Providing evidence that quantum computers can efficiently prepare low-energy or thermal states of physically relevant interacting quantum systems is a major challenge in quantum information science. A newly developed quantum Gibbs sampling algorithm by Chen, Kastoryano, and Gily\'en provides an efficient simulation of the detailed-balanced dissipative dynamics of non-commutative quantum systems. The running time of this algorithm depends on the mixing time of the corresponding quantum Markov chain, which has not been rigorously bounded except in the high-temperature regime. In this work, we establish a polylog(n) upper bound on its mixing time for various families of random n by n sparse Hamiltonians at any constant temperature. We further analyze how the choice of the jump operators for the algorithm and the spectral properties of these sparse Hamiltonians influence the mixing time. Our result places this method for Gibbs sampling on par with other efficient algorithms for preparing low-energy states of quantumly easy Hamiltonians.

翻译：证明量子计算机能够高效制备物理相关相互作用量子系统的低能态或热态是量子信息科学中的一个主要挑战。Chen、Kastoryano和Gilyén新近开发的量子吉布斯采样算法，为非对易量子系统的细致平衡耗散动力学提供了高效模拟。该算法的运行时间取决于对应量子马尔可夫链的混合时间，而除高温区域外，该混合时间尚未得到严格界定。本工作中，我们针对任意恒定温度下各类n×n随机稀疏哈密顿量族，建立了其混合时间的polylog(n)上界。我们进一步分析了算法中跳跃算子的选择以及这些稀疏哈密顿量的谱特性如何影响混合时间。我们的研究结果表明，这种吉布斯采样方法在制备量子易解哈密顿量低能态方面，与其他高效算法具有同等效能。