A Polylogarithmic-Time Quantum Algorithm for the Laplace Transform

Quantum Physics arXiv:2512.17980 (quant-ph) [Submitted on 19 Dec 2025] Title:A Polylogarithmic-Time Quantum Algorithm for the Laplace Transform Authors:Akash Kumar Singh, Ashish Kumar Patra, Anurag K.S.V., Sai Shankar P., Ruchika Bhat, Jaiganesh G View a PDF of the paper titled A Polylogarithmic-Time Quantum Algorithm for the Laplace Transform, by Akash Kumar Singh and 5 other authors View PDF HTML (experimental) Abstract:We introduce a quantum algorithm to perform the Laplace transform on quantum computers. Already, the quantum Fourier transform (QFT) is the cornerstone of many quantum algorithms, but the Laplace transform or its discrete version has not seen any efficient implementation on quantum computers due to its dissipative nature and hence non-unitary dynamics. However, a recent work has shown an efficient implementation for certain cases on quantum computers using the Taylor series. Unlike previous work, our work provides a completely different algorithm for doing Laplace Transform using Quantum Eigenvalue Transformation and Lap-LCHS, very efficiently at points which form an arithmetic progression. Our algorithm can implement $N \times N$ discrete Laplace transform in gate complexity that grows as $O((log\,N)^3)$, ignoring the state preparation cost, where $N=2^n$ and $n$ is the number of qubits, which is a superpolynomial speedup in number of gates over the best classical counterpart that has complexity $O(N\cdot log\,N)$ for the same cases. Also, the circuit width grows as $O(log\,N)$.

Quantum Laplace Transform (QLT) may enable new Quantum algorithms for cases like solving differential equations in the Laplace domain, developing an inverse Laplace transform algorithm on quantum computers, imaginary time evolution in the resolvent domain for calculating ground state energy, and spectral estimation of non-Hermitian matrices. Comments: Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2512.17980 [quant-ph] (or arXiv:2512.17980v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2512.17980 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Ashish Kumar Patra [view email] [v1] Fri, 19 Dec 2025 13:31:39 UTC (183 KB) Full-text links: Access Paper: View a PDF of the paper titled A Polylogarithmic-Time Quantum Algorithm for the Laplace Transform, by Akash Kumar Singh and 5 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2025-12 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?)