High-Order Splitting of Non-Unitary Operators on Quantum Computers

Quantum Physics arXiv:2511.19659 (quant-ph) [Submitted on 24 Nov 2025] Title:High-Order Splitting of Non-Unitary Operators on Quantum Computers Authors:Peter Brearley, Philipp Pfeffer View a PDF of the paper titled High-Order Splitting of Non-Unitary Operators on Quantum Computers, by Peter Brearley and 1 other authors View PDF HTML (experimental) Abstract:We present a high-order splitting method for simulating non-unitary dynamics by sequential real- and imaginary-time Hamiltonian evolutions. Complex-coefficient splitting methods with positive real parts are chosen for stable integration in a quantum circuit, avoiding the unstable, norm-amplifying negative steps that arise from real-coefficient splitting at high orders. The method is most beneficial for dynamics that naturally separate into unitary and dissipative components, with broad applications across science and engineering. These systems frequently admit compact spectral representations of the split operators, which we demonstrate by deriving efficient quantum circuits for simulating the damped-wave equation with up to sixth-order accuracy in time. A single sixth-order step in three dimensions on 35 trillion cells requires 1,562 CNOT gates, which can be executed within the coherence time of modern quantum processors. Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2511.19659 [quant-ph] (or arXiv:2511.19659v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2511.19659 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Peter Brearley [view email] [v1] Mon, 24 Nov 2025 19:45:06 UTC (786 KB) Full-text links: Access Paper: View a PDF of the paper titled High-Order Splitting of Non-Unitary Operators on Quantum Computers, by Peter Brearley and 1 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?)