Polylog-depth Quantum Thermal Simulation via Local Recovery Channels

arXiv:2609.39674 · quant-ph · Submitted 2026-09-30 · Read on arXiv

quant-ph

Submitted: 2026-09-30

Updated: 2026-09-30

Terminology

• Trace — 34× in this paper · explained in 2 episodes
• Gibbs State — 30× in this paper · explained in 2 episodes
• Accuracy — 21× in this paper · explained in 1 episode
• Effective Hamiltonian — 10× in this paper · explained in 2 episodes
• Clustering — 4× in this paper · explained in 2 episodes
• Hilbert Space — 4× in this paper · explained in 2 episodes
• Block Encoding — 3× in this paper · explained in 4 episodes
• Embeddings — 3× in this paper · explained in 2 episodes
• Entanglement — 2× in this paper · explained in 4 episodes
• Trace Distance — 2× in this paper · explained in 3 episodes
• Ancillary Qubits — 1× in this paper · explained in 1 episode
• Axioms — 1× in this paper · explained in 2 episodes
• Generalization — 1× in this paper · explained in 13 episodes
• Quantum Circuits — 1× in this paper · explained in 2 episodes
• Quantum Singular Value Transformation (QSVT) — 1× in this paper · explained in 4 episodes
• Sample Complexity — 1× in this paper · explained in 15 episodes

Sources

• Quantum Gibbs states are locally Markovian
• Clustering of Conditional Mutual Information via Quantum Belief-Propagation Channels
• Quantum singular value transformation and beyond: exponential improvements for quantum matrix arithmetics
• An efficient and exact noncommutative quantum Gibbs sampler
• Quantum generalizations of Glauber and Metropolis dynamics
• Classical Estimation of the Free Energy and Quantum Gibbs Sampling from the Markov Entropy Decomposition
• Quantum Speed-ups for Semidefinite Programming
• Sample-efficient learning of quantum many-body systems
• Fast Mixing of Quantum Spin Chains at All Temperatures
• When quantum thermal states look classical
• Mixed-state phases from local reversibility
• Circuit-based characterization of finite-temperature quantum phases and self-correcting quantum memory
• High-Temperature Fermionic Gibbs States are Mixtures of Gaussian States
• Hamiltonian Simulation in the Interaction Picture
• Fast algorithm for quantum polar decomposition, pretty-good measurements, and the Procrustes problem

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