Reducing Circuit Resources in Grover's Algorithm via Constraint-Aware Initialization
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Quantum Physics arXiv:2601.17725 (quant-ph) [Submitted on 25 Jan 2026] Title:Reducing Circuit Resources in Grover's Algorithm via Constraint-Aware Initialization Authors:Eunok Bae, Jeonghyeon Shin, Minjin Choi View a PDF of the paper titled Reducing Circuit Resources in Grover's Algorithm via Constraint-Aware Initialization, by Eunok Bae and Jeonghyeon Shin and Minjin Choi View PDF Abstract:Grover's search algorithm provides a quadratic speedup over classical brute-force search in terms of query complexity and is widely used as a versatile subroutine in numerous quantum algorithms, including those for combinatorial problems with large search spaces. For such problems, it is natural to reduce the effective search space by incorporating problem constraints at the initialization step, which in Grover's algorithm can be achieved by preparing structured initial states that encode constraint information. In this work, we present a systematic framework with a simple preprocessing procedure for constraint-aware initialization in Grover's algorithm, focusing on problems with linear constraints. While such structured initial states can reduce the number of oracle queries required to obtain a solution, their preparation incurs additional circuit-level costs. We therefore offer a conservative circuit-level resource analysis, showing that the resulting constraint-aware initialization can improve resource efficiency in terms of gate counts and circuit depth. The validity of the framework is further demonstrated numerically using the exact-cover problem. Overall, our results indicate that this approach serves as a practical baseline for achieving more resource-efficient implementations of Grover's algorithm compared to the standard uniform initialization. Comments: Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2601.17725 [quant-ph] (or arXiv:2601.17725v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2601.17725 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Eunok Bae [view email] [v1] Sun, 25 Jan 2026 07:31:06 UTC (320 KB) Full-text links: Access Paper: View a PDF of the paper titled Reducing Circuit Resources in Grover's Algorithm via Constraint-Aware Initialization, by Eunok Bae and Jeonghyeon Shin and Minjin ChoiView PDFTeX Source view license Current browse context: quant-ph new | recent | 2026-01 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?)