Thermal-Drift Sampling: Generating Thermal Ensembles for Learning Many-Body Systems

TL;DR

This paper introduces a quantum algorithm for efficiently generating thermal states and their Hamiltonians for many-body systems, enabling scalable thermodynamic simulations and machine learning applications.

Contribution

The authors develop a polynomial-resource quantum sampling method for thermal states, including a novel thermal-drift channel and analysis of the distribution of sampled Hamiltonians.

Findings

Efficient polynomial scaling of gate count with system size and inverse temperature.

Sampled Hamiltonians follow a normal distribution reweighted by partition functions.

Thermal states exhibit signatures of quantum chaos, such as Wigner-Dyson statistics.

Abstract

Thermal equilibrium states of many-body Hamiltonians are essential for probing quantum chaos, finite-temperature phases of matter, and training quantum machine learning models, yet generating large collections of such states across different Hamiltonians remains costly with existing methods. We introduce a powerful operation, the quantum thermal-drift channel, to construct a measurement-controlled sampling algorithm that autonomously generates thermal states together with their system Hamiltonians as labels for general physical models. We prove that our algorithm is efficient: the total gate count scales polynomially with system size and quadratically with inverse temperature, providing the first polynomial resource bound for random thermal state generation. We characterize the distribution of sampled Hamiltonians as a normal distribution reweighted by partition functions, which quantifies a trade-off between sampling accuracy and effective label range. Level-spacing statistics computed from sampled thermal states of a 2D transverse-field Ising model show a crossover to Wigner-Dyson universality, confirming that the sampler captures nontrivial chaotic correlations. Finally, a variational quantum classifier trained on the generated dataset achieves near-optimal accuracy in predicting Hamiltonian properties of unseen states. These results establish a scalable, quantum-native route for thermodynamic simulation and labeled quantum data generation in many-body systems.