Distributed Variational Quantum Linear Solver

Quantum Physics [Submitted on 1 Apr 2026] Distributed Variational Quantum Linear Solver Tong Shen, Zeru Zhu, Ji Liu 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. Subjects: Quantum Physics (quant-ph); Distributed, Parallel, and Cluster Computing (cs.DC); Optimization and Control (math.OC) Cite as: arXiv:2604.01426 [quant-ph]   (or arXiv:2604.01426v1 [quant-ph] for this version)   https://doi.org/10.48550/arXiv.2604.01426 Focus to learn more Submission history From: Ji Liu [view email] [v1] Wed, 1 Apr 2026 22:06:47 UTC (908 KB) Access Paper: HTML (experimental) view license Current browse context: quant-ph < prev   |   next > new | recent | 2026-04 Change to browse by: cs cs.DC math math.OC References & Citations INSPIRE HEP NASA ADS Google Scholar Semantic Scholar Export BibTeX Citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Demos Related Papers About arXivLabs Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)