Transmutation based Quantum Simulation for Non-unitary Dynamics
Summarize this article with:
Quantum Physics arXiv:2601.03616 (quant-ph) [Submitted on 7 Jan 2026] Title:Transmutation based Quantum Simulation for Non-unitary Dynamics Authors:Shi Jin, Chuwen Ma, Enrique Zuazua View a PDF of the paper titled Transmutation based Quantum Simulation for Non-unitary Dynamics, by Shi Jin and Chuwen Ma and Enrique Zuazua View PDF HTML (experimental) Abstract:We present a quantum algorithm for simulating dissipative diffusion dynamics generated by positive semidefinite operators of the form $A=L^\dagger L$, a structure that arises naturally in standard discretizations of elliptic operators. Our main tool is the Kannai transform, which represents the diffusion semigroup $e^{-TA}$ as a Gaussian-weighted superposition of unitary wave propagators. This representation leads to a linear-combination-of-unitaries implementation with a Gaussian tail and yields query complexity $\tilde{\mathcal{O}}(\sqrt{\|A\| T \log(1/\varepsilon)})$, up to standard dependence on state-preparation and output norms, improving the scaling in $\|A\|, T$ and $\varepsilon$ compared with generic Hamiltonian-simulation-based methods. We instantiate the method for the heat equation and biharmonic diffusion under non-periodic physical boundary conditions, and we further use it as a subroutine for constant-coefficient linear parabolic surrogates arising in entropy-penalization schemes for viscous Hamilton--Jacobi equations. In the long-time regime, the same framework yields a structured quantum linear solver for $A\mathbf{x}=\mathbf{b}$ with $A=L^\dagger L$, achieving $\tilde{\mathcal{O}}(\kappa^{3/2}\log^2(1/\varepsilon))$ queries and improving the condition-number dependence over standard quantum linear-system algorithms in this factorized setting. Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2601.03616 [quant-ph] (or arXiv:2601.03616v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2601.03616 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Chuwen Ma [view email] [v1] Wed, 7 Jan 2026 05:47:22 UTC (289 KB) Full-text links: Access Paper: View a PDF of the paper titled Transmutation based Quantum Simulation for Non-unitary Dynamics, by Shi Jin and Chuwen Ma and Enrique ZuazuaView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-01 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?)