[Paper Review] Thermal-Drift Sampling: Generating Thermal Ensembles for Learning Many-Body Systems

Jiyu Jiang, Mingrui Jing+3 more|arXiv (Cornell University)|Feb 5, 2026

Quantum many-body systems0 citations

TL;DR

This paper introduces a quantum thermal-drift channel and a measurement-controlled sampler that generate random thermal states with Hamiltonian labels, proving polynomial resource scaling and demonstrating chaos signatures and a learning application.

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.

Motivation & Objective

• Motivate the need for large, labeled thermal-state data from many-body Hamiltonians for benchmarking and learning.
• Develop a quantum-native algorithm that produces thermal states together with their Hamiltonian labels in one workflow.
• Prove theoretical resource bounds showing polynomial scaling with system size and inverse temperature.
• Demonstrate physical relevance by analyzing level statistics and showcasing a learning-task classifier trained on generated data.
• Provide a scalable path for thermodynamic simulation and labeled quantum data generation in many-body physics.

Proposed method

• Define the thermal-drift channel Nσ as the core operation enabling measurement-driven drift toward thermalization.
• Construct a circuit that applies a sequence of thermal-drift channels with Pauli-style control to sample Hamiltonians H = sum_j cj σj with |cj| ≤ hj.
• Weight the selection of Pauli terms by bounds hj/λ to realize a thermal-weighted random walk in Hamiltonian space.
• Record mid-circuit measurement outcomes to simultaneously generate the Hamiltonian label and steer state evolution, yielding a Gβ,H target state.
• Prove sampling precision bounds showing gate count scales polynomially in system size n and inverse temperature β, with error decreasing as N increases.
• Model the label distribution asymptotically as a normal distribution reweighted by a partition function, yielding a trade-off between accuracy and label range.

Experimental results

Research questions

• RQ1 Can one efficiently generate random thermal states together with their Hamiltonian labels for a whole family of Hamiltonians?
• RQ2 What are the resource requirements (gates, steps) to produce labeled thermal states with provable polynomial scaling?
• RQ3 How do sampled Hamiltonians and their labels distribute, and how do partition functions and normal reweighting shape the sampling?
• RQ4 Do generated thermal ensembles exhibit physical signatures (e.g., level statistics) of chaotic dynamics across Hamiltonians?
• RQ5 Can the generated labeled thermal data support learning tasks such as Hamiltonian-property classification?

Key findings

• The quantum thermal-drift sampler generates thermal states together with their Hamiltonian labels with a polynomial gate cost in n and β.
• Sampling precision improves as the number of thermal-drift steps N increases, with a bound scaling roughly as O(n3/2 λ3 β3 N−3/2) for fixed failure probability.
• The label distribution converges to a normal distribution reweighted by the partition function, combining thermodynamic bias and central-limit effects.
• Level statistics of sampled thermal states show a crossover from Poisson to Wigner–Dyson GOE behavior, signaling chaotic correlations typical of ergodic regimes.
• A variational quantum classifier trained on the generated labeled thermal data achieves near-optimal accuracy on unseen thermal states, validating the data usefulness for learning tasks.