Walsh-Transform Realization of Dense-to-Sparse Quantum State Preparation

Quantum Physics arXiv:2609.28760 (quant-ph) [Submitted on 23 Sep 2026] Title:Walsh-Transform Realization of Dense-to-Sparse Quantum State Preparation Authors:Emad Rezaei Fard Boosari View a PDF of the paper titled Walsh-Transform Realization of Dense-to-Sparse Quantum State Preparation, by Emad Rezaei Fard Boosari View PDF HTML (experimental) Abstract:We propose a hybrid quantum state preparation method based on the Walsh--Hadamard transform within the dense-to-sparse quantum state preparation framework. The method approximately prepares structured classical data in a quantum circuit through an indirect approach. Instead of directly preparing the dense amplitude-encoded state, the method first transforms the classical data into the Walsh domain and prepares only the largest-magnitude coefficients using a sparse state-preparation algorithm. The original state can then be approximately recovered through a parallel layer of Hadamard gates. Since this reconstruction requires no CNOT gates and has circuit depth 1, the proposed method introduces no additional CNOT or circuit-depth overhead, and its quantum preparation cost is determined by the underlying sparse state-preparation algorithm. Numerical results on representative benchmark signals demonstrate that the proposed method enables accurate state preparation for signals admitting sparse or approximately sparse representations in the Walsh domain. Comments: Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2609.28760 [quant-ph] (or arXiv:2609.28760v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2609.28760 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Emad Rezaei Fard Boosari [view email] [v1] Wed, 23 Sep 2026 20:12:52 UTC (985 KB) Full-text links: Access Paper: View a PDF of the paper titled Walsh-Transform Realization of Dense-to-Sparse Quantum State Preparation, by Emad Rezaei Fard BoosariView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-09 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?) 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?)