography of Multiphoton States”.
Multipartite entangled quantum states offer great opportunities with potential applications in quantuminformation processing. Therefore, practical tools fo r entanglement detection and characterization are needed. However, conventional state tomography suffers from an exponentially increasing measurement effort with the number of qubits. In contrast, pure or symmetric states like W-, Dicke- or GHZ-states enable tomographic analysis at reduced effort. Here, we apply these schemes to experimentally analyze six photon symmetric Dicke states. For data processing, a fitting algorithm based on convex optimization is used offering significant improvements in terms of speed and accuracy.
Furthermore, it will be shown that implying additional constraints in quantum-state estimation, such as non-negativity of a quantum state, can introduce significant systematic errors.
David L. Goodwin (U. Southampton, Ilya Kuprov’s group) will give a perspective talk on “Taking Optimal Control toward a Tensor Formalism”
While reviewing the current state of Gradient Assisted Pulse Engineering (GRAPE), questions will be asked on the applicability of a Tensor version of this successful numerical optimal control algorithm. This Tensor-GRAPE is envisaged to use elements DMRG (or MPO), which sits in the low temperature approximation, and the successes of the SPINACH software toolbox in reducing state spaces and having efficient optimal control for simulation of spin system, sitting in the high-temperature approximation.
This talk will ask questions from the point of view of one that works with GRAPE, seeking hints at answers and possible problems that the audience may identify. Subjects of interest include: the use of an augmented exponential to compute exact control derivatives within SPINACH; recent publications of the Tensor-Trains formalism of Savostyanov et.al. to simulate exact 1D spin chains (as occurring also in protein backbones), and t-DMRG.
Prof. Norbert Schuch (now MPQ Garching) will talk on “Tensor network models for the study of correlated quantum systems”
Tensor network models provide a means of understanding the behaviour of correlated quantum systems from a local perspective. In this talk, I will give an introduction to the framework of tensor network models, and discuss examples of how they can be used to study the physics of complex quantum many-body systems, with a focus on systems with physical symmetries and those which display topological order.
Nicola Pancotti will talk on “Many body gates: from small chains to networks”
During the last years a great effort has been made in order tocharacterize, implement and optimize entangling gates between two distant particles. Here we study the evolution of a quantum complex system and we search whether there exists an optimal time t* in which a perfect entangling gate G is implemented. The aim of this research is dual. On one side we propose a brand new numeric method acquired from the machine learning community which gives a good speed up compared to the previous ones. On the other side we look for new, unknown solutions, Jopt , that parametrize the Hamiltonian so that exp(−iH ( Jopt ) t* ) = G ⊗ S; S is an operator which leaves the rest of the system in an unknown (don’t care) state. We start from a very simple 3-spins chain, for which we already know the solution. We move then forward to a N-spins chain and finally we enlarge the line to obtain a network. We aim to find perfect topologies and optimal two body interactions capable of implementing fast and high fidelity gates such as entangling, Toffoli, CCZ, etc.
Dr Mari-Carmen Banuls we will give a lecture on “Numerical studies of many-body systems using tensor networks”
Tensor network states have proven very successful in describing ground states of quantum many body systems. The paradigmatic example is that of Matrix Product States (MPS), which underlie the celebrated DMRG method for the study of one dimensional systems. Using these methods it is also possible to simulate dynamics. And the ansatz can be also extended to describe operators, in particular, mixed states.
In the last years, the progress has been fast both in the theoretical understanding and the application of tensor networks to diverse problems. In this talk, I will present these methods from the practical point of view, focusing on their application to the numerical study of diverse quantum many-body problems, and illustrate their potential with some recent results.
“Contextuality as a resource for qubit quantum computation”
With Dr. Ville Bergholm (U. Helsinki) we will give a short double feature on “A First Glance into Quantum Control Engineering”
We go from a sketch of the unified background (by Thomas) to Ville showing on-line examples on the computer from optimized quantum state transfer and gate (or map) synthesis in closed and open systems. These examples include spin chains, NV centres, and exciton transfer in light-harvesting FMO complexes.
We give an outlook on the limits of open-loop versus closed-loop control.
Julian Roos will talk on “Looking inside a lithium-ion battery electrode: A materials modelling study”
In 1990, Sony introduced the first commercially viable Lithium-ion battery to the market, sparking a revolution in consumer portable electronics. This breakthrough was mainly due to the incorporation of John Goodenough’s layered intercalation cathode LiCoO2 into the cell, raising the energy density of such batteries to a practical level for the first time. Today, cathode materials are still regarded the major bottleneck (batteries with LiCoO2 are still found in most devices) and the route to new generation lithium-ion batteries is linked to the search for superior materials and their optimization. This calls for a better understanding of solid state properties and the fundamental physical processes inside electrode materials on the atomic scale. In this talk I will highlight the use of several numerical simulation techniques (both classical and quantum mechanical types) in providing complimentary insights to an experimental study of the novel exotic lithium-rich cathode Li7Mn(BO3)3, illustrating how such computational materials modelling is indispensable in modern materials optimization.
Prof. Enrique Solano (Univ. Bilbao) will talk on “From Quantum Theatre to Scalable Quantum Simulators”
We will introduce the field of quantum simulations from a wide aesthetic and scientific perspective. Along these lines, we will discuss the relevance of quantum simulations as a playground for our quantum theatre, as communicating vessels between unconnected fields, and as a scalable quantum technology. We will also provide pedagogical examples of quantum simulations in trapped ions and superconducting circuits, relating nonrelativistic and relativistic quantum dynamics, physical and unphysical quantum operations, as well as strong and ultrastrong light-matter interactions. Finally, we will discuss the advantages and disadvantages of current paradigms of quantum simulators, involving digital and analog concepts, and propose novel paths and concepts for assuring their scalability.
Dr Christian Gogolin (ICFO Barcelona) will talk on “Equilibration, thermalization, and local stability of thermal states”
In this talk it is shown how finite dimensional quantum systems in pure states, which evolve unitarily according to the Schrödinger equation, can exhibit thermodynamic behavior. More precisely, it will be discussed under which conditions local equilibration and thermalization can be ensured in such systems. I then discuss results on structural properties of thermal states of locally interacting quantum systems that in particular imply lower bounds on the critical temperatures below which such systems can exhibit phases with long range order. Finally, I touch on some work in progress concerning many-body localization.
Dr Thorsten Wahl (with Ignacio’s group) will give his farewell talk before moving to Oxford about “Tensor network states for the description of quantum many-body systems”
Tensor network states (TNS) are applied to one and two dimensional systems: All translationally invariant matrix product states (one dimensional TNS) possessing long-range localizable entanglement, which is a non-local hidden order, are characterized. Furthermore, the first examples of chiral topological projected entangled pair states (two dimensional TNS) are presented. Their topological properties can be traced back to symmetries of the tensors describing the states. They are ground states of local gapless Hamiltonians and long-range gapped Hamiltonians.
Prof. Robert König (with Michael Wolf’s group) talk on “Protected gates for topological quantum field theories”
We give restrictions on locality-preserving unitary automorphisms U, which are protected gates, for 2-dimensional topologically ordered systems. For generic anyon models, we show that such unitaries only generate a finite group, and hence do not provide universality. For non-abelian models, we find that such automorphisms are very limited: for example, there is no non-trivial gate for Fibonacci anyons. More generally, systems with computationally universal braiding have no such gates. For Ising anyons, protected gates are elements of the Pauli group.These results are derived by relating such automorphisms to symmetries of the underlying anyon model: protected gates realize automorphisms of the Verlinde algebra. We additionally use the compatibility with basis changes to characterize the logical action.
This is joint work with M. Beverland, O. Buerschaper, F. Pastawski, J. Preskill and S. Sijher.
In this talk I will introduce a family of exactly solvable toy models of a holographic correspondence based on a novel construction of quantum error-correcting codes with a tensor network structure. The building block for these models are a special type of tensor with maximal entanglement along any bipartition, which gives rise to an exact isometry from bulk operators to boundary operators. The entire tensor network is a quantum error-correcting code, where the bulk and boundary degrees of freedom may be identified as logical and physical degrees of freedom respectively. These models capture key features of entanglement in the holographic correspondence; in particular, the Ryu-Takayanagi formula and the negativity of tripartite information are obeyed exactly in many cases. I will describe how bulk operators may be represented on the boundary regions mimicking the Rindler-wedge reconstruction.
Michael Fischer (group R. Gross) will talk on On-Chip Superconducting Microwave Interferometers
In recent years, important progress towards using superconducting circuits for quantum information processing (QIP) has been made. In circuit quantum electrodynamics, photons inside superconducting transmission lines and resonators interact with artificial atoms, called qubits. In our approach to QIP, the qubit information may be encoded in a dual-rail setup, consisting of two superconducting transmission lines. Similarly to all-optical quantum computing the qubit states are superpositions of a microwave photon travelling in either one of the transmission lines. In QIP, operations between multiple qubits are needed to perform quantum algorithms. In order to use the dual-rail setup, these so called gates need to be implemented for two dual-rail encoded qubits. One important two qubit gate, a controlled phase gate, can be built with an interferometer equipped with a photon number dependent phase shifter. In this talk, I will present theoretical calculations and simulations, as well as measurements of on-chip interferometers fit for the application in such phase gates.
Dr. Guido Bacciagaluppi (Reader at U Aberdeen) will talk on Did Bohr Understand EPR?
Contrary to widespread belief, I argue that Niels Bohr’s arguments in his reply to Einstein Podolsky and Rosen in 1935 take fully into account the separation between the two particles. Specifically, I argue that there is no sleight of hand in the passage from Bohr’s discussion of a single particle passing through a slit and his subsequent discussion of the EPR example.
Dr Jukka Kiukas (U Nottingham, formerly with Reinhard Werner) on: Local asymptotic normality for the estimation of dynamical parameters of an open quantum system
Input-output formalism is a well-known framework for describing continual monitoring of a Markovian open quantum system via measurements made on its environment (typically a quantised radiation field). Mathematically, the environmental noise is described in terms of quantum stochastic Wiener processes on the field Fock space. We consider the problem of identifying and estimating unknown dynamical parameters (Hamiltonian and the quantum jump operators) from the output field state. For this purpose, we first use quantum Ito calculus to derive an information geometric structure on the set of parameters, arising from the quantum Fisher information of the output state. The geometry comes with an associated CCR-algebra, and we then show that local estimation reduces asymptotically (with long observation times) to a Gaussian estimation problem on that CCR-algebra.
Jakob Wierzbowski will talk on “Polarization control in few-layer MoS2 by electric-field-induced symmetry breaking”
Moritz August will talk on A Brief Introduction to Neural Networks
During the last decade, Machine Learning has become one of the most innovative and challenging fields at the intersection of Computer Science and Math. It has already been successfully applied to a wide array of domains, examples being the natural sciences, robotics and advertisement. Among the various techniques developed in the field, (Artificial) Neural Networks have proven to be one of the most powerful methods today and have led to significant improvements in many applications. Under the label of “Deep Learning” they also have gained attention in the public media and are the catalyst of the recent debate about the dangers of Artificial Intelligence.
In this talk, a brief introduction to the fundamentals of Neural Networks will be given. The talk will focus on their mathematical nature rather than on the neuroscientific interpretation and it will be explained what the term “Deep Learning” actually refers to.”
Stephan Welte will talk on Experiments with single atoms and photons
In the field if cavity quantum electrodynamics, the deterministic interaction of single photons with single atoms can be achieved. I will present our experimental setup that allows to study and exploit atom-photon interactions in the strong-coupling regime. This is achieved by optically trapping atoms at the center of a high finesse cavity. As an example for the rich set of applications possible with this system, I will present the nondestructive detection of optical photons which are reflected off the cavity.
[Reiserer et al. Nondestructive Detection of an Optical Photon, Science342, 1349 (2013)]
After my talk, a lab tour is planned. All ExQM members are cordially invited to participate.
Claudius Hubig will talk on “Strictly Single-Site DMRG (DMRG3S) with Subspace Expansion”
The talk will also include an intro into finding ground states by DMRG before going into research results of http://arxiv.org/abs/1501.05504v1
Next Fri, Feb. 13th at 10.15am in MPQ (seminar room B0.22) we have the pleasure to hear
Dr Volkher Scholz (ETH Zurich) talk on Operationally-Motivated Uncertainty Relations for Joint Measurability and the Error-Disturbance Tradeoff
We derive new Heisenberg-type uncertainty relations for both joint measurability and the error- disturbance tradeoff for arbitrary observables of finite-dimensional systems (I will shortly mention the extension to position/momentum). The relations are formulated in terms of a directly operational quantity, namely the probability of distinguishing the actual operation of a device from its hypothetical ideal, by any possible testing procedure whatsoever. Moreover, they may be directly applied in information processing settings, for example to infer that devices which can faithfully transmit information regarding one observable do not leak any information about conjugate observables to the environment.
joint work with Joe Renes and Stefan Huber, ETH Zurich
Lukas Knips (ExQM student in Weinfurter’s group) talk on “Multipartite Entanglement Detection with Minimal Effort”
Certifying entanglement in a multipartite state is a demanding task. As a state of $N$ qubits is parametrized by $4^N-1$ real numbers, one may expect that the measurement complexity of generic entanglement detection is also exponential with $N$.
However, in special cases we can design indicators for genuine multipartite quantum entanglement using measurements in only two settings. I will describe the general method of deriving such criteria, which are based on a more general entanglement criterion using correlation measurements.
In the corresponding experiment we test two such non-linear witnesses, one constructed for four-qubit GHZ states, the other for Cluster states.
After introducing the theory and explaining our scheme for detecting genuine multipartite entanglement, I would like to show you around in our lab.
Fri Jan. 30th at 9.00am till Sat Jan. 31st at 18.30pm.
The venues are at LMU in the centre, see plans: http://www.qcompinfo2015.philosophie.uni-muenchen.de/practical-info/index.html
Apart from the more philosophial oriented talks, there are also some closer to us, in particular by
— Brukner (from Vienna, Zeilinger)
— Schack
— Briegel
For details, please see:
http://www.qcompinfo2015.philosophie.uni-muenchen.de/program/index.html
and:
http://www.qcompinfo2015.philosophie.uni-muenchen.de/program/program_v10.pdf
“An atomic Hong-Ou-Mandel experiment”
The celebrated Hong, Ou and Mandel (HOM) effect is one of the simplest illustrations of two-particle interference, and is unique to the quantum realm. In the original experiment, two photons arriving simultaneously in the input channels of a beam-splitter were observed to always emerge together in one of the output channels. Here, we report on the realisation of a closely analogous experiment with atoms instead of photons. This opens the prospect of testing Bell’s inequalities involving mechanical observables of massive particles, such as momentum, using methods inspired by quantum optics, with an eye on theories of the quantum-to-classical transition. Our work also demonstrates a new way to produce and benchmark twin-atom pairs that may be of interest for quantum information processing and quantum simulation.
Anna-Lena Hashagen will give a survey talk on her masters work in finance mathematics (should be a good New Year refreshment)
“The Flesaker-Hughston Model for the Term-Structure of Interest Rates”,
An interesting and still widely debated problem is the mathematical modelling of the term-structure of interest rates. Even though many attempts have been made to put forward an interest-rate model that fulfils all the desirable properties, these models usually have more than one shortcoming. Another major issue that is common to nearly all areas within financial mathematics is the urge of agreement with market practice. In order to minimise these shortcomings, Flesaker and Hughston have put forward a new methodology of interest-rate term-structure modelling called the Flesaker-Hughston model. This model class is very tractable and guarantees the positivity of interest rates. In the last few years, one very special model of theirs that has received particular interest is called the Flesaker-Hughston rational lognormal model. On top of the guaranteed positivity it resembles well-known market pricing formulas for popular interest-rate derivatives such as caps and floors as well as swaptions. This talk discusses the Flesaker-Hughston model class and places it within the environment of already existing models. We then thoroughly analyse the Flesaker-Hughston rational lognormal model with respect to the underlying dynamics of the instantaneous short-rate and the bond price, as well as the inherent boundaries that appear in this new framework.
Pricing formulas for caps and swaptions are derived by letting the martingale follow a diffusion process. Generalising this to an exponential L\'{e}vy process and using a method called the generalised Fourier transform, we also derive the price of a cap in this more realistic setting that includes jumps. The model is then calibrated to a full data set of risk-free zero-coupon bond prices in conjunction with either cap implied volatility, cap price, caplet price or caplet implied volatility mid-quotes on the US dollar three-month LIBOR rate.
Since the Flesaker-Hughston rational lognormal model gives closed-form expressions for caps, the calibration is extremely efficient. Using the real market data sets, the calibration analysis and the thorough analysis of the inherent model boundaries reveal that the instantaneous short-rate is bounded to such an extend that the Flesaker-Hughston rational lognormal model seems useful to price interest-rate options only in very specific cases — for those cases that lie within the boundaries. The guaranteed positivity of the instantaneous short-rate, i.e. the lower bound of zero, comes at a price of a restrictive upper
bound.
Dr Volckmar Nebendahl (Blatt group, Innsbruck) on “Optimized Quantum Error Correction Codes for Experiments”.
Details in http://arxiv.org/pdf/1411.1779v1.pdf.
Luca Arceci from Univ. of Bologna on “Quantum solitons in the XXZ model with staggered external field”.
The 1-D 1/2-spin XXZ model with staggered external magnetic field, when restricting to low field, can be mapped into the quantum sine-Gordon model through bosonization: this assures the presence of soliton, antisoliton and breather excitations in it. In particular, the action of the staggered field opens a gap so that these physical objects are stable against energetic fluctuations.
In the present work, this model is studied both analytically and numerically. On the one hand, analytical calculations are made to solve exactly the model through Bethe ansatz: the solution for the XX + h staggered model is found by means of Jordan-Wigner transformation and Bethe ansatz separately, while eff orts are made to extend the latter approach to the XXZ + h staggered model (without finding its solution). On the other hand, grounding on results from the application of quantum fi eld theories on the quantum sine-Gordon model, the energies of these excitations are pinpointed through static DMRG (Density Matrix Renormalization Group) for diff erent values of the parameters in the hamiltonian. Breathers are found to be in the antiferromagnetic region only, while solitons and antisolitons are present both in the ferromagnetic and antiferromagnetic region. Their single-site z- magnetization expectation values are also computed to see how they appear in real space, and time-dependent DMRG is employed to realize quenches on the hamiltonian parameters to monitor their time-evolution.
The results obtained reveal the quantum nature of these objects and provide some information about their features. Further study of their properties could lead to the realization of a two-state qubit through a soliton-antisoliton pair.
Dr Oleg Szehr (who just moved to Cambridge, UK) on “On Quantum Phases in Systems with Matrix-Product Ground States”
We introduce Matrix Product states and their parent Hamiltonians and define the notion of a quantum phase in this framework. We provide a classification of phases of one-dimensional systems both with unique as well as degenerate ground states. We address the question of how robust the energy gap in the parent Hamiltonian model is to perturbations and provide conditions under which robustness is guaranteed.
Our methods rely on a close connection between translation-invariant Matrix product states and the Perron-Frobenius theory of certain associated quantum channels.
Matteo Rossi from Univ. of Parma on “Dynamics of Quantum Correlations for Two-Qubit Systems Interacting with Classical Noisy Environments”.
In this talk we consider single- and two-qubit systems coupled to classical stochastic fields and address both the decoherence and the non-Markovianity induced by the external fields.
Studying the interaction of a quantum system with its environment plays a fundamental role in the development of quantum technologies. Decoherence is detrimental for applications and it may be induced by classical or quantum noise, i.e. by the interaction with an environment described classically or quantum-mechanically. The classical description is often more realistic to describes environments with a very large number of degrees of freedom and it has also been shown that certain quantum environments may be described with equivalent classical models. We thus analyze in detail the dynamics of quantum correlations (entanglement and quantum discord) and evaluate the non-Markovianity of the induced dynamical quantum map for two-qubit systems interacting with classical stochastic fields, focusing on Gaussian processes.
On Friday, May 16th 2014 at 10.00am (sharp) in MPQ on campus Garching Small Lecture Hall we will have a Post-QCCC/Pre-ExQM seminar by:
Dr. Dmitry Savostyanov, University of Southampton (Co-authors: Sergey Dolgov, MPI MiS Leipzig, and Ilya Kuprov, U Southampton) on “Alternating Minimal Energy Methods for Linear Systems in Higher Dimensions”
When high-dimensional problems are concerned, not many algorithms can break the curse of dimensionality and solve them efficiently and reliably. Among those, tensor product algorithms seem to be the most promising.
The first attempt to merge classical iterative algorithms and DMRG/MPS methods was made in a way, where the second Krylov vector is used to expand the search space on the optimisation step. The idea proved to be useful, but the implementation was based on the fair amount of physical intuition, and the algorithm is not completely justified.
We have recently proposed the AMEn algorithm for linear systems [3, 4], that also injects the gradient direction in the optimisation step, but in a way that allows to prove the global convergence of the resulted scheme. The scheme can be easily applied for the computation of the ground state—the differences to the algorithm of S. White [13] are emphasized in [5]. The AMEn scheme was recently applied for the computation of extreme eigenstates [7], using the block-TT format proposed in [2].
We aim to extend this framework and the analysis to other problems: eigenproblems, time-dependent problems, high-dimensional interpolation, and matrix functions; as well as to a wider list of high-dimensional problems.
This is a jointwork with Sergey Dolgov at the Max-Planck Institute for Mathematics in the Sciences, Leipzig, and Ilya Kuprov at the University of Southampton, UK.
selected refs.:
[2] S. V. Dolgov, B. N. Khoromskij, I. V. Oseledets, and D. V. Savostyanov. Computation of extreme eigenvalues in higher dimensions using block tensor train format.
Computer Phys. Comm., 185(4):1207–1216, 2014. doi:10.1016/j.cpc.2013.12.017.
[3] S.V. Dolgov and D.V. Savostyanov. Alternating minimal energy methods for linear systems in higher dimensions. Part I: SPD systems. arXiv preprint 1301.6068, 2013.
URL: http://arxiv.org/abs/1301.6068.
[4] S. V. Dolgov and D. V. Savostyanov. Alternating minimal energy methods for linear systems in higher dimensions. Part II: Faster algorithm and application to nonsymmetric systems. arXiv preprint 1304.1222, 2013. URL: http://arxiv.org/abs/
1304.1222.
[5] S. V. Dolgov and D. V. Savostyanov. Corrected one-site density matrix renormalization group and alternating minimal energy algorithm. In Proc. of ENUMATH 2013, accepted, 2014. URL: http://arxiv.org/abs/1312.6542.
[7] D. Kressner, M. Steinlechner, and A. Uschmajew. Low-rank tensor methods with subspace correction for symmetric eigenvalue problems. MATHICSE preprint 40.2013, EPFL, Lausanne, 2013.
[13] Steven R. White. Density matrix renormalization group algorithms with a single center site. Phys. Rev. B, 72(18):180403, 2005. doi:10.1103/PhysRevB.72.180403.
more details can be found in: SavostjanovMPQ14.pdf
Dr. Andreas Ruschhaupt, Cork University, Ireland (formerly jun. Prof. with Reinhard Werner) on “Shortcuts to Adiabaticity”
Quantum adiabatic processes -that keep constant the populations in the instantaneous eigenbasis of a time-dependent Hamiltonian-are very useful to prepare and manipulate states, but take typically a long time. This is often problematic because decoherence and noise may spoil the desired final state, or because some applications require many repetitions.
“Shortcuts to adiabaticity” are alternative fast processes which reproduce the same final populations, or even the same final state, as the adiabatic process in a finite, shorter time [1]. We present such “shortcuts to adiabaticity” for the manipulation of the atomic motional state [2] as well as for the passage from one internal atomic state to another [3-5]. We especially study and compare the stability of different shortcut schemes concerning different types of perturbations like, for example systematic and noise errors [4, 6] or errors originating from unwanted transitions to other levels [7].
References:
[1] E. Torrontegui, S. Ibáñez, S. Martínez-Garaot, M. Modugno,
A. del Campo, D. Guéry-Odelin, A. Ruschhaupt, Xi Chen and J. G. Muga,
Adv. At. Mol. Opt. Phys. 62 (2013) 117
[2] Xi Chen, A. Ruschhaupt, S. Schmidt, A. del Campo,
D. Guéry-Odelin and J. G. Muga,
Phys. Rev. Lett. 104 (2010) 063002
[3] Xi Chen, I. Lizuain, A. Ruschhaupt, D. Guéry-Odelin and J. G. Muga,
Phys. Rev. Lett. 105 (2010) 123003
[4] A. Ruschhaupt, X. Chen, D. Alonso and J. G. Muga,
New J. Phys. 14 (2012) 093040
[5] S. Ibáñez, Xi Chen, E. Torrontegui, J. G. Muga and A. Ruschhaupt,
Phys. Rev. Lett. 109 (2012) 100403
[6] D. Daems, A. Ruschhaupt, D. Sugny and S. Guerin,
Phys. Rev. Lett. 111 (2013) 050404
[7] A. Kiely and A. Ruschhaupt, arXiv:1312.3210
Former PhD Programme QCCC (Quantum Computing, Control, and Communication):
We meet Tue Nov. 12th, at the MPQ with the schedule as follows:
11:30am coffee/lunch gathering at MPQ cafeteria.
Seminar Room of Cirac Group (2nd floor):
12:00 am Prof. Schollwöck: “Nature of the Spin-Liquid Ground State of the S=1/2 Heisenberg Model
on the Kagome Lattice”
12:45 am extended discussion: Identifying Cutting Edge Problems
1:00-1.30pm coffee break
Seminar Room B0.21 of MPQ (ground floor):
1.30pm Thomas Barthel: “Some tensor network state techniques and entanglement in condensed matter systems with application to fermionic systems”
2.00pm : Thomas Schulte-Herbrüggen : “Symmetry Principles in the Quantum Systems Theory of Many-Body Systems”
2.45-3.15 pm Coffee
3.15-3.45 pm “Robert Zeier: “Two Teasers: 1. Simulating Sparse Qubit Systems,
2. Further Results on Fermionic Systems”
3.45-4.15 pm Marie Carmen Banuls: “Tensor Network Methods Applied to Lattice Gauge Theories”
4.15-4.45 pm Prof. Thomas Huckle/Konrad Waldherr: “(1) General Overview on Recent Tensor Methods in Maths
plus (2) Numerical (Multi-)Linear Algebra in Quantum Tensor Networks (Results and Perspectives)”
5.00 pm general discussion
~5.45 pm end with option to have dinner in Garching
Dr. Daniel Reitzner (TUM)
Measurements in quantum mechanics are, compared to classical measurements, somewhat non-intuitive and in particular can be incompatible; i.e. a pair of measurements on a single system can turn out to be impossible to perform at once. Although it is quite often stated that this is a basis for Heisenberg uncertainties; we will show the limitations and dangers of this description.
With a more modern and in a sense more general definition of quantum measurement via POVMs that we shall introduce as well, we will see, that simultaneous (and/or sequential) measurements are a tricky and still unresolved concept that has an impact on modern applications within quantum information community.
Thorsten Wahl (MPQ)
This talk consists of two parts. In the first one I will introduce the concept of Localizable Entanglement, which is important for the detection of topological quantum phase transitions and ideal quantum repeaters in the case where the Localizable Entanglement is constant over arbitrary long distances. Finally, I will provide a necessary and sufficient condition for the later case (also denoted as long-range Localizable Entanglement) for Matrix Product States.
The second part of my talk is devoted to the approximation of topological insulators by Gaussian fermionic PEPS which are the free Fermionic version of Projected Entangled Pair States. I will show under which conditions Gaussian fermionic PEPS are topologically non-trivial.
Quantum Information Theory in Infinite Dimensions: An Operator-Algebra Approach.
PD Prof. Michael Keyl (FU Berlin)
Most of quantum information theory is developed in the framework of finite dimensional Hilbert spaces, and therefore not directly applicable to systems like free and interacting non-relativistic particles, spin-systems in the thermodynamic limit or relativistic field models, where an infinite dimensional description is required. In some cases a more or less direct generalization is possible (e.g. by replacing finite sums with absolutely converging sequences) but this approach is very limited and misses many of the more interesting aspects of infinite dimensional systems. In other words mathematically and conceptually new tools are needed. In this context the theory of operator algebras provides a very powerful framework, which is particularly useful for the study of infinite degrees of freedom systems.
The purpose of this lecture series is to introduce into this theory and its applications in qantum physics. Apart from the corresponding mathematical foundations we will show how elementary concepts of quantum theory can be reformulated and how the differences between finite dimensions, infinite dimensions but finite degrees of freedom, and infinite degrees of freedom can be related to operator algebras and their representations. Furthermore we will study infinite spin systems, their entanglement properties and their connection to advanced operator algebraic topics, like type and cassification of von Neumann algebras.
Oleg Szehr (TUM)
In this talk I present a new framework that yields spectral bounds on norms of functions of transition maps for finite, homogeneous Markov chains. The techniques employed work for bounded semigroups, in particular for classical as well as for quantum Markov chains and they do not require additional assumptions like detailed balance, irreducibility or aperiodicity. I use the method in order to derive convergence bounds that improve significantly upon known spectral bounds. The core technical observation is that power-boundedness of transition maps of Markov chains enables a Wiener algebra functional calculus in order to upper bound any norm of any holomorphic function of the transition map.
PD Prof. Michael Keyl (FU Berlin)
In this talk I will review a number of research projects from different areas of quantum physics, including: Mean field flucutations of spin-systems and their relation to continuous variable quantum systems; quantum field theory in space-times with causality violations; and quantum control of bosonic and Fermionic systems.
Prof. Michael M. Wolf (TUM)
The talk aims at providing a taste of Quantum Information Theory exemplified through two problems from different branches of the field.
In the first part we will encounter quantum correlations that are arbitrarily stronger than their classical counterparts. In physics this is related to the foundations of quantum theory, in mathematics to Grothendieck type inequalities within operator space theory, and in theoretical computer science to the reduction of communication complexity. The latter perspective suggests how – in the distant future – the scheduling of the colloquium mightbe made more efficient.
The second part will shed new light on the energy gap problem from condensed matter theory. Despite considerable effort and interest, there is basically neither a proof technique nor a numerical method known for solving this type of problem. We will argue that the roots of this difficulty may be deeper than expected by showing that there are cases for which there cannot be a proof (in the sense of Gödel) or an algorithm (in the sense of Turing).
Prof. David Gross (Uni Freiburg)
Very time the release button of a digital camera is pressed, several megabytes of raw data are recorded. But the size of a typical jpeg output file is only 10% of that. What a waste! Can’t we design a process which records only the relevant 10% of the data to begin with? The recently developed theory of compressed sensing achieves this trick for sparse signals. I will give a short introduction to the ideas and the math behind compressed sensing.
A basis-independent notion of “sparsity” for a matrix is its rank. One is thus naturally led to the “low-rank matrix recovery” problem: can one reconstruct and unknown low-rank matrix from few linear measurements? The answer is affirmative. The arguably simplest proof to date is based on ideas from quantum information theory. In the second half of the presentation, I will talk about applications and proof techniques for the matrix theory, including the links to quantum.
Abstract: We investigate the problem of quantum searching on a noisy quantum computer. Taking a “fault-ignorant” approach, we design quantum algorithms that solve the task for various different noise strengths, possibly unknown beforehand. The rationale is to avoid costly overheads, such as traditional quantum error correction.
Proving lower bounds on algorithm runtimes, which may depend on the actual level of noise, we find that the quadratic speedup is lost (in our noise models). Nevertheless, for low noise levels, our algorithms outperform the best noiseless classical search algorithm. Finally, we provide a more general framework to formulate fault-ignorant algorithms.
In the second part of the lecture, we will introduce a different setup that is a realization of a traverse-field Ising model with long-range interactions. This time we coupled the atoms to a laser beam driving a transition to a highly-excited electronic state, a so-called Rydberg state. The enormous van der Waals interaction between two atoms in such a state gives rise to strong spatial correlations over distances much larger than the interparticle distance. Here we could observe the spontaneous formation of well-defined geometric structures of a few Rydberg excitations and gather some evidence that the system had been excited to a highly-entangled many-body state.
In our system we strongly couple a single atom to the light field of an optical resonator. I will give a brief introduction to what can be deduced from the phase of the intra-cavity field and how we can build a single atom phase shifter with this system.
In this talk I’ll show that there is no superactivation for Gaussian channels that are generated by passive means.
Recently we have investigated the computational power of normaliser circuits and found that, in spite of their apparent quantumness, they can be efficiently simulated in a classical computer. Thus, a quantum computer operating within this set of gates can not offer exponential quantum speed-ups over classical computation, regardless e.g. the number of QFT it uses. Our result generalises a well-known theorem of Gottesman and Knill, valid for qubits, to systems that do not decompose as products of small subsystems.
Format:
I will introduce some elements of group theory needed to understand our theorem and the main tool we developed to prove it: a stabiliser formalism for high dimensions. The latter may be of independent interest in quantum error correction and fault tolerant quantum computing. I will also explain the relation of these results with Shor’s algorithm.
We explore reachable sets of open $n$-qubit quantum systems the coherent parts of which are under full unitary control and that have just one qubit whose unital or non-unital noise amplitudes can be modulated in time such as to provide an additional degree of incoherent control. In particular, adding bang-bang control of amplitude damping noise (non-unital) allows the dynamic system to act transitively on the entire set of density operators. This means one can transform any initial quantum state into any desired target state. Adding switchable bit-flip noise (unital), on the other hand, suffices to explore all states majorised by the initial state. We have extended our optimal control algorithm (DYNAMO) by degrees of incoherent control so that these unprecedented reachable sets can systematically be exploited for experimental settings. Numerical results are compared to constructive analytical schemes.
Abstract: It is clear that if the transition matrix of an irreducible quantum Markov-process has a sub dominant eigenvalue which is close to 1 then the quantum Markov-process is ill conditioned in the sense that there are stationary states which are sensitive to perturbations in the transition matrix. However, the converse of this statement has heretofore been unresolved. The purpose of this talk is to present upper and lower bounds on the condition number of the chain such that the bounding terms are determined by the closeness of the sub dominant eigenvalue to unity.
We obtain perturbation bounds which relate the sensitivity of the chain under perturbation to its rate of convergence to stationarity.
Polynomial invariants provide a tool to characterise quantum states with respect to local unitary transformations. Unfortunately, the situation becomes very complicated already for mixed states of three qubits due to combinatorial explosion.
After an introduction to the mathematical background and general tools, the talk will present preliminary results for mixed quantum states and Hamiltonians for three-qubit systems.
The talk is based on joint work in progress with Robert Zeier.
In particular, I will show that bounding the gap of the channel is sometimes insufficient for bounding the convergence time.
I will review some of the tools which are available (and some which will soon be), and discuss some of the difficulties in extending classical mixing time methods to the quantum setting.
Finally, I will provide some applications of these methods introduced, and give an outlook on some open problems.
First we present an algorithm for the approximation of ground states (GS) that is based on the computation of the gradient of the energy [1]. We achieve a scaling of the computational cost of O(D3n2) + O(D3mn), where D is the virtual bond dimension of the MPS and m and n are some parameters that will be explained in more detail in the talk. There is a tradeoff between the parameters n and m and we show how to find the optimal balance. The analysis of the numerical results confirms previous observations regarding the induced correlation length of MPS with finite D [2, 3]. Furthermore we observe a crossover between the finite-N scaling and finite-D scaling in the context of critical quantum spin chains similar to the one observed by Nishino [4] in the context of classical two dimensional systems.
Next we present an algorithm for the approximation of dispersion relations that uses as an ansatz MPS-based states with well defined momentum [5]. Here, we achieve a scaling of the computational cost of O(D6N2). Due to the large D scaling we are restricted to comparatively small D. Nonetheless we obtain very good approximations of one-particle excitations. The numerical results yield some insight into the interpretation of the quasiparticles that occur in the exact solution of the Quantum Ising Model with PBC.
With new mathematical tools from quantum information theory becoming available, there has been a renewed effort to settle this old question.
I will present and discuss a necessary and a sufficient condition for the emergence of Gibbs states from the unitary dynamics of quantum mechanics and show how these new insights into the process of equilibration and thermalization can be used to design a quantum algorithm that prepares thermal states on a quantum computer/simulator.
This talk introduces a Matlab toolbox, along with the underlying methodology and algorithms, providing a convenient way to work with this format. The toolbox not only allows for the efficient storage and manipulation of tensors but also offers a set of tools for the development of higher-level algorithms.
As an example for the use of the toolbox, an algorithm for solving high-dimensional linear systems, namely parameter-dependent elliptic PDEs, is shown. This is joint work with Daniel Kressner, ETH Zurich.
We propose a generalization of entanglement monotones that may provide greater flexibility in the quantification of entanglement. Rather than quantifying the entanglement of a state directly, we suggest a relative quantification: a direct comparison of one entangled state to another. We provide an example of such relative quantification for a quantum information resource known as frameness.
In the context of quantum information processing, this difficulty becomes the main source of power: in some situations, information processors based in quantum mechanics can process information exponentially faster than classical systems. From the perspective of a physicist, one of the most interesting applications of this type of information processing is the simulation of quantum systems. We call a quantum information processor that simulates other quantum systems a quantum simulator.
Using a kind of nuclear magnetic resonance simulator, we implement the simulations of the Heisenberg spin models by the use of average Hamiltonian theory and observe the quantum phase transitions by using different measurements, e.g., entanglement, fidelity decay and geometric phase: the qualitative changes that the ground states of some quantum mechanical systems exhibit when some parameters in their Hamiltonians change through some critical points. In particular, we consider the effect of the many-body interactions. Depending on the type and strength of interactions, the ground states can be product states or they can be maximally entangled states representing different types of entanglement.
When the many-body interaction (such as the three-body interaction) takes part in the competition, new critical phenomena that cannot be detected by the traditional two-spin correlation functions will occur.
By quantifying different types of entanglement, or by using suitable entanglement witnesses, we successfully detect two types of quantum transitions. Besides this, using such a NMR quantum simulator, we can also simulate the static properties and dynamics of chemical systems, such as the ground-state energy of Hydrogen molecule.
Describing system environment interactions in the non-perturbative regime
Recent experiments have provided strong evidence for the existence of quantum coherence in the early stages of photosynthesis. Subsequent theory work shows that the optimal operating regime lies in the regime where the system-environment interaction is strong so that the system is neither fully quantum coherent nor fully classical, but rather half way in between. In this regime perturbative treatments of the system environment interaction are not valid. Here I discuss the above issue and then present a novel approach to the numerical and analytical study of spin systems in strong contact with environments made up of harmonic oscillators.
This talk is based on
M.B. Plenio and S.F. Huelga
– Dephasing assisted transport: Quantum networks and biomolecules –
New J. Phys. 10, 113019 (2008) and E-print arXiv:0807.4902 [quant-ph]
F. Caruso, A.W. Chin, A. Datta, S.F. Huelga and M.B. Plenio
– Highly efficient energy excitation transfer in light-harvesting complexes: The fundamental role of noise-assisted transport –
J. Chem. Phys. 131, 105106 (2009) and E-print arXiv:0901.4454 [quant-ph]
J. Prior, A.W. Chin, S.F. Huelga and M.B. Plenio
– Efficient simulation of strong system-environment interactions –
Phys. Rev. Lett. 105, 050404 (2010) and E-print arXiv:1003.5503 [quant-ph]
A.W. Chin, A. Rivas, S.F. Huelga and M.B. Plenio
– Exact mapping between system-reservoir quantum models and semi-infinite discrete chains using orthogonal polynomials –
J. Math. Phys. 51, 092109 (2010) and E-print arXiv:1006.4507 [quant-ph]
We consider the optimal control problem of transferring population between states of a quantum system where the coupling proceeds only via intermediate states that are subject to decay. We pose the question whether it is generally possible to carry out this transfer.
For a single intermediate decaying state, we recover the Stimulated Raman Adiabatic Passage (STIRAP) process for which we present analytic solutions in the finite time case. The solutions yield perfect state transfer only in the limit of infinite time.
We also present analytic solutions for the case of transfer that has to proceed via two consecutive intermediate decaying states. We show that in this case, for finite power the optimal control does not approach perfect state transfer even in the infinite time limit. We generalize our findings to characterize the topologies of paths that can be achieved by coherent control.
This talk will serve as an introduction to two classes of completely positive maps: the Schur maps which arise from the Schur matrix product and maps which are equal to their adjoint.
After focusing on results concerning the geometry of these two sets of CP maps, we introduce a general framework that unifies certain classes of CP maps in terms of C*-subalgebras of Mn.
On the Role of Quantum Coherence in Photosynthetic Energy Transfer
Recent experiments have provided evidence for long-lived electronic coherence in photosynthetic light-harvesting complexes at room temperature. This talk presents some of the work performed in theAspuru-Guzik group on the Fenna-Matthews-Olson complex. This includes the basic concept of environment-assisted excitonic transport and a quantification of the role of coherence by its contribution to the transport efficiency.
We find that, depending on the spatial correlations in the phonon environment, there is about a 10% contribution of coherent dynamics to the exciton transfer efficiency. In addition, we investigate a time-convolutionless non-Markovian master equation approach and show our quantum chemistry inspired way of incorporating atomistic detail of the protein environment into the exciton dynamics.
Quantum optics on a chip – photon counters and NOON states
Circuit quantum electrodynamics is a maturing field in which the physics of quantum optical setups is realized in cryogenic electric circuits, profiting from large achievable coupling strengths. Elements like cavities, artificial atoms, mirrors, and beamsplitters have been successfully demonstrated. The missing element is a single-photon counter as microwave photons are usually amplified instead of counted, and as most of these amplifiers are noisy.
I will present the Josephson Photomultiplier, a simple device that allows single photon counting at high efficiency and bandwidth. Quantum optics with multiple modes has highlightes NOON states – states in which N photons are in a superposition of two arms of an interferometer for quantum-enhanced metrology. I am going to show how these can be created deterministically in circuit QED.
The success of such an experiment is difficult to determine as the reconstruction of a two-mode density matrix at large photon number is forbiddingly cumbersome. We are going to show that it is much more efficient to test for a hypothesis state and then estimate the overlap between the hypothetical state and the physical state using nonlinear programming.
The uncertainty principle lies at the heart of quantum theory, illuminating a dramatic difference with classical mechanics. The principle bounds the uncertainties of the outcomes of any two observables on a system in terms of the expectation value of their commutator. It implies that an observer cannot predict the outcomes of two incompatible measurements to arbitrary precision.
However, this implication is only valid if the observer does not possess a quantum memory, an unrealistic assumption in light of recent technological advances. In this work we strengthen the uncertainty principle to one that applies even if the observer has a quantum memory. We provide a lower bound on the uncertainty of the outcomes of two measurements which depends on the entanglement between the system and the quantum memory.
We expect our uncertainty principle to have widespread use in quantum information theory, and describe in detail its application to quantum cryptography. The talk is based on joint work with Mario Berta, Roger Colbeck, Joe Renes and Renato Renner (http://arxiv.org/abs/0909.0950).
“Dynamical Quantum Systems: Controllability, Symmetries, and Representation Theory”
We analyze the controllability of dynamical quantum systems. One can decide controllability by computing the Lie closure [1] which is sometimes cumbersome. These topics can be discussed likewise for translationally invariant lattices [2]. Building on previous work [3,4], we propose an additional method which utilizes the symmetry properties of the considered system.
We obtain as a necessary condition for controllability that the system should not have any symmetries and act therefore irreducibly. But this condition is not sufficient as there exist irreducible subalgebras of the maximal possible system Lie algebra. We classify the irreducible subalgebras and their inclusion relations relying on results of Dynkin [5]. Using optimized computer programs we can tabulate irreducible subalgebras up to dimension 215 (i.e. 15 qubits) complementing results of McKay and Patera [6].
For concrete dynamical quantum systems many irreducible subalgebras can be ruled out as obstructions for full controllability and we present algorithms to this end. Our results provide an insight into the question when spin, bosonic, and fermionic systems can simulate each other. We will give a short introduction to the relevant representation theory of Lie algebras.
[1] Jurdjevic/Sussmann, J. Diff. Eq. 12, 313 (1972)
[2] Kraus/Wolf/Cirac, Phys. Rev. A 75, 022303 (2007)
[3] Sander/Schulte-Herbrüggen, http://arxiv.org/abs/0904.4654
[4] Polack/Suchowski/Tannor, Phys. Rev. A 79, 053403 (2009)
[5] Borel/Siebenthal, Comment. Math. Helv. 23, 200 (1949);
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In this paper, we present a unified computational method based on pseudospectral approximations for the design of optimal pulse sequences in open quantum systems. The proposed method transforms the problem of optimal pulse design, which is formulated as a continuous-time optimal control problem, to a finite dimensional constrained nonlinear programming problem.
This resulting optimization problem can then be solved using existing numerical optimization suites. We apply the Legendre pseudospectral method to a series of optimal control problems on open quantum systems that arise in Nuclear Magnetic Resonance (NMR) spectroscopy in liquids. These problems have been well studied in previous literature and analytical optimal controls have been found.
We find an excellent agreement between the maximum transfer efficiency produced by our computational method and the analytical expressions. Moreover, our method permits us to extend the analysis and address practical concerns, including smoothing discontinuous controls as well as deriving minimum-energy and time-optimal controls. The method is not restricted to the systems studied in this article and is applicable to optimal manipulation of both closed and open quantum systems.
The relationship between characteristics of quantum channels and the geometry of their respective sets can provide a useful insight to some of their underlying properties. First we will discuss a special class of random unitary channels, namely, the Schur maps. We then use the generalization of these maps to motivate the study of what we call Self-Dual quantum channels. Some preliminary geometric properties of the set of such maps are investigated and compared to the geometry of the set of Schur maps. Finally, some preliminary algebraic results are discussed which involve the eigenvalues of Self-Dual quantum channels.
Anderson Localization in Disordered Quantum Walks
(**Volkher Scholz**, Albert Werner, and Andre Ahlbrecht)
We study a Spin-$\frac{1}{2}$-particle moving in a one dimensional lattice subjected to disorder induced by a random space dependent coin. The discrete time evolution is given by a family of random unitary quantum walk operators, where the shift operation is assumed to be non-random. Each coin is an independent identically distributed random variable with values in the group of two dimensional unitary matrices. We find that if the probability distribution of the coins is absolutely continuous with respect to the Haar measure, then the system exhibits localization. That is, every initially localized particle remains on average and up to exponential corrections in a finite region of space for all times.
It is shown that Majorana fermions trapped in three p-wave superfluid vortices form a qubit in a topological quantum computing (TQC). Several similar ideas have already been proposed: Ivanov [Phys. Rev. Lett. 86, 268 (2001)] and Zhang et al [Phys. Rev. Lett. 99, 220502 (2007)] suggested schemes in which a qubit is implemented with two and four Majorana fermions, respectively, where a qubit operation is performed by braiding the world lines of these Majorana fermions. Naturally the set of quantum gates thus obtained is a discrete subset of the relevant unitary group.
We propose a new scheme, where three Majorana fermions form a qubit. We show that continuous qubit operations are made possible by braiding the Majorana fermions complemented with dynamical phase change. Moreover, it is possible to introduce entanglement between two such qubits by geometrical manipulation of some vortices involved.
How Long Can Passive Quantum Memories Withstand Depolarizing Noise?
Abstract: Existing fault tolerance theorems state that robust quantum computation and in particular, quantum memories may be achieved by growing the number of dedicated resources. Such theorems assume the availability of fresh ancillas (qubits in a predefined state) and the possibility of periodically applying recovery operations. Experimentally however, these requirements have shown to be hard to meet. In an attempt to provide a simpler path, many body Hamiltonians have been proposed with the hope that they could through their dynamics alone provide long protection times to quantum information. I will explain recent results which show that under a depolarizing noise model, protection times may not exceed O(log N) and such scaling is achievable by many body non-local Hamiltonians. I will go on to mention existing proposals for protecting Hamiltonians and describe some limitations we have found for the information lifetime under comparatively weak Hamiltonian perturbations.
Exploration of Side Channels in our BB84 Freespace Quantum Key Distribution System
The security of quantum key distribution, (QKD) is based on physical laws rather than assumptions about computational complexity: An adversary will necessarily disturb the communication by his quantum measurement. However, real implementations will be sensitive to side-channel attacks, i.e. to information losses due to distinguishabilities in other degrees of freedom, which an adversary can measure without causing errors.
We are running an implementation of the BB84 protocol installed on top of two university buildings in downtown Munich. Using attenuated laser pulses in combination with decoy states we are able to establish a secret key over a distance of 500 m. Our system is fully remote controlled and allows for continuous and fast QKD. I will report on the characterization of this QKD system with respect to side channels of the transmitter and the receiver and also show some attacks.
Abstract: The use of local, typically gradient based, optimisation algorithms has proven to be particularly effective in achieving control objectives for quantum mechanical systems. Some authors have sought a theoretical justification for this empirical observation of the numerical techniques’ behavior. A set of papers, falling under the banner of “optimal control landscapes” claim to offer such a justification, in the form of proofs that such optimisation always achieves the control objective (ignoring numerical limitations). I will present a number of problems inherent in said “landscape” analysis.
In this talk we discuss relationships between topology and quantum computation.
Since the discovery of Peter Shor’s quantum algorithm for the prime factorization of natural numbers, there has been intense interest in the discovery of new quantum algorithms and in the construction of quantum computers. It is possible that topology will enter in a deep way in the construction of quantum computers based on phenomena such as the quantum Hall effect, where braiding of quasiparticles describes unitary transformations rich enough to produce the quantum computations.
This talk will describe the mathematics of such braiding and its relationship with algorithms to compute topological invariants such as the Jones polynomial.
Just so, relationships with braiding go beyond the quantum Hall effect and are of interest for constructing quantum gates and quantum algorithms. The talk will discuss these directions and our present project in collaboration with the research group of Prof. Glaser (on this campus) to instantiate quantum algorithms for the Jones polynomial using NMR (Nuclear Magnetic Resonance Spectroscopy).
The talk will be self-contained both in terms of mathematics and physics.
The understanding of the Kronecker coefficients of the symmetric group (the multiplicities of decomposition into irreducible the tensor products of two irreducible representations of the symmetric group) is a longstanding open problem. Recently, its study has appeared naturally in some seemingly unrelated areas.
For instance, Matthias Christandl has showed that the problem of the nonvanishing of Kronecker coefficients is equivalent to the problem of compatibility of local spectra, and Ketan Mulmuley has set the problem of proving that the positivity of a Kronecker coefÞcients can be decided in polynomial time at the heart of his Geometric Complexity Theory.
In view of the difficulty of studying of the Kronecker coefÞcients, it is legitimate to consider some closely related, and maybe simpler objects, the reduced Kronecker coefficients, defined as limits of certain stationary sequences of Kronecker coefficients. We attempt to show that the study of the reduced Kronecker coefficients could sheld light on the Kronecker coefficients.
We will introduce the reduced Kronecker coefficients, and describe some of their known properties. Then, we will describe a useful formula to compute Kronecker coefficients from the reduced ones, and, among other results, present a sharp bound for a family of Kronecker products to stabilize.
Post-selection technique for quantum channels with applications to quantum cryptography
We propose a general method for studying properties of quantum channels acting on an n-partite system, whose action is invariant under permutations of the subsystems. Our main result is that, in order to prove that a certain property holds for any arbitrary input, it is sufficient to consider the special case where the input is a particular de Finetti-type state, i.e., a state which consists of n identical and independent copies of an (unknown) state on a single subsystem. A similar statement holds for more general channels which are covariant with respect to the action of an arbitrary finite or locally compact group.
Our technique can be applied to the analysis of information-theoretic problems. For example, in quantum cryptography, we get a simple proof for the fact that security of a discrete-variable quantum key distribution protocol against collective attacks implies security of the protocol against the most general attacks. The resulting security bounds are tighter than previously known bounds obtained by proofs relying on the exponential de Finetti theorem [Renner, Nature Physics 3,645(2007)]. This is joint work with Robert Koenig and Renato Renner http://arxiv.org/abs/0809.3019
We consider quantum chains in cluster states under the influence of a variable magnetic field. After reviewing the derivation of the ground state we compute the localisable entanglement of the two outermost qubits, after local measurements have been made on the inner ones, for different chain lengths. The result is mostly as intuitively expected: the entanglement decreases monotonously with the field strength.
Title: DISENTANGLING MANY-BODY QUANTUM SYSTEMS AND LARGE-SCALE LINEAR ALGEBRA
In this talk I want to show how many important questions of quantum many-body physics (solid state physics, quantum optics) naturally lead to a highly efficient description of quantum states by sets of matrices whose manipulation involves large-scale linear algebra of sparse matrices. I will illustrate the various challenges by current physical problems from solid state physics and quantum optics and would like to try to give a flavour why theoretical physicists would be interested in insights from computer science and numerical mathematics to tackle such problems.
Titel: “Charge-density wave behaviour in the t-J-Holstein Model”
Zusammenfassung:
“We study the charge-density wave behaviour in the one-dimensional t-J-Holstein Model. Using the Projector-based Renormalization Method (PRM), we investigate the influence of a small exchange interaction on the metal-insulator transition known from the spinless Holstein Model. In this talk, I will review the work on my diploma thesis and will present some results.”
Speaker: Anne Nielsen
The ability to control and manipulate the state of quantum systems is important in order to use such systems for technological purposes and fundamental studies of quantum mechanics. Subjecting a system to different Hamiltonians leads to different unitary time evolutions, but the state collapse accompanying quantum mechanical measurements opens several additional possibilities to change the state of a quantum system in a desired way, and measurements thus constitute a powerful state preparation tool. In the talk we investigate the influence of measurements on the dynamics of quantum systems and provide examples of various state preparation protocols that are based on optical measurements.
Title: Quantum Control of Coupled Spin Systems: Algebraic and Open System Approach
Speaker: Daniel Burgarth, Oxford
We compare two independent methods of controlling qubits which are coupled by an always-on Hamiltonian. In either case, it is possible to perform algorithms on large arrays by acting on a small subset. While the algebraic method has the advantage of requiring minimal resources, the open system approach provides an explicit way how to achieve control. We give examples of systems which are controllable only by the open system approach and show new results on spin chains as universal quantum interfaces.
Title: Quantum Computing and Quantum Topology
Speaker: Louis H. Kauffman, UIC
Abstract:
This talk will discuss the construction of sets of universal gates for quantum computing and quantum information theory and their relationship with topological computing, quantum algorithms for computing quantum link invariants such as the Jones polynomial and questions about the relationship between quantum entanglement and topological entanglement. We will discuss the creation of universal gates (in the presence of local unitary transformations) by using solutions to the Yang-Baxter equation and we will discuss the use of braided recoupling theory (q-deforemed spin networks) to create unitary representations of the braid group rich enough to support quantum information theory and quantum computing. In particular we give quantum algorithms for computing the colored Jones polynomials and the Witten-Reshetikhin-Turaev invariants.