This paper develops a distributed variational quantum algorithm for solving large-scale linear equations. For a linear system of the form $Ax=b$, the large square matrix $A$ is partitioned into smaller square block submatrices, each of which is known only to a single noisy intermediate-scale quantum (NISQ) computer. Each NISQ computer communicates with certain other quantum computers in the same row and column of the block partition, where the communication patterns are described by the row- and column-neighbor graphs, both of which are connected. The proposed algorithm integrates a variant of the variational quantum linear solver at each computer with distributed classical optimization techniques. The derivation of the quantum cost function provides insight into the design of the distributed algorithm. Numerical quantum simulations demonstrate that the proposed distributed quantum algorithm can solve linear systems whose size scales with the number of computers and is therefore not limited by the capacity of a single quantum computer.

翻译：本文开发了一种分布式变分量子算法，用于求解大规模线性方程组。考虑形如$Ax=b$的线性系统，其中大型方阵$A$被划分为较小的方块子矩阵，每个子矩阵仅由单个含噪中等规模量子（NISQ）计算机掌握。每台NISQ计算机与块划分中相同行和列的特定其他量子计算机进行通信，通信模式由行邻接图和列邻接图描述，两者均为连通图。所提出的算法将每台计算机上的变分量子线性求解器变体与分布式经典优化技术相结合。量子代价函数的推导为分布式算法的设计提供了依据。数值量子模拟表明，所提出的分布式量子算法能够求解规模随计算机数量扩展的线性系统，因此不受单台量子计算机容量的限制。