Distributed Variational Quantum Linear Solver

TL;DR

This paper introduces a distributed variational quantum algorithm that enables large-scale linear systems to be solved across multiple NISQ computers, overcoming individual capacity limits.

Contribution

It presents a novel distributed quantum algorithm that partitions large matrices and combines quantum and classical methods for scalable linear system solving.

Findings

The algorithm scales with the number of quantum computers involved.

Numerical simulations validate the effectiveness of the distributed approach.

The method leverages communication patterns based on row and column neighbor graphs.

Abstract

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.