Fast mixing of all-to-all quantum systems at high temperatures

It is shown that arbitrary quantum $k$-local Hamiltonians with bounded strength interactions admit a quantum Gibbs sampler [CKG23] with a system-size independent spectral gap, at sufficiently high temperatures. This generalizes the existing quantum fast-mixing results beyond the geometrically-local setting. As a consequence, such systems admit fully-polynomial time quantum approximation algorithms for partition functions and global expectation values.

Source: arXiv:2606.26090v1 - http://arxiv.org/abs/2606.26090v1 PDF: https://arxiv.org/pdf/2606.26090v1 Original Link: http://arxiv.org/abs/2606.26090v1