A new rigorous Gibbs sampling method is given for bosonic models by proving that their dissipative generators have positive spectral gaps, enabling efficient quantum preparation of thermal states for Bose-Hubbard Hamiltonians.
& Tang, E.A Dobrushin condition for quantum Markov chains: Rapid mixing and conditional mutual information at high tempera- tureen
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The unitary contribution from weak system-bath coupling in collision-model thermal state preparation tightens the fixed-point error bound, scaling rigorously as J² where J is the coupling strength.
Products of finite-dimensional quantum channels asymptotically forget input states under decay of the centered trace-Dobrushin coefficient, yielding unique replacement channels and convergence for deterministic and random inhomogeneous MPS.
Locally stable states are equivalent to short-range correlated states and define phases invariant under locally reversible channels, with decay of nonlinear correlators and links to canonical purifications.
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.
Robust protocols are identified for three quantum Shannon tasks under three notions of almost i.i.d. structure that preserve i.i.d. rates, along with new concepts of almost i.i.d. process and club distance.
The strong Markov property holds if and only if the state has correlation decay for suitable observables, enabling single-copy multi-observable estimation and forcing local marginals of such states to be close or well-separated.
High-temperature Gibbs states with arbitrary external fields admit O(log n) quantum mixing via a detailed-balance Lindbladian and exhibit classical sampling hardness for β < 1.
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.
citing papers explorer
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Simulating Thermal Properties of Bose-Hubbard Models on a Quantum Computer
A new rigorous Gibbs sampling method is given for bosonic models by proving that their dissipative generators have positive spectral gaps, enabling efficient quantum preparation of thermal states for Bose-Hubbard Hamiltonians.
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Rigorous error bounds for dissipative thermal state preparation from weak system-bath coupling
The unitary contribution from weak system-bath coupling in collision-model thermal state preparation tightens the fixed-point error bound, scaling rigorously as J² where J is the coupling strength.
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Asymptotic Replacement for Quantum Channel Products with Applications to Inhomogeneous Matrix Product States
Products of finite-dimensional quantum channels asymptotically forget input states under decay of the centered trace-Dobrushin coefficient, yielding unique replacement channels and convergence for deterministic and random inhomogeneous MPS.
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A Unified Framework for Locally Stable Phases
Locally stable states are equivalent to short-range correlated states and define phases invariant under locally reversible channels, with decay of nonlinear correlators and links to canonical purifications.
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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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Quantum Shannon theory made robust: a tale of three protocols for almost i.i.d. sources
Robust protocols are identified for three quantum Shannon tasks under three notions of almost i.i.d. structure that preserve i.i.d. rates, along with new concepts of almost i.i.d. process and club distance.
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Note on Strong Quantum Markov Properties
The strong Markov property holds if and only if the state has correlation decay for suitable observables, enabling single-copy multi-observable estimation and forcing local marginals of such states to be close or well-separated.
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Rapid mixing for high-temperature Gibbs states with arbitrary external fields
High-temperature Gibbs states with arbitrary external fields admit O(log n) quantum mixing via a detailed-balance Lindbladian and exhibit classical sampling hardness for β < 1.
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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.
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