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This research introduces a critical distinction between quantum Gibbs sampling mixing times and the separate resampling time required to recover thermal correlations after disruptive measurements. By identifying a phase transition in systems with non-local order parameters, the study proposes a structured fast-measurement protocol that significantly accelerates data extraction without compromising state integrity. This advancement addresses fundamental bottlenecks in using quantum computers for statistical mechanics simulations and thermal state preparation.
Gibbs resampling transitions and structured fast-measurement protocols
arXiv:2609.22425v1 Announce Type: new Abstract: Quantum Gibbs sampling algorithms generalize classical Markov chain Monte Carlo (cMCMC) methods, and prepare thermal states on quantum computers by implementing local dissipative evolution for a mixing time $t_{\rm mix}$. Since quantum measurements disrupt the prepared state, the rate of extracting unbiased information from the system depends on the recovery of the underlying thermal correlations. The corresponding ''Gibbs resampling'' time $t_{\rm res}$ is distinct both from $t_{\rm mix}$ and from the autocorrelation time relevant to cMCMC sampling. We study this problem in effective classical models that emulate disruptive quantum measurements of local observables on extensive subsystems. When such subsystems are chosen randomly, in models with non-local order parameters we uncover a ''resampling transition'' as a function of the fraction of sites $p$ that are measured, from $t_{\rm res}\propto \log L$ for small $p$ to $t_{\rm res}\propto {\rm poly} L$ for large $p$, in systems of linear size $L$. We argue that this transition is generically absent in systems with local order parameters, and relate this dichotomy to one between the coarsening of initial states that break 1- and 0-form symmetries under Glauber dynamics. Finally, we devise a structured fast-measurement protocol that evades slow resampling even with non-local order parameters, while leaving only a vanishing fraction of all sites unmeasured.
Abstract:Quantum Gibbs sampling algorithms generalize classical Markov chain Monte Carlo (cMCMC) methods, and prepare thermal states on quantum computers by implementing local dissipative evolution for a mixing time $t_{\rm mix}$. Since quantum measurements disrupt the prepared state, the rate of extracting unbiased information from the system depends on the recovery of the underlying thermal correlations. The corresponding ''Gibbs resampling'' time $t_{\rm res}$ is distinct both from $t_{\rm mix}$ and from the autocorrelation time relevant to cMCMC sampling. We study this problem in effective classical models that emulate disruptive quantum measurements of local observables on extensive subsystems. When such subsystems are chosen randomly, in models with non-local order parameters we uncover a ''resampling transition'' as a function of the fraction of sites $p$ that are measured, from $t_{\rm res}\propto \log L$ for small $p$ to $t_{\rm res}\propto {\rm poly} L$ for large $p$, in systems of linear size $L$. We argue that this transition is generically absent in systems with local order parameters, and relate this dichotomy to one between the coarsening of initial states that break 1- and 0-form symmetries under Glauber dynamics. Finally, we devise a structured fast-measurement protocol that evades slow resampling even with non-local order parameters, while leaving only a vanishing fraction of all sites unmeasured.
arXiv:2609.22425 [quant-ph]
(or arXiv:2609.22425v1 [quant-ph] for this version)
https://doi.org/10.48550/arXiv.2609.22425 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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