Improved constant factors for qubitized Hamiltonian simulation

Quantum Physics arXiv:2608.02734 (quant-ph) [Submitted on 3 Aug 2026] Title:Improved constant factors for qubitized Hamiltonian simulation Authors:Matthew Pocrnic, Danial Motlagh View a PDF of the paper titled Improved constant factors for qubitized Hamiltonian simulation, by Matthew Pocrnic and Danial Motlagh View PDF Abstract:Quantum signal processing (QSP) serves as the asymptotically optimal technique for Hamiltonian simulation on a quantum computer. By approximating the time evolution operator via the Jacobi-Anger expansion, the Hamiltonian simulation problem reduces to a problem in polynomial approximation theory: find a sufficient degree-$d$ polynomial series to approximate $e^{-i\tau x}$ on $[-1,1]$ within error $\epsilon$. While $d\in\tilde{\mathcal{O}}(\tau)$ is known to be asymptotically optimal, there exists a gap between state-of-the-art bounds and the optimal constant multiplicative factor, which is approximately equal to 1. Here, we close this gap almost entirely, to the point where possible future improvements will not be of practical significance. Our improvement resides in a careful treatment of the Bessel tail in the Jacobi-Anger series using Kapteyn's and Watson's inequalities, thereby reducing the overhead estimates for all Hamiltonian simulation tasks on quantum computers by a factor of $\approx e/2$. Comments: Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2608.02734 [quant-ph] (or arXiv:2608.02734v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2608.02734 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Matthew Pocrnic [view email] [v1] Mon, 3 Aug 2026 18:00:03 UTC (299 KB) Full-text links: Access Paper: View a PDF of the paper titled Improved constant factors for qubitized Hamiltonian simulation, by Matthew Pocrnic and Danial MotlaghView PDFTeX Source view license Current browse context: quant-ph new | recent | 2026-08 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?)