Efficient Quantum Circuits for the Hilbert Transform

Quantum Physics arXiv:2601.10876 (quant-ph) [Submitted on 15 Jan 2026] Title:Efficient Quantum Circuits for the Hilbert Transform Authors:Henry Zhang, Joseph Li View a PDF of the paper titled Efficient Quantum Circuits for the Hilbert Transform, by Henry Zhang and 1 other authors View PDF Abstract:The quantum Fourier transform and quantum wavelet transform have been cornerstones of quantum information processing. However, for non-stationary signals and anomaly detection, the Hilbert transform can be a more powerful tool, yet no prior work has provided efficient quantum implementations for the discrete Hilbert transform. This letter presents a novel construction for a quantum Hilbert transform in polylogarithmic size and logarithmic depth for a signal of length $N$, exponentially fewer operations than classical algorithms for the same mapping. We generalize this algorithm to create any $d$-dimensional Hilbert transform in depth $O(d\log N)$. Simulations demonstrate effectiveness for tasks such as power systems control and image processing, with exact agreement with classical results. Comments: Subjects: Quantum Physics (quant-ph); Signal Processing (eess.SP) Cite as: arXiv:2601.10876 [quant-ph] (or arXiv:2601.10876v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2601.10876 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Related DOI: https://doi.org/10.1109/LSP.2026.3654893 Focus to learn more DOI(s) linking to related resources Submission history From: Joseph Li [view email] [v1] Thu, 15 Jan 2026 22:02:32 UTC (986 KB) Full-text links: Access Paper: View a PDF of the paper titled Efficient Quantum Circuits for the Hilbert Transform, by Henry Zhang and 1 other authorsView PDFTeX Source view license Current browse context: quant-ph new | recent | 2026-01 Change to browse by: eess eess.SP 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?)