Quantum score matching with applications to learning thermal states

arXiv:2609.28391 · quant-ph, cs.LG · Submitted 2026-09-23 · Read on arXiv

quant-ph, cs.LG

Submitted: 2026-09-23

Updated: 2026-09-23

Comments: 57 pages, 5 figures, 3 tables, with an accompanying GitHub repository at https://github.com/dongsnaq/Quantum-Score-Matching

Code: https://github.com/dongsnaq/Quantum-Score-Matching

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Terminology

• Gibbs State — 31× in this paper · explained in 2 episodes
• Hamiltonian Learning — 13× in this paper · explained in 2 episodes
• Accuracy — 9× in this paper · explained in 1 episode
• Sample Complexity — 8× in this paper · explained in 15 episodes
• Trace — 6× in this paper · explained in 2 episodes
• Fisher Information — 5× in this paper · explained in 3 episodes
• Alignment — 2× in this paper · explained in 1 episode
• Cosine Similarity — 2× in this paper · explained in 3 episodes
• Diffusion Model — 2× in this paper · explained in 8 episodes
• Diffusion Models — 2× in this paper · explained in 6 episodes
• Generalization — 2× in this paper · explained in 13 episodes
• Generative Modeling — 2× in this paper · explained in 3 episodes
• Gradient Flow — 2× in this paper · explained in 2 episodes
• Score Function — 2× in this paper · explained in 4 episodes
• Theoretical Guarantees — 2× in this paper · explained in 2 episodes
• Anisotropy — 1× in this paper · explained in 3 episodes
• Consistency — 1× in this paper · explained in 3 episodes
• Convergence Guarantees — 1× in this paper · explained in 3 episodes
• Optimal Transport — 1× in this paper · explained in 5 episodes
• Quantum Circuits — 1× in this paper · explained in 2 episodes
• Unitary Dynamics — 1× in this paper · explained in 2 episodes

Sources

• Sample-efficient learning of quantum many-body systems
• Learning quantum Hamiltonians at any temperature in polynomial time
• Structure learning of Hamiltonians from real-time evolution
• Learning quantum Gibbs states locally and efficiently
• Ground state preparation and energy estimation on early fault-tolerant quantum computers via quantum eigenvalue transformation of unitary matrices
• The advantage of quantum control in many-body Hamiltonian learning
• Optimal learning of quantum Hamiltonians from high-temperature Gibbs states
• Ansatz-free Hamiltonian learning with Heisenberg-limited scaling
• Learning many-body Hamiltonians with Heisenberg-limited scaling
• Quantum Fisher information matrix and multiparameter estimation
• Measurement-Based Quantum Diffusion Models
• Learning k-body Hamiltonians via compressed sensing
• Propagation of Correlations in Quantum Lattice Systems
• Quasi-Locality Bounds for Quantum Lattice Systems. Part I. Lieb-Robinson Bounds, Quasi-Local Maps, and Spectral Flow Automorphisms
• Quantum estimation for quantum technology
• Generative Modeling by Estimating Gradients of the Data Distribution
• Operator Score Matching for Learning Quantum Hamiltonians
• Score-Based Generative Modeling through Stochastic Differential Equations
• Fundamentals of quantum Boltzmann machine learning with visible and hidden units
• Generative training of quantum Boltzmann machines with hidden units

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