Double Localization for Quantum Gibbs Sampler Gaps: From an Abstract Framework to Finite-Group Models

arXiv:2609.39802 · quant-ph · Submitted 2026-09-30 · Read on arXiv

quant-ph

Submitted: 2026-09-30

Updated: 2026-09-30

Comments: 76 pages

Code: https://github.com/ryuhayakawa/double-localization-finite-groups

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

Terminology

• Trace — 22× in this paper · explained in 2 episodes
• Gibbs State — 18× in this paper · explained in 2 episodes
• Hilbert Space — 18× in this paper · explained in 2 episodes
• Spectral Gap — 16× in this paper · explained in 5 episodes
• Verification — 11× in this paper · explained in 2 episodes
• Clustering — 5× in this paper · explained in 2 episodes
• Decoupling — 5× in this paper · explained in 2 episodes
• Calibration — 3× in this paper · explained in 7 episodes
• Frustration — 3× in this paper · explained in 2 episodes
• Superadditivity — 2× in this paper · explained in 2 episodes
• Anyons — 1× in this paper · explained in 2 episodes
• CSS Codes — 1× in this paper · explained in 2 episodes
• Hamming Distance — 1× in this paper · explained in 2 episodes
• Homogeneity — 1× in this paper · explained in 2 episodes
• Unified Framework — 1× in this paper · explained in 5 episodes
• Wasserstein Distance — 1× in this paper · explained in 4 episodes

Sources

• Fast mixing of all-to-all quantum systems at high temperatures
• On quantum to classical comparison for Davies generators
• A Dobrushin condition for quantum Markov chains: Rapid mixing and conditional mutual information at high temperature
• An efficient and exact noncommutative quantum Gibbs sampler
• Gibbs state preparation for commuting Hamiltonian: Mapping to classical Gibbs sampling
• Stability property for the quantum jump operators of an open system
• Efficient and simple Gibbs state preparation of the 2D toric code via duality to classical Ising chains
• Optimal quantum algorithm for Gibbs state preparation
• Modified logarithmic Sobolev inequalities for Abelian quantum double models

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