单射态PEPS和Gibbs态的快速绝热制备
Rapid adiabatic preparation of injective PEPS and Gibbs states
摘要：
我们提出了一个多体态制备的量子算法。它特别适用于单射PEPS和热态的局部交换哈密顿在一个格子上。我们表明，对于一个均匀的间隙和足够光滑的路径，绝热运行时间和电路深度的$O(\operatorname{polylog}N)$可以实现$O(N)$自旋。这是一个几乎指数的改善，在以前的界限。基本门的总数按比例缩放为$O(N\operatorname{polylog}N)$。这也是最好的已知的上界的$O(N^2)$的混合时间的蒙特卡罗马尔可夫链算法采样的经典系统在热平衡更快。
英文摘要：
We propose a quantum algorithm for many-body state preparation. It is especially suited for injective PEPS and thermal states of local commuting Hamiltonians on a lattice. We show that for a uniform gap and sufficiently smooth paths, an adiabatic runtime and circuit depth of $O(\operatorname{polylog}N)$ can be achieved for $O(N)$ spins. This is an almost exponential improvement over previous bounds. The total number of elementary gates scales as $O(N\operatorname{polylog}N)$. This is also faster than the best known upper bound of $O(N^2)$ on the mixing times of Monte Carlo Markov chain algorithms for sampling classical systems in thermal equilibrium.
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