A factorization of the parent Hamiltonian into noncommutative first-order operators enables a walk-free QSVT algorithm with quadratic gap improvement for preparing purified Gibbs states under exact KMS detailed balance.
Quantum Gibbs sampling through the detectability lemma
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abstract
Gibbs state preparation is an important subroutine in quantum computing. In this work we use the detectability lemma to improve Gibbs state preparation. Specifically, we design new Gibbs state preparation methods that do not rely on simulating Lindbladian evolution, thus avoiding the overhead from it. For local Lindbladians consisting of $M$ terms, this approach reduces the cost by a factor of $O(M)$. We also combine the detectability lemma operator and quantum singular value transformation to implement ground state projection operators of frustration-free Hamiltonians, resulting in a quadratic speedup in the spectral gap dependence. Applying this method to Lindbladians for the Gibbs state of local commuting Hamiltonians, we achieve quadratically better dependence on the Lindbladian spectral gap.
fields
quant-ph 2years
2026 2verdicts
UNVERDICTED 2representative citing papers
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.
citing papers explorer
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Accelerating quantum Gibbs sampling without quantum walks
A factorization of the parent Hamiltonian into noncommutative first-order operators enables a walk-free QSVT algorithm with quadratic gap improvement for preparing purified Gibbs states under exact KMS detailed balance.
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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.