标题： 一维量子系统的自由能更快算法 显示英文标题

标题： A Faster Algorithm for the Free Energy in One-Dimensional Quantum Systems

摘要： 我们考虑近似一个具有有限范围的平移不变的一维量子自旋系统自由能密度的问题。 尽管由于其与已知困难结果的问题的紧密联系，该问题的复杂性是非平凡的，但最近已提出一种经典次多项式时间算法 [Fawzi 等，2022]。 结合之前用于相关问题的几种算法技术，我们提出了一种在渐近意义上优于该结果的算法，并给出了其运行时间的严格界限。 我们的主要技术是使用来自相变不存在结果中的 Araki 展开式，以及矩阵乘积算子构造。 我们还回顾了一种使用量子信念传播 [Kuwahara 等，2018] 的相关方法，该方法与我们的发现结合可得到等效结果。 显示英文摘要

摘要： We consider the problem of approximating the free energy density of a translation-invariant, one-dimensional quantum spin system with finite range. While the complexity of this problem is nontrivial due to its close connection to problems with known hardness results, a classical subpolynomial-time algorithm has recently been proposed [Fawzi et al., 2022]. Combining several algorithmic techniques previously used for related problems, we propose an algorithm outperforming this result asymptotically and give rigorous bounds on its runtime. Our main techniques are the use of Araki expansionals, known from results on the nonexistence of phase transitions, and a matrix product operator construction. We also review a related approach using the Quantum Belief Propagation [Kuwahara et al., 2018], which in combination with our findings yields an equivalent result.