Efficient Hamiltonian Truncation: Fast Matrix Construction and Quantum Krylov Diagonalization

Quantum Physics arXiv:2608.13691 (quant-ph) [Submitted on 13 Aug 2026] Title:Efficient Hamiltonian Truncation: Fast Matrix Construction and Quantum Krylov Diagonalization Authors:Rachel Houtz, Marco Knipfer, Konstantin Matchev, Alexander Roman, Mia West View a PDF of the paper titled Efficient Hamiltonian Truncation: Fast Matrix Construction and Quantum Krylov Diagonalization, by Rachel Houtz and 4 other authors View PDF HTML (experimental) Abstract:Hamiltonian truncation offers a nonperturbative route to quantum field theory, yet its accuracy is limited by the rapid expansion of the truncated Hilbert space, which drives up computational cost. We tackle this bottleneck with a hybrid strategy that pairs classical and quantum algorithms: 1) we develop an efficient basis-generation scheme built on integer partitions; 2) we speed up the construction of the sparse Hamiltonian matrix using symmetry-aware algorithms; and 3) we explore quantum Krylov diagonalization as a route to the low-lying spectrum. Benchmarking against the free massive scalar and $\phi^4$ theories in two spacetime dimensions, we achieve substantial gains in the computational efficiency of Hamiltonian truncation and chart a path toward future quantum implementations. Comments: Subjects: Quantum Physics (quant-ph); High Energy Physics - Lattice (hep-lat); High Energy Physics - Phenomenology (hep-ph); High Energy Physics - Theory (hep-th) Report number: KA-TP-19-2026 Cite as: arXiv:2608.13691 [quant-ph] (or arXiv:2608.13691v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2608.13691 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Mia West [view email] [v1] Thu, 13 Aug 2026 18:37:19 UTC (5,055 KB) Full-text links: Access Paper: View a PDF of the paper titled Efficient Hamiltonian Truncation: Fast Matrix Construction and Quantum Krylov Diagonalization, by Rachel Houtz and 4 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-08 Change to browse by: hep-lat hep-ph hep-th 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?)