Mirror subspace diagonalization: a quantum Krylov algorithm with near-optimal sampling cost

Quantum Physics arXiv:2511.20998 (quant-ph) [Submitted on 26 Nov 2025] Title:Mirror subspace diagonalization: a quantum Krylov algorithm with near-optimal sampling cost Authors:Shota Kanasugi, Yuya O. Nakagawa, Norifumi Matsumoto, Yuichiro Hidaka, Kazunori Maruyama, Hirotaka Oshima View a PDF of the paper titled Mirror subspace diagonalization: a quantum Krylov algorithm with near-optimal sampling cost, by Shota Kanasugi and 5 other authors View PDF HTML (experimental) Abstract:Quantum Krylov algorithms have emerged as a promising approach for ground-state energy estimation in the near-term quantum computing era. A major challenge, however, lies in their inherently substantial sampling cost, primarily due to the individual measurement of each term in the Hamiltonian. While various techniques have been proposed to mitigate this issue, the sampling overhead remains a significant bottleneck, especially for practical large-scale electronic structure problems. In this work, we introduce an alternative method, dubbed mirror subspace diagonalization (MSD), which approaches the theoretical lower bound of the sampling cost for quantum Krylov algorithms. MSD leverages a finite-difference formula to express the Hamiltonian operator as a linear combination of time-evolution unitaries with symmetrically shifted timesteps, enabling efficient estimation of the Hamiltonian matrix within the Krylov subspace. In this scheme, the finite difference and statistical errors are simultaneously minimized by optimizing the timestep parameter and shifting the energy spectrum. Consequently, MSD attains the lower bound of the sampling cost of the quantum Krylov algorithms up to a logarithmic factor. Furthermore, we employ classical post-processing to infer Hamiltonian moments, which are used to mitigate the ground state energy error based on the Lanczos scheme. Through theoretical analysis of the sampling cost, we demonstrate that MSD is particularly effective when the spectral norm of the Hamiltonian is significantly smaller than its 1-norm. Such a situation arises, for example, in high-accuracy simulations of molecules using large basis sets that incorporate strong electronic correlations. Numerical results for various molecular models reveal that MSD can achieve sampling cost reductions ranging from approximately 10 to 10,000 times compared to the conventional quantum Krylov algorithm. Comments: Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2511.20998 [quant-ph] (or arXiv:2511.20998v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2511.20998 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Shota Kanasugi [view email] [v1] Wed, 26 Nov 2025 02:53:22 UTC (349 KB) Full-text links: Access Paper: View a PDF of the paper titled Mirror subspace diagonalization: a quantum Krylov algorithm with near-optimal sampling cost, by Shota Kanasugi and 5 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2025-11 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?) Links to Code Toggle Papers with Code (What is Papers with Code?) 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?)