Distributed Variational Quantum Linear Solver

2026-04-01

AI Summary

This work addresses the challenge of solving large-scale linear systems on noisy intermediate-scale quantum (NISQ) devices, which are constrained by limited qubit counts. The authors propose a distributed variational quantum linear solver that partitions the coefficient matrix into blocks and distributes them across multiple quantum processors. Leveraging a connectivity structure defined by row/column neighbor graphs, the method integrates variational quantum algorithms with distributed classical optimization, coordinated through a hybrid quantum–classical communication protocol. This approach constitutes the first realization of a variational quantum linear solver based on a distributed architecture, effectively circumventing the qubit limitations of individual quantum devices. Numerical experiments demonstrate that the solvable problem size scales linearly with the number of participating nodes, substantially surpassing the capacity of single-device implementations.

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.

Problem

• distributed quantum computing
• variational quantum algorithm
• linear system
• NISQ devices
• large-scale linear equations

Innovation

• distributed quantum computing
• variational quantum algorithm
• quantum linear solver
• NISQ devices
• block matrix partitioning