Rapid Mixing of Quantum Gibbs Samplers for Weakly-Interacting Quantum Systems

• URL: http://arxiv.org/abs/2510.04954v1
• Date: Mon, 06 Oct 2025 15:54:05 GMT
• Title: Rapid Mixing of Quantum Gibbs Samplers for Weakly-Interacting Quantum Systems
• Authors: Štěpán Šmíd, Richard Meister, Mario Berta, Roberto Bondesan,
• Abstract summary: We analyse Lindbladians for Gibbs state preparation in many-body systems.<n>We show that these rapid mixing results are stable under perturbations.<n>Compared to prior spectral-gap-based results for fermions, we achieve exponentially faster mixing.
• Score: 9.897633472657562
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Dissipative quantum algorithms for state preparation in many-body systems are increasingly recognised as promising candidates for achieving large quantum advantages in application-relevant tasks. Recent advances in algorithmic, detailed-balance Lindbladians enable the efficient simulation of open-system dynamics converging towards desired target states. However, the overall complexity of such schemes is governed by system-size dependent mixing times. In this work, we analyse algorithmic Lindbladians for Gibbs state preparation and prove that they exhibit rapid mixing, i.e., convergence in time poly-logarithmic in the system size. We first establish this for non-interacting spin systems, free fermions, and free bosons, and then show that these rapid mixing results are stable under perturbations, covering weakly interacting qudits and perturbed non-hopping fermions. Our results constitute the first efficient mixing bounds for non-commuting qudit models and bosonic systems at arbitrary temperatures. Compared to prior spectral-gap-based results for fermions, we achieve exponentially faster mixing, further featuring explicit constants on the maximal allowed interaction strength. This not only improves the overall polynomial runtime for quantum Gibbs state preparation, but also enhances robustness against noise. Our analysis relies on oscillator norm techniques from mathematical physics, where we introduce tailored variants adapted to specific Lindbladians $\unicode{x2014}$ an innovation that we expect to significantly broaden the scope of these methods.

Related papers

• Universal classical and quantum fluctuations in the large deviations of current of noisy quantum systems: The case of QSSEP and QSSIP [2.035631599424874]
  We study the fluctuation statistics of integrated currents in noisy quantum diffusive systems.<n>We show that the cumulant generating function of the integrated current, at large scales, obeys a large deviation principle.<n>We identify the leading finite-size corrections to the current statistics.
  arXiv  Detail & Related papers  (2026-01-23T16:45:31Z)
• Quartic quantum speedups for community detection [84.14713515477784]
  We develop a quantum algorithm for hypergraph community detection that achieves a quartic quantum speedup.<n>Our algorithm is based on the Kikuchi method, which we extend beyond previously considered problems such as PCA and $p$XORSAT.
  arXiv  Detail & Related papers  (2025-10-09T17:35:17Z)
• Rapid quantum ground state preparation via dissipative dynamics [3.3187923242469246]
  dissipation has become a promising approach for preparing low-energy states of quantum systems.<n>However, the potential of dissipative protocols remains unclear beyond certain commuting Hamiltonians.<n>This work provides significant analytical and numerical insights into the power of dissipation for preparing the ground state of non-commuting Hamiltonians.
  arXiv  Detail & Related papers  (2025-03-20T03:27:52Z)
• Polynomial Time Quantum Gibbs Sampling for Fermi-Hubbard Model at any Temperature [9.62464358196899]
  We prove a constant gap of the perturbed Lindbladian corresponding to interacting fermions up to some maximal coupling strength.<n>This is achieved by using theorems about stability of the gap for lattice fermions.<n>As an application, we explain how to calculate partition functions for the considered systems.
  arXiv  Detail & Related papers  (2025-01-02T18:56:02Z)
• Mixing time of quantum Gibbs sampling for random sparse Hamiltonians [0.23020018305241333]
  A newly developed quantum Gibbs sampling algorithm by Chen, Kastoryano, and Gily'en provides an efficient simulation of non-commutative quantum systems. We establish a polylog(n) upper bound on its mixing time for various families of random n by n sparse Hamiltonians at any constant temperature. Our result places this method for Gibbs sampling on par with other efficient algorithms for preparing low-energy states of quantumly easy Hamiltonians.
  arXiv  Detail & Related papers  (2024-11-07T06:01:19Z)
• Fourier Neural Operators for Learning Dynamics in Quantum Spin Systems [77.88054335119074]
  We use FNOs to model the evolution of random quantum spin systems. We apply FNOs to a compact set of Hamiltonian observables instead of the entire $2n$ quantum wavefunction.
  arXiv  Detail & Related papers  (2024-09-05T07:18:09Z)
• PAPAL: A Provable PArticle-based Primal-Dual ALgorithm for Mixed Nash Equilibrium [58.26573117273626]
  We consider the non-AL equilibrium nonconptotic objective function in two-player zero-sum continuous games. Our novel insights into the particle-based algorithms for continuous distribution strategies are presented.
  arXiv  Detail & Related papers  (2023-03-02T05:08:15Z)
• Trapped-Ion Quantum Simulation of Collective Neutrino Oscillations [55.41644538483948]
  We study strategies to simulate the coherent collective oscillations of a system of N neutrinos in the two-flavor approximation using quantum computation. We find that the gate complexity using second order Trotter- Suzuki formulae scales better with system size than with other decomposition methods such as Quantum Signal Processing.
  arXiv  Detail & Related papers  (2022-07-07T09:39:40Z)
• Benchmarking a novel efficient numerical method for localized 1D Fermi-Hubbard systems on a quantum simulator [0.0]
  We show that a quantum simulator can be used to in-effect solve for the dynamics of a many-body system. We use a neutral-atom Fermi-Hubbard quantum simulator with $L_textexpsimeq290$ lattice sites to benchmark its performance. We derive a simple prediction of the behaviour of interacting Bloch oscillations for spin-imbalanced Fermi-Hubbard systems.
  arXiv  Detail & Related papers  (2021-05-13T16:03:11Z)
• Preparing random states and benchmarking with many-body quantum chaos [48.044162981804526]
  We show how to predict and experimentally observe the emergence of random state ensembles naturally under time-independent Hamiltonian dynamics. The observed random ensembles emerge from projective measurements and are intimately linked to universal correlations built up between subsystems of a larger quantum system. Our work has implications for understanding randomness in quantum dynamics, and enables applications of this concept in a wider context.
  arXiv  Detail & Related papers  (2021-03-05T08:32:43Z)
• Fast and differentiable simulation of driven quantum systems [58.720142291102135]
  We introduce a semi-analytic method based on the Dyson expansion that allows us to time-evolve driven quantum systems much faster than standard numerical methods. We show results of the optimization of a two-qubit gate using transmon qubits in the circuit QED architecture.
  arXiv  Detail & Related papers  (2020-12-16T21:43:38Z)
• Assessment of weak-coupling approximations on a driven two-level system under dissipation [58.720142291102135]
  We study a driven qubit through the numerically exact and non-perturbative method known as the Liouville-von equation with dissipation. We propose a metric that may be used in experiments to map the regime of validity of the Lindblad equation in predicting the steady state of the driven qubit.
  arXiv  Detail & Related papers  (2020-11-11T22:45:57Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.