Old QCCC Events

In order to prepare for „life after QCCC“, we will have an informal mini-workshop
to exchange ideas on quantum many-body systems with Prof. Schollwöck, who could not come to Prien. More precisely, the goal is to exchange ideas of numerical methods and the demands for them in backing quantum simulations of multi-body systems.

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

Three lectures on „Quantum Measurement Theory“ by Rob Spekkens, Paul Busch and Teiko Heinosaari, supported by QCCC.

Business Meeting regarding the 4th QCCC Workshop in Prien.

Talk on
Quantum measurements and joint measurability

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.

Talk on
Localizable Entanglement & Gaussian Fermionic PEPS

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.

Block course on:

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.

Talk on
Spectral Convergence Bounds for Finite Classical and Quantum Markov Chains

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.

Talk on
Mathematical Physics with \hbar

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.

Lecture on
Short Stories from Quantum Information Theory

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).

Talk on
Compressed Sensing and Matrix Completion: From Single Pixel Cameras to Quantum State Tomography

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.

„Fault-Ignorant Quantum Search“

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 this lecture, we will present two recent experimental results obtained in the Bloch group that illustrate the potential of ultracold atomic gases to understand the emergence of many-body phenomena. In a first part, we will show that a gas of ultracold atoms in a Mott-insulating state represent a fairly good realization of the Heisenberg model, with the electronic hyperfine state playing the role of an effective spin. Using a new experimental technique, we were able to directly reveal the Heisenberg coupling by monitoring the real-time dynamics of a single spin impurity introduced in the system in a controlled way. Beyond this paradigmatic, but analytically solvable problem, we also explored a regime where real particle hopping becomes important and the spin impurity gets dressed by the surrounding bath to form a polaronic quasiparticle.

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.

„Controllable Single-Atom Phase Shifter Working in the Single-Photon Level“

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.

The talk is dedicated to the topic of superactivation of the quantum capacity of Gaussian channels. Smith et. al. have recently shown that for two such channels with zero capacity Superactivation (0 + 0 > 0) can be achieved. They provided explicit examples that make use of active optical devices like squeezers.

In this talk I’ll show that there is no superactivation for Gaussian channels that are generated by passive means.

In this seminar, I will introduce „normaliser circuits“, a family of quantum operations that play a relevant role in quantum algorithms:
prominent examples of normaliser gates are quantum Fourier transforms (QFT)—sometimes said to be „the source of various exponential quantum speedups“—, subroutines that generate highly entangled states and adaptive measurements.

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.

„Combining Coherent and Noise Control:“
‚How to Transfer between Arbitrary n-Qubit States by Coherent Control and Simplest Switchable Noise on a Single Qubit‘

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.

Seminar by Prof. Mark Sherwin from Santa Barbara on „Extreme Optics in Semiconductors: When Quasiparticles Collide, and 1+1=11“.]

Titel: Perturbation Theory for Fixed Points of Quantum Channels

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.

Seminar by Dr David Gross.

Seminar by Dr Markus Grassl on „Polynomial Invariants of Three-Qubit Systems“:

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.

Invitation to the CoQuS Summer School.

Invitation to the Heraeus Summer School „Modern Statistical Methods in QIP“, 22-26 August 2011, Bad Honnef.

I will give a brief introduction to the problem of estimating the convergence time a quantum channel to its fixed point(s).

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.

ENB Forum: From the Nobel Prize to Being Entrepreneur
Lectures by

• Theodor W. Hänsch: Passion for Precision
• Ronald Holzwarth: Firmerngründung mit Nobelpreistechnologie

We present several algorithms for the simulation of translationally invariant (TI) quantum spin chains with periodic boundary conditions (PBC). By using TI matrix product states (MPS) we can in general reduce the computational cost by a factor N, with N the number of spins in the chain.

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.

Using the assumption that thermodynamic systems evolve towards Gibbs states, i.e. states with a well defined temperature, statistical mechanics and thermodynamics have been amazingly successful in explaining a wide range of physical phenomena. In stark contrast to this strong justification by corroboration of these theories, the question of whether and how the methods of statistical mechanics and thermodynamics can be justified microscopically was still wide open until recently.

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.

We study information theoretic questions on von-Neumann algebras. There, one first has to discuss the notion of independent subsystems, which leads to a well-known open question in operator algebra theory, the embedding problem of Connes. I will clarify the equivalence, and proceed by describing some information theoretic tasks in the setting of von-Neumann algebras, as well as discussing the connection to quantum cryptography. 

Guided Lab Tour

Seminar by John Marriott on Optimal control theory and its application to maximizing contrast in magnetic resonance imaging

The hierarchical Tucker format is a storage-efficient scheme to approximate and represent tensors of possibly high order. From a tensor network perspective, it represents a network of order-3 tensors without cycles. Thus, it is a generalization of the Tensor Train or Matrix Product States (MPS) format.

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.

Seminar by Boris Khoromskij on Quantics-TT approach to high-dimensional SPDEs and to DMRG in quantum molecular dynamics.

A full quantification of the entanglement of a quantum state is desirable if the degradation of entanglement in some quantum information processing task is to be minimized. A protocol for the accomplishment of a task can then be evaluated by the amount of entanglement consumed to enact that protocol. Such quantification is typically provided by a collection of entanglement monotones.

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.

Simulating quantum mechanical systems is a classical hard problem because the computational difficulties hinges on the exponential growth of the size of Hilbert space with the number of particles in the system.

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.

Prof. Martin Plenio (Universitaet Ulm):

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]

Optimal Control of Quantum Systems

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.

Completely positive linear mappings between C*-algebras were originally developed in the 1950’s as a special case of positive linear operators between matrix algebras. Within the last two decades, mathematical physicists have determined that completely positive maps play a crucial role in quantum information theory as structures which model information transfer between quantum systems.

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.

Seminar by Patrick Rebentrost

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.

Workshop on Optomechanics (programme)

Seminar by Frank Wilhelm

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.

Seminar by Noomen Belmechri on Single atom interferometry with neutral atoms in a state-selective 1D optical lattice

Seminar by Prof. M. Christandl

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).

Seminar by Dr. Robert Zeier

„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);
Dynkin, Trudy Mosov. Mat. Obsh. 1, 39 (1952),
Amer. Math. Soc. Transl. (2) 6, 245 (1957);
Dynkin, Mat. Sbornik (N.S.) 30(72), 349 (1952),
Amer. Math. Soc. Transl. (2) 6, 111 (1957)
[6] McKay/Patera, Tables of Dimensions, Indices, and Branching Rules
for Representations of Simple Lie Algebras (1981)

Seminar by Dr. Ilya Kuprov on „Squeezing the Matrix: efficient spin dynamics simulation algorithms“.

Seminar by Prof. Bernard Bonnard on „The Energy Minimization Problem in the Control of Dissipative Spin-1/2 Particles“.

Seminar by Prof. Jr-Shin Li and by Justin Ruths

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.

Seminar by Corey O’Meara

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.

Seminar by Volkher Scholz

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.

Seminar by Shai Machnes on „Optimal control for superfast cooling of trapped ions, using a Matlab toolbox for quantum information calculations„

Seminar by Prof. Mikio Nakahara

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.

Seminar by Fernando Pastawski

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.

Seminar by Sebastian Nauerth

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.

Limitations of Quantum Optimal Control

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.

Seminar by Louis H. Kauffman

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.

Seminar by Howard Carmichael on „Open Quantum Systems: Cavity QED with Dissipation“

The reduced Kronecker coefficients of the symmetric group Mercedes Rosas, Universidad de Sevilla, Spain. (in collaboration with Emmanuel Briand, U. de Sevilla, and Rosa Orellana, Dartmouth College).

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.

Seminar by Wu Xing on „Experiments on a Superconducting Atom Chip“.

Seminar by Dmitry Yudin on Dynamics of a dilute Fermi-Bose condensed gas mixture.

Seminar by Matthias Christandl

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

Seminar by Matthew B. Hastings on „A Counterexample to Additivity of Minimum Output Entropy“ (How to kill a most famous conjecture in quantum information – alternative title, not by the author).

Title: Localisable entanglement of 1D cluster states

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.

Seminar by Dominique Sugny on Geometric optimal control of dissipative quantum systems.

Seminar by Ulrich Schollwöck

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.

Seminar by Andreas Eberlein

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.“

Seminar by Guifre Vidal on Entanglement Renormalization.

Summer School „Complex Quantum Systems“ hosted as a CoQuS-QCCC get-together by the CoQuS Phd programme of excellence at the University of Vienna.

Seminar by Peter Pemberton-Ross on Controllability of Spin Systems.

Title: State Preparation by Means of Optical Measurements

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.

Seminar by Daniel Burgarth

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.

Guest lecture by Louis H. Kauffman

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.

Elite-Cup 2008 (ENB soccer tournament) in Neufahrn near Freising

QCCC Miniworkshop on „Mathematical Control Theory and Quantum Applications“ (with TopMath)“

Talk by Amr Fahmy on „Thermal State Quantum Computing“

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