Distributed Variational Quantum Linear Solver

Quantum Physics [Submitted on 15 Apr 2026] Distributed Variational Quantum Linear Solver Chao Lu, Pooja Rao, Muralikrishnan Gopalakrishnan Meena, Kalyana Chakaravarthi Gottiparthi The Variational Quantum Linear Solver (VQLS), a hybrid quantum-classical algorithm for solving linear systems, faces a practical scalability bottleneck: the Linear Combination of Unitaries (LCU) decomposition requires O(L^2) circuit evaluations per optimizer iteration, where L can grow as 4^n for n-qubit systems for the worst case scenario. We address this computational bottleneck through two complementary strategies. First, we present a distributed VQLS (D-VQLS) framework, built on NVIDIA CUDA-Q, that enables asynchronous, scalable distribution of the O(L^2) cost-function evaluations. Second, a fast Walsh--Hadamard transform (FWHT)-based Pauli decomposition with 1% coefficient thresholding curbs the exponential growth of LCU terms, reducing L from O}(2^n) to O(1) for n > 6 qubits and compressing the per-iteration circuit complexity from O(n * 4^n) to O(n) for sparse, structured matrices. For a 10-qubit tridiagonal Toeplitz system, this yields a 256x reduction, from 23 million to 90,112 circuits per iteration, while preserving over 99.99\% solution fidelity. Additionally, to inform feasibility on early fault-tolerant QPUs, the paper provides resource estimates -- gate counts, qubit requirements, and circuit evaluations per iteration -- for VQLS applied to arbitrary matrices. The D-VQLS framework is validated on the NERSC Perlmutter supercomputer using multi-node, multi-GPU ideal state-vector simulations, achieving over 99.99% fidelity against classical solutions on tridiagonal Toeplitz and Hele--Shaw flow benchmarks, with near-ideal strong scaling up to 24 GPUs and 95.3% weak scaling efficiency at 96 GPUs processing 360,448 circuits per iteration for a 10-qubit system. Systematic profiling identifies the optimal resource allocation for distributed quantum circuit workloads, yielding a 2.52x speedup for the configurations studied. Subjects: Quantum Physics (quant-ph); Distributed, Parallel, and Cluster Computing (cs.DC) Cite as: arXiv:2604.14435 [quant-ph]   (or arXiv:2604.14435v1 [quant-ph] for this version)   https://doi.org/10.48550/arXiv.2604.14435 Focus to learn more Submission history From: Chao Lu [view email] [v1] Wed, 15 Apr 2026 21:27:16 UTC (850 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 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?)