Localised Davies generators with stationary Gibbs states exist for natural classes of unbounded and pseudodifferential operators, and the jump operators remain pseudodifferential.
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Detectability lemma enables Gibbs sampling without Lindbladian simulation, yielding O(M) cost reduction for M-term local Lindbladians and quadratic speedup in spectral gap for frustration-free and commuting cases.
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Localised Davies generators for (pseudo)differential operators
Localised Davies generators with stationary Gibbs states exist for natural classes of unbounded and pseudodifferential operators, and the jump operators remain pseudodifferential.
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Quantum Gibbs sampling through the detectability lemma
Detectability lemma enables Gibbs sampling without Lindbladian simulation, yielding O(M) cost reduction for M-term local Lindbladians and quadratic speedup in spectral gap for frustration-free and commuting cases.