Solving a Linear System of Equations on a Quantum Computer by Measurement
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Quantum Physics arXiv:2604.26098 (quant-ph) [Submitted on 28 Apr 2026] Title:Solving a Linear System of Equations on a Quantum Computer by Measurement Authors:Alain Giresse Tene, Thomas Konrad View a PDF of the paper titled Solving a Linear System of Equations on a Quantum Computer by Measurement, by Alain Giresse Tene and Thomas Konrad View PDF Abstract:We present a variational algorithm for fault tolerant quantum computing to solve a system of linear equations which directly maximises the parameters of the target fidelity. This so-called measurement test algorithm can be applied to any computational task with a solution that is represented as eigenvector of a self-adjoint matrix. The solution is prepared as state of a register in the quantum computer by a von Neumann measurement of a corresponding observable, which is implemented using the phase estimation algorithm. The probability to project the system thus into the unknown target state, which equals the target fidelity, is measured in terms of relative frequencies and iteratively optimised to read out the target state. The new algorithm overcomes three issues of previous variational quantum algorithms: i) It does not rely on a decomposition in terms of Pauli strings and therefore can compute eigenvectors of dense matrices. ii) The accuracy is not limited by the condition number $\kappa$ of the matrix, provided a logarithmic number ($O(\log\kappa)$) of qubits is used to encode the eigenvalues and iii) the target fidelity $F_T = 1-\epsilon$ can be reached with an accuracy $\epsilon$ that scales with $1/N$ for $N$ measurements per iteration. We demonstrate this by numerical simulations for dense random real-valued $16\times 16$ matrices with non-vanishing determinant. Comments: Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2604.26098 [quant-ph] (or arXiv:2604.26098v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2604.26098 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Thomas Konrad [view email] [v1] Tue, 28 Apr 2026 20:28:28 UTC (111 KB) Full-text links: Access Paper: View a PDF of the paper titled Solving a Linear System of Equations on a Quantum Computer by Measurement, by Alain Giresse Tene and Thomas KonradView PDFTeX Source view license Current browse context: quant-ph new | recent | 2026-04 References & Citations INSPIRE HEP NASA ADSGoogle Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: 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 Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv (What is alphaXiv?) Links to Code Toggle CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub Toggle DagsHub (What is DagsHub?) GotitPub Toggle Gotit.pub (What is GotitPub?) Huggingface Toggle Hugging Face (What is Huggingface?) ScienceCast Toggle ScienceCast (What is ScienceCast?) Demos Demos Replicate Toggle Replicate (What is Replicate?) Spaces Toggle Hugging Face Spaces (What is Spaces?) Spaces Toggle TXYZ.AI (What is TXYZ.AI?) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower (What are Influence Flowers?) Core recommender toggle CORE Recommender (What is CORE?) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs. Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)