Budapest Open Quantum Systems Seminar
Tondo seminar room, 2nd floor, Rényi Institute, Budapest, Hungary
Seminar series on problems related to open quantum systems at the heart of Budapest.
Organizers:
András Gilyén
Rényi Institute
liam-e: uh[tod]iyner[ta]neylig
Zoltán Zimborás
Institute for Particle and Nuclear Physics, Wigner RCP
liam-e: uh[tod]rengiw[ta]natloz[tod]sarobmiz
Upcoming and past seminars:
2025. February 6. 12:45-14:00 CET (note the earlier than usual time-slot) Sepaker: József Mák Title: Sampling Gibbs States of Quadratic Fermi Systems: A Computational Perspective
Abstract: We discuss how to efficiently simulate simple Lindbladian dynamics converging to free-fermionic Gibbs states.
Recent developments have shown how to efficiently sample Gibbs states of local Hamiltonians on a quantum computer. Here we take the specific Gibbs sampler quantum algorithm in [GCDK24]:, and show how to efficiently monitor the algorithm's convergence towards the thermal state of quadratic fermionic systems.
2025. January 30. 14:15-15:45 CET Sepaker: João Doriguello Title: Rapid mixing of non-commuting quantum Gibbs samplers at high temperatures
Abstract: Review the recent result of Rouzé, Stilck França, and Alhambra [RSFA24]:
It is of great interest to understand the thermalization of open quantum many-body systems, and how quantum computers are able to efficiently simulate that process. A recently introduced disispative evolution, inspired by existing models of open system thermalization, has been shown to be efficiently implementable on a quantum computer. Here, we prove that, at high enough temperatures, this evolution reaches the Gibbs state in time scaling logarithmically with system size. The result holds for Hamiltonians that satisfy the Lieb-Robinson bound, such as local Hamiltonians on a lattice, and includes long-range systems. To the best of our knowledge, these are the first results rigorously establishing the rapid mixing property of high-temperature quantum Gibbs samplers, which is known to give the fastest possible speed for thermalization in the many-body setting. We then employ our result to the problem of estimating partition functions at high temperature, showing an improved performance over previous classical and quantum algorithms.
2025. January 23. 14:15-15:45 CET Sepaker: Tibor Rakovszky Title: Bottlenecks in quantum channels and finite temperature phases of matter
Abstract: We prove an analogue of the "bottleneck theorem", well-known for classical Markov chains, for Markovian quantum channels.
In particular, we show that if two regions (subspaces) of Hilbert space are separated by a region that has very low weight in the channel's steady state, then states initialized on one side of this barrier will take a long time to relax, putting a lower bound on the mixing time in terms of an appropriately defined "quantum bottleneck ratio". Importantly, this bottleneck ratio involves not only the probabilities of the relevant subspaces, but also the size of off-diagonal matrix elements between them. For low-temperature quantum many-body systems, we use the bottleneck theorem to bound the performance of any quasi-local Gibbs sampler. This leads to a new perspective on thermally stable quantum phases in terms of a decomposition of the Gibbs state into multiple components separated by bottlenecks. As a concrete application, we show rigorously that weakly perturbed commuting projector models with extensive energy barriers (including certain classical and quantum expander codes) have exponentially large mixing times.
2025. January 16. 15:00-15:30 CET Location: Turán room (part of the Drafting Workshop) Sepaker: Raz Firanko Title: Quantum Markov Processes and their Steady States
Abstract: We study quantum generalizations of Markov processes with local transition rules and their density-matrix fixed points, also known as steady states. Specifically, we focus on quantum maps acting on many-particle systems arranged on a graph, which admit a Kraus decomposition in terms of local operators. These maps serve as quantum analogs of classical Markov processes and can be implemented on a quantum computer.
We address the question of when these fixed points correspond to Gibbs measures (equilibrium states) of a local Hamiltonian. By perturbatively interpolating from a 1-local map to a 2-local map, we show that the fixed-point Gibbs Hamiltonian perturbs into a quasi-local Hamiltonian, where the range of the Hamiltonian terms grows with the perturbative order.
Our result is established using a multi-parameter perturbation framework that respects the geometric structure of the system.
In this talk, I will provide an introduction to the key concepts and questions, present partial results, and outline the proof of the main theorem.
2025. January 09. 14:15-15:45 CET Sepaker: Zoltán Zimborás Title: Quasi-free and quadratic Lindblad master equations for open fermionic systems
Abstract: Free-fermionic systems can be efficiently simulated classicaly due to an effective dimensionality reduction of the Fock space. The situation is more complicated when the Lindbladian has quadratic terms, but in some cases it is still tractable as show by Barthel and Zhang [BZ21].
2024. December 12. 14:15-15:45 CET Sepaker: João Doriguello Title: Fast Gibbs state preparation in high temperatures - Part II
Abstract: The preparation of Gibbs or thermal states are an important step in quantum simulation. In this presentation, I review the recent result of Rouzé, Stilck França, and Alhambra [RSFA24]
who proved that the construction from Chen, Kastoryano, and Gilyén [CKG23] thermalizes to the Gibbs state in polynomial time on the system size at high enough temperatures for any Hamiltonian that satisfies a Lieb-Robinson bound. I shall describe their main techniques and give a high-level analysis of their proof, which mainly proves that the Lindbladian from Chen, Kastoryano, and Gilyén is gapped at high enough temperatures.
2024. December 05. 14:15-15:45 CET Sepaker: João Doriguello Title: Fast Gibbs state preparation in high temperatures - Part I
Abstract: The preparation of Gibbs or thermal states are an important step in quantum simulation. In this presentation, I review the recent result of Rouzé, Stilck França, and Alhambra [RSFA24]
who proved that the construction from Chen, Kastoryano, and Gilyén [CKG23] thermalizes to the Gibbs state in polynomial time on the system size at high enough temperatures for any Hamiltonian that satisfies a Lieb-Robinson bound. I shall describe their main techniques and give a high-level analysis of their proof, which mainly proves that the Lindbladian from Chen, Kastoryano, and Gilyén is gapped at high enough temperatures.
2024. November 28. 14:15-15:45 CET (online on zoom) Sepaker: András Gilyén Title: Quantum generalizations of Glauber and Metropolis dynamics
Abstract: Classical Markov Chain Monte Carlo methods have been essential for simulating statistical physical
systems and have proven well applicable to other systems with complex degrees of freedom. Motivated by the statistical physics origins, Chen, Kastoryano, and Gilyén [CKG23] proposed a continuous-time quantum thermodynamic analog to Glauber dynamic that is (i) exactly detailed balanced, (ii) efficiently implementable, and (iii) quasi-local for geometrically local systems.
Physically, their construction
gives a smooth variant of the Davies’ generator derived from weak system-bath interaction. In
this work, we give an efficiently implementable discrete-time quantum counterpart to Metropolis
sampling that also enjoys the desirable features (i)-(iii). Also, we give an alternative highly coherent
quantum generalization of detailed balanced dynamics that resembles another physically derived
master equation, and propose a smooth interpolation between this and earlier constructions. We study
generic properties of all constructions, including the uniqueness of the fixed-point and the locality of
the resulting operators. We hope our results provide a systematic approach to the possible quantum
generalizations of classical Glauber and Metropolis dynamics.
2024. September 26. 14:15-15:45 CET Sepaker: András Gilyén Title:[In Hungarian] Kvantum csatornák Stinespring reprezentációja. Klasszikus Metropolis és Glauber dinamika és kvantumos megfelelőik.
Abstract: Általános Hölder egyenlőtlenség Schatten normákra, Hilbert-Schmidt belső szorzat, Adjungált szuperoperátor, Stinespring reprezentáció, Klasszikus Glauber és Metropolis algoritmus.
