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