Is rapid mixing stable?

arXiv:2609.36016 · quant-ph, math-ph, math.MP · Submitted 2026-09-28 · Read on arXiv

quant-ph, math-ph, math.MP

Submitted: 2026-09-28

Updated: 2026-09-28

Terminology

• Trace — 69× in this paper · explained in 2 episodes
• Hilbert Space — 11× in this paper · explained in 2 episodes
• Spectral Gap — 8× in this paper · explained in 5 episodes
• Robustness — 5× in this paper · explained in 5 episodes
• Additivity — 4× in this paper · explained in 1 episode
• Gibbs State — 4× in this paper · explained in 2 episodes
• Accuracy — 2× in this paper · explained in 1 episode
• Lindblad master equation — 2× in this paper · explained in 2 episodes
• Quantization — 2× in this paper · explained in 12 episodes
• Trace Distance — 2× in this paper · explained in 3 episodes
• Adam — 1× in this paper · explained in 2 episodes
• Adaptation — 1× in this paper · explained in 1 episode
• Degeneracy — 1× in this paper · explained in 3 episodes
• Gradient Flow — 1× in this paper · explained in 2 episodes
• Non-Hermitian Skin Effect — 1× in this paper · explained in 2 episodes
• Stochastic Dynamics — 1× in this paper · explained in 2 episodes
• Topological Order — 1× in this paper · explained in 2 episodes

Sources

• Stability of local quantum dissipative systems
• Optimal quantum algorithm for Gibbs state preparation
• Rapid Mixing of Quantum Gibbs Samplers for Weakly-Interacting Quantum Systems
• Rapid thermalization of dissipative many-body dynamics of commuting Hamiltonians
• Rapid quantum ground state preparation via dissipative dynamics
• Dissipative preparation of injective tensor network states
• Spectral convergence bounds for classical and quantum Markov processes
• Block factorization of the relative entropy via spatial mixing
• Quantum logarithmic Sobolev inequalities and rapid mixing
• Gradient flow and entropy inequalities for quantum Markov semigroups with detailed balance
• Hypercontractivity and logarithmic Sobolev Inequality for non-primitive quantum Markov semigroups and estimation of decoherence rates
• Complete entropic inequalities for quantum Markov chains
• Quantum conditional relative entropy and quasi-factorization of the relative entropy
• Approximate tensorization of the relative entropy for noncommuting conditional expectations
• On the modified logarithmic Sobolev inequality for the heat-bath dynamics for 1D systems
• The modified logarithmic Sobolev inequality for quantum spin systems: classical and commuting nearest neighbour interactions
• Entropy decay for Davies semigroups of a one dimensional quantum lattice
• Perturbative criteria for the ergodicity of interacting dissipative quantum lattice systems
• Quantum Gibbs Samplers: the commuting case
• Lieb-Robinson bounds and the generation of correlations and topological quantum order

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