Code-space recovery for sample-based quantum diagonalization beyond native symmetry constraints

Quantum Physics arXiv:2607.10227 (quant-ph) [Submitted on 11 Jul 2026] Title:Code-space recovery for sample-based quantum diagonalization beyond native symmetry constraints Authors:Byeongyong Park, Sanha Kang, Doyeol Ahn, Keunhong Jeong View a PDF of the paper titled Code-space recovery for sample-based quantum diagonalization beyond native symmetry constraints, by Byeongyong Park and 3 other authors View PDF HTML (experimental) Abstract:Sample-based quantum diagonalization (SQD) diagonalizes a Hamiltonian in a compact subspace built from quantum samples, and its performance often relies on recovery procedures that exploit native constraints such as particle-number symmetry. For a broad class of eigenvalue problems, however, no analogous constraint is guaranteed, limiting the applicability of SQD-type recovery. Here, we introduce code-space recovery, which engineers recoverable structure through encoding rather than assuming it in the target problem. Using a dual-rail representation, each logical qubit is mapped to a physical pair, $|0\rangle \to |01\rangle$ and $|1\rangle \to |10\rangle$, making code-space violations in noisy samples detectable and repairable. We combine this encoding with self-consistent recovery and benchmark it on transverse- and mixed-field Ising models with up to 36 spin sites. Despite increased circuit overhead, code-space recovery yields lower projected Ritz energies than unencoded sample-support diagonalization even at smaller projected-basis dimensions, suggesting that engineered recoverable structure can extend SQD beyond native constraints. Comments: Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2607.10227 [quant-ph] (or arXiv:2607.10227v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2607.10227 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Byeongyong Park [view email] [v1] Sat, 11 Jul 2026 09:31:50 UTC (1,285 KB) Full-text links: Access Paper: View a PDF of the paper titled Code-space recovery for sample-based quantum diagonalization beyond native symmetry constraints, by Byeongyong Park and 3 other authorsView PDFHTML (experimental)TeX Source view license Ancillary-file links: Ancillary files (details): Code_space_recovery_SI.pdf Current browse context: quant-ph new | recent | 2026-07 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?)