Quantum Gibbs sampling through the detectability lemma
This work addresses the computational bottleneck of Gibbs state preparation for quantum computing applications, offering significant efficiency improvements.
The paper tackles the problem of Gibbs state preparation in quantum computing by using the detectability lemma to design new methods that avoid simulating Lindbladian evolution, reducing the cost by a factor of O(M) for local Lindbladians with M terms and achieving a quadratic speedup in spectral gap dependence for certain Hamiltonians.
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.