Quantum Gibbs samplers thermalize to Gibbs states in polynomial time at high temperatures for Lieb-Robinson bounded Hamiltonians and are BQP-complete at low temperatures via circuit-to-Hamiltonian reductions.
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Rapid mixing and frustration-freeness of short- or long-range Lindbladians imply polynomial (not exponential) decay of CMI and MI of the fixed point; long-range Gibbs states are locally Markovian at any temperature.
Mixing time of Lindblad-governed open quantum systems is determined by the Liouvillian gap plus trace-norm factors of eigenmodes, yielding rapid mixing conditions via sparsity constraints on the Hamiltonian and local Lindblad operators.
Extends KMS-detailed balance constructions from open quantum systems to prepare microcanonical ensembles and other stationary states with criteria for efficient implementation.
A literature review synthesizing developments in quantum Wasserstein distances, their applications, and unresolved questions.
citing papers explorer
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Efficient thermalization and universal quantum computing with quantum Gibbs samplers
Quantum Gibbs samplers thermalize to Gibbs states in polynomial time at high temperatures for Lieb-Robinson bounded Hamiltonians and are BQP-complete at low temperatures via circuit-to-Hamiltonian reductions.
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Static features from mixing in short- and long-range Lindbladians: Markov property and correlations
Rapid mixing and frustration-freeness of short- or long-range Lindbladians imply polynomial (not exponential) decay of CMI and MI of the fixed point; long-range Gibbs states are locally Markovian at any temperature.
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Universal Predictors for Mixing Time more than Liouvillian Gap
Mixing time of Lindblad-governed open quantum systems is determined by the Liouvillian gap plus trace-norm factors of eigenmodes, yielding rapid mixing conditions via sparsity constraints on the Hamiltonian and local Lindblad operators.
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Dissipative microcanonical ensemble preparation from KMS-detailed balance
Extends KMS-detailed balance constructions from open quantum systems to prepare microcanonical ensembles and other stationary states with criteria for efficient implementation.
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Wasserstein Distances on Quantum Structures: an Overview
A literature review synthesizing developments in quantum Wasserstein distances, their applications, and unresolved questions.