High-Precision Variational Quantum SVD via Classical Orthogonality Correction
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Quantum Physics arXiv:2605.08683 (quant-ph) [Submitted on 9 May 2026] Title:High-Precision Variational Quantum SVD via Classical Orthogonality Correction Authors:Shohei Miyakoshi, Takanori Sugimoto, Tomonori Shirakawa, Seiji Yunoki, Hiroshi Ueda View a PDF of the paper titled High-Precision Variational Quantum SVD via Classical Orthogonality Correction, by Shohei Miyakoshi and 3 other authors View PDF HTML (experimental) Abstract:Evaluating the entanglement spectrum is essential for characterizing exotic quantum phases such as quantum criticality and topological order. However, for large quantum many-body systems, this task is hindered by the exponential measurement complexity of standard tomographic techniques. To address this challenge, we introduce a hybrid quantum-classical variational framework for partial singular value decomposition of bipartite states, built on the canonical form of matrix product states. We employ a deflation-based optimization approach to sequentially extract dominant and subdominant Schmidt components of target states. Because hardware noise and finite circuit depth can compromise the mutual orthogonality of these extracted vectors, we propose an improved deflation algorithm incorporating explicit classical orthogonality correction. This classical post-processing acts as an error-filtering mechanism, enabling shallow and suboptimal quantum circuits. As a result, numerical accuracy is decoupled from quantum circuit optimization, mitigating optimization difficulties caused by barren plateaus and hardware noise. Furthermore, shallow ansatzes enable a concurrent execution strategy. Overlap matrices are evaluated by classical tensor network contractions, while cross terms between the target state and the extracted vectors are computed using an auxiliary reference state. This concurrent hybrid design improves computational throughput and bypasses the overhead of controlled target-state preparation. Numerical benchmarks on the ground states of one- and two-dimensional Heisenberg models demonstrate improved accuracy and numerical stability. By mitigating hurdles of circuit depth, optimization hardness, and measurement complexity, our framework provides a robust pathway for large-scale entanglement spectrum estimation on advanced near-term quantum devices. Comments: Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2605.08683 [quant-ph] (or arXiv:2605.08683v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2605.08683 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Shohei Miyakoshi [view email] [v1] Sat, 9 May 2026 04:49:05 UTC (7,955 KB) Full-text links: Access Paper: View a PDF of the paper titled High-Precision Variational Quantum SVD via Classical Orthogonality Correction, by Shohei Miyakoshi and 3 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-05 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?)