Approximate Sparse State Preparation with the Grover-Rudolph Algorithm
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Quantum Physics arXiv:2604.24973 (quant-ph) [Submitted on 27 Apr 2026] Title:Approximate Sparse State Preparation with the Grover-Rudolph Algorithm Authors:Debora Ramacciotti, Martin Steinbach, Bence Temesi, Andreea-Iulia Lefterovici, Antonio F. Rotundo View a PDF of the paper titled Approximate Sparse State Preparation with the Grover-Rudolph Algorithm, by Debora Ramacciotti and 4 other authors View PDF HTML (experimental) Abstract:Sparse quantum state preparation is a common subroutine in quantum algorithms, where classical data with few nonzero entries must be loaded into a quantum state. In this work, we consider the Grover-Rudolph algorithm, which has recently been shown to efficiently prepare sparse states, and we propose two improvements. First, we extend an existing gate-merging procedure by allowing rotations to merge with virtual zero-angle gates on unreachable branches of the preparation tree, reducing the number of CNOTs and control qubits. Second, we introduce an approximate variant in which rotations with similar but not identical angles are merged at the cost of a small, controllable error in the prepared state. We derive a classically computable estimate of the resulting overlap with the target state, which is used to guide the merging decisions. Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2604.24973 [quant-ph] (or arXiv:2604.24973v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2604.24973 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Andreea-Iulia Lefterovici [view email] [v1] Mon, 27 Apr 2026 20:15:04 UTC (746 KB) Full-text links: Access Paper: View a PDF of the paper titled Approximate Sparse State Preparation with the Grover-Rudolph Algorithm, by Debora Ramacciotti and 4 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-04 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?)