k-local quantum Hamiltonians admit system-size-independent spectral gap for Gibbs samplers at high temperature, enabling FPT quantum approximation algorithms for partition functions.
Quantum logarithmic Sobolev inequalities and rapid mixing
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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.
A literature review synthesizing developments in quantum Wasserstein distances, their applications, and unresolved questions.
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Fast mixing of all-to-all quantum systems at high temperatures
k-local quantum Hamiltonians admit system-size-independent spectral gap for Gibbs samplers at high temperature, enabling FPT quantum approximation algorithms for partition functions.
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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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Wasserstein Distances on Quantum Structures: an Overview
A literature review synthesizing developments in quantum Wasserstein distances, their applications, and unresolved questions.