Distributed Variational Quantum Linear Solver
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866914477263290368 |
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| author | Lu, Chao Rao, Pooja Meena, Muralikrishnan Gopalakrishnan Gottiparthi, Kalyana Chakaravarthi |
| author_facet | Lu, Chao Rao, Pooja Meena, Muralikrishnan Gopalakrishnan Gottiparthi, Kalyana Chakaravarthi |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_14435 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Distributed Variational Quantum Linear Solver Lu, Chao Rao, Pooja Meena, Muralikrishnan Gopalakrishnan Gottiparthi, Kalyana Chakaravarthi Quantum Physics Distributed, Parallel, and Cluster Computing 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. |
| title | Distributed Variational Quantum Linear Solver |
| topic | Quantum Physics Distributed, Parallel, and Cluster Computing |
| url | https://arxiv.org/abs/2604.14435 |