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.
Note that, given our choice ofNandTas in Lemma 7, the normalization factorC∶= ∑N−1 k=0 gk is a constant close to∫ ∞ −∞g(t)dt=1/2
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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.