Single-Trajectory Gibbs Sampling for Non-Commuting Observables

• URL: http://arxiv.org/abs/2603.21595v1
• Date: Mon, 23 Mar 2026 05:44:17 GMT
• Title: Single-Trajectory Gibbs Sampling for Non-Commuting Observables
• Abstract summary: Estimating thermal expectation values of quantum many-body systems is a central challenge in physics, chemistry, and materials science.<n>Standard quantum Gibbs sampling protocols address this task by preparing the Gibbs state from scratch after every measurement.<n>Recent advances in single-trajectory Gibbs sampling citejiang2026 substantially reduce this overhead.
• Score: 18.042679841864114
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Estimating thermal expectation values of quantum many-body systems is a central challenge in physics, chemistry, and materials science. Standard quantum Gibbs sampling protocols address this task by preparing the Gibbs state from scratch after every measurement, incurring a full mixing-time cost at each step. Recent advances in single-trajectory Gibbs sampling \cite{jiang2026} substantially reduce this overhead: once stationarity is reached, measurements can be collected along a single trajectory without re-thermalizing, provided the measurement channel preserves the Gibbs ensemble. However, explicit constructions of such non-destructive measurements have been limited primarily to observables that commute with the Hamiltonian. In this work, we fundamentally extend the single-trajectory framework to arbitrary, non-commuting observables. We provide two measurement constructions that extract measurement information without fully destroying the Gibbs state, thereby eliminating the need for full re-mixing between samples. First, we construct a measurement that satisfies exact detailed balance. This ensures the system remains in equilibrium throughout the trajectory, allowing measurement outcomes to decorrelate in an autocorrelation time that could be significantly shorter than the global mixing time. Second, assuming the underlying quantum Gibbs sampler has a positive spectral gap, we design a simplified measurement scheme that ensures the post-selected state serves as a warm start for rapid re-mixing. This approach successfully decouples the resampling cost from the global mixing time. Both measurement schemes admit efficient quantum circuit implementations, requiring only polylogarithmic Hamiltonian simulation time.

Related papers

• Constant-time equilibration of observables under rapid Lindbladian dynamics [9.897633472657562]
  We introduce and study observable-specific mixing times for quantum information science.<n>For quasi-local, rapidly mixing Lindbladians, sums of geometrically local observables equilibrate in a time independent of system size.<n>We develop a quantum-inspired classical algorithm for estimating the same quantities.
  arXiv  Detail & Related papers  (2026-08-28T15:40:45Z)
• Symmetry Constrained Quantum Error Mitigation for the Schwinger Model [39.146761527401424]
  We exploit the parity and fermion-number symmetries of a gauge theory under depolarising noise.<n>We investigate symmetry verification under digital quantum simulation.
  arXiv  Detail & Related papers  (2026-08-21T13:49:11Z)
• The quantum mechanics of experiments [45.88028371034407]
  The dissipative nature of the quantum-mechanical time-evolution of averages of states over large ensembles of identical isolated systems is discussed.<n>The importance of dissipation for the successful completion of measurements is highlighted.<n>A solution of the Measurement Problem'' is sketched in an idealized model of a double-slit experiment.
  arXiv  Detail & Related papers  (2026-03-26T11:25:21Z)
• Predicting properties of quantum thermal states from a single trajectory [3.300950917481495]
  Estimating thermal expectation values of observables is a fundamental task in quantum physics.<n>We show that the sampling cost can be substantially reduced by using a single Gibbs-sampling trajectory.
  arXiv  Detail & Related papers  (2026-02-13T02:40:23Z)
• Freeness Reined in by a Single Qubit [36.94429692322632]
  We find that, even in this setting, the correlation functions predicted by free probability theory receive corrections of order $O(1)$.<n>We trace their origin to non-uniformly distributed stationary quantum states, which we characterize analytically and confirm numerically.
  arXiv  Detail & Related papers  (2025-12-15T19:00:09Z)
• Quasi-optimal sampling from Gibbs states via non-commutative optimal transport metrics [1.5999407512883517]
  We study the problem of sampling from and preparing quantum Gibbs states of local commuting Hamiltonians on hypercubic lattices of arbitrary dimension.<n>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.
  arXiv  Detail & Related papers  (2024-12-02T17:25:24Z)
• Breakdown of Measurement-Induced Phase Transitions Under Information Loss [39.36827689390718]
  A quantum-many body system can feature measurement-induced phase transitions (MIPTs)<n>MIPTs cannot be revealed through ensemble-averaged observables, but it requires the ability to discriminate each trajectory separately.<n>We explore the fate of MIPTs under an observer's reduced ability to discriminate each measurement outcome.
  arXiv  Detail & Related papers  (2024-07-18T18:10:52Z)
• Evolution of many-body systems under ancilla quantum measurements [58.720142291102135]
  We study the concept of implementing quantum measurements by coupling a many-body lattice system to an ancillary degree of freedom. We find evidence of a disentangling-entangling measurement-induced transition as was previously observed in more abstract models.
  arXiv  Detail & Related papers  (2023-03-13T13:06:40Z)
• Importance sampling for stochastic quantum simulations [68.8204255655161]
  We introduce the qDrift protocol, which builds random product formulas by sampling from the Hamiltonian according to the coefficients. We show that the simulation cost can be reduced while achieving the same accuracy, by considering the individual simulation cost during the sampling stage. Results are confirmed by numerical simulations performed on a lattice nuclear effective field theory.
  arXiv  Detail & Related papers  (2022-12-12T15:06:32Z)
• Snapshotting Quantum Dynamics at Multiple Time Points [10.226937603741474]
  We propose a method to extract dynamic information from a quantum system at intermediate time points. We reconstruct a multi-time quasi-probability distribution (QPD) that correctly recovers the probability at the respective time points.
  arXiv  Detail & Related papers  (2022-07-13T10:28:01Z)
• Measurement-induced purification in large-N hybrid Brownian circuits [0.0]
  Competition between unitary dynamics that scrambles quantum information non-locally can result in a measurement-induced entanglement phase transition. We study this phenomenon in an analytically tractable all-to-all Brownian hybrid circuit model composed of qubits.
  arXiv  Detail & Related papers  (2021-04-15T18:00:15Z)
• Proposal to measure out-of-time-ordered correlations using Bell states [0.0]
  We present a protocol to experimentally measure the infinite-temperature out-of-time-ordered correlation (OTOC) OTOC is a probe of quantum information scrambling in a system. We show that the OTOC can be obtained by preparing two entangled systems.
  arXiv  Detail & Related papers  (2020-06-26T16:51:32Z)

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.