Quantum-Inspired Algorithms beyond Unitary Circuits: the Laplace Transform
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Quantum Physics arXiv:2601.17724 (quant-ph) [Submitted on 25 Jan 2026] Title:Quantum-Inspired Algorithms beyond Unitary Circuits: the Laplace Transform Authors:Noufal Jaseem, Sergi Ramos-Calderer, Gauthameshwar S., Dingzu Wang, José Ignacio Latorre, Dario Poletti View a PDF of the paper titled Quantum-Inspired Algorithms beyond Unitary Circuits: the Laplace Transform, by Noufal Jaseem and 5 other authors View PDF Abstract:Quantum-inspired algorithms can deliver substantial speedups over classical state-of-the-art methods by executing quantum algorithms with tensor networks on conventional hardware. Unlike circuit models restricted to unitary gates, tensor networks naturally accommodate non-unitary maps. This flexibility lets us design quantum-inspired methods that start from a quantum algorithmic structure, yet go beyond unitarity to achieve speedups. Here we introduce a tensor-network approach to compute the discrete Laplace transform, a non-unitary, aperiodic transform (in contrast to the Fourier transform). We encode a length-$N$ signal on two paired $n$-qubit registers and decompose the overall map into a non-unitary exponential Damping Transform followed by a Quantum Fourier Transform, both compressed in a single matrix-product operator. This decomposition admits strong MPO compression to low bond dimension resulting in significant acceleration. We demonstrate simulations up to $N=2^{30}$ input data points, with up to $2^{60}$ output data points, and quantify how bond dimension controls runtime and accuracy, including precise and efficient pole identification. Comments: Subjects: Quantum Physics (quant-ph); Mathematical Physics (math-ph); Data Analysis, Statistics and Probability (physics.data-an) Cite as: arXiv:2601.17724 [quant-ph] (or arXiv:2601.17724v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2601.17724 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Noufal Jaseem [view email] [v1] Sun, 25 Jan 2026 07:19:56 UTC (1,168 KB) Full-text links: Access Paper: View a PDF of the paper titled Quantum-Inspired Algorithms beyond Unitary Circuits: the Laplace Transform, by Noufal Jaseem and 5 other authorsView PDFTeX Source view license Current browse context: quant-ph new | recent | 2026-01 Change to browse by: math math-ph math.MP physics physics.data-an 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?)