Accelerating quantum Gibbs sampling without quantum walks
This work develops a walk-free quantum algorithm to prepare purified Gibbs states for many quantum Gibbs samplers that satisfy exact Kubo–Martin–Schwinger detailed balance. The core result is an explicit factorization of the parent Hamiltonian, enabling a Quantum Singular Value Transformation (QSVT) that achieves a quadratic improvement in spectral-gap dependence for state preparation.