Quasi-optimal sampling from Gibbs states via non-commutative optimal transport metrics

• URL: http://arxiv.org/abs/2412.01732v1
• Date: Mon, 02 Dec 2024 17:25:24 GMT
• Title: Quasi-optimal sampling from Gibbs states via non-commutative optimal transport metrics
• Authors: Ángela Capel, Paul Gondolf, Jan Kochanowski, Cambyse Rouzé,
• Abstract summary: We study the problem of sampling from and preparing quantum Gibbs states of local commuting Hamiltonians on hypercubic lattices of arbitrary dimension. We prove that any such Gibbs state which satisfies a clustering condition that we coin decay of matrix-valued quantum conditional mutual information can be quasi-optimally prepared on a quantum computer.
• Score: 1.5999407512883517
• License:
• Abstract: We study the problem of sampling from and preparing quantum Gibbs states of local commuting Hamiltonians on hypercubic lattices of arbitrary dimension. We prove that any such Gibbs state which satisfies a clustering condition that we coin decay of matrix-valued quantum conditional mutual information (MCMI) can be quasi-optimally prepared on a quantum computer. We do this by controlling the mixing time of the corresponding Davies evolution in a normalized quantum Wasserstein distance of order one. To the best of our knowledge, this is the first time that such a non-commutative transport metric has been used in the study of quantum dynamics, and the first time quasi-rapid mixing is implied by solely an explicit clustering condition. Our result is based on a weak approximate tensorization and a weak modified logarithmic Sobolev inequality for such systems, as well as a new general weak transport cost inequality. If we furthermore assume a constraint on the local gap of the thermalizing dynamics, we obtain rapid mixing in trace distance for interactions beyond the range of two, thereby extending the state-of-the-art results that only cover the nearest neighbor case. We conclude by showing that systems that admit effective local Hamiltonians, like quantum CSS codes at high temperature, satisfy this MCMI decay and can thus be efficiently prepared and sampled from.

Related papers

• 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)
• Optimizing random local Hamiltonians by dissipation [44.99833362998488]
  We prove that a simplified quantum Gibbs sampling algorithm achieves a $Omega(frac1k)$-fraction approximation of the optimum. Our results suggest that finding low-energy states for sparsified (quasi)local spin and fermionic models is quantumly easy but classically nontrivial.
  arXiv  Detail & Related papers  (2024-11-04T20:21:16Z)
• Nonlocality under Jaynes-Cummings evolution: beyond pseudospin operators [44.99833362998488]
  We re-visit the generation and evolution of (Bell) nonlocality in hybrid scenarios whose dynamics is determined by the Jaynes-Cummings Hamiltonian. Recent results on the optimal Bell violation in qubit-qudit systems show that the nonlocality is much greater than previously estimated.
  arXiv  Detail & Related papers  (2024-10-14T16:01:23Z)
• Efficiency of Dynamical Decoupling for (Almost) Any Spin-Boson Model [44.99833362998488]
  We analytically study the dynamical decoupling of a two-level system coupled with a structured bosonic environment. We find sufficient conditions under which dynamical decoupling works for such systems. Our bounds reproduce the correct scaling in various relevant system parameters.
  arXiv  Detail & Related papers  (2024-09-24T04:58:28Z)
• Generating Entanglement by Quantum Resetting [0.0]
  We consider a closed quantum system subjected to Poissonian resetting with rate $r$ to its initial state. We show that quantum resetting provides a simple and effective mechanism to enhance entanglement between two parts of an interacting quantum system.
  arXiv  Detail & Related papers  (2023-07-14T17:12:08Z)
• Sparse random Hamiltonians are quantumly easy [105.6788971265845]
  A candidate application for quantum computers is to simulate the low-temperature properties of quantum systems. This paper shows that, for most random Hamiltonians, the maximally mixed state is a sufficiently good trial state. Phase estimation efficiently prepares states with energy arbitrarily close to the ground energy.
  arXiv  Detail & Related papers  (2023-02-07T10:57:36Z)
• Probing finite-temperature observables in quantum simulators of spin systems with short-time dynamics [62.997667081978825]
  We show how finite-temperature observables can be obtained with an algorithm motivated from the Jarzynski equality. We show that a finite temperature phase transition in the long-range transverse field Ising model can be characterized in trapped ion quantum simulators.
  arXiv  Detail & Related papers  (2022-06-03T18:00:02Z)
• Probing infinite many-body quantum systems with finite-size quantum simulators [0.0]
  We propose a protocol that makes optimal use of a given finite-size simulator by directly preparing, on its bulk region, a mixed state. For systems of free fermions in one and two spatial dimensions, we illustrate and explain the underlying physics. For the example of a non-integrable extended Su-Schrieffer-Heeger model, we demonstrate that our protocol enables a more accurate study of QPTs.
  arXiv  Detail & Related papers  (2021-08-27T16:27:46Z)
• Perils of Embedding for Quantum Sampling [0.0]
  A common approach is to minor embed the desired Hamiltonian in a native Hamiltonian. Here, we consider quantum thermal sampling in the transverse-field Ising model. We simulate systems of much larger sizes and larger transverse-field strengths than would otherwise be possible.
  arXiv  Detail & Related papers  (2021-03-12T01:49:52Z)
• The modified logarithmic Sobolev inequality for quantum spin systems: classical and commuting nearest neighbour interactions [2.148535041822524]
  We prove a strong exponential convergence in relative entropy of the system to equilibrium under a condition of spatial mixing. We show that our notion of spatial mixing is a consequence of the recent quantum generalization of Dobrushin and Shlosman's complete analyticity of the free-energy at equilibrium. Our results have wide-ranging applications in quantum information.
  arXiv  Detail & Related papers  (2020-09-24T16:54:06Z)
• Einselection from incompatible decoherence channels [62.997667081978825]
  We analyze an open quantum dynamics inspired by CQED experiments with two non-commuting Lindblad operators. We show that Fock states remain the most robust states to decoherence up to a critical coupling.
  arXiv  Detail & Related papers  (2020-01-29T14:15:19Z)

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.