A Bi-directional Multi-solution Scalable Grover Search Algorithm

[2404.15616] A Bi-directional Multi-solution Scalable Grover Search Algorithm Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Quantum Physics arXiv:2404.15616 (quant-ph) [Submitted on 24 Apr 2024 ( v1 ), last revised 15 Aug 2026 (this version, v2)] Title: A Bi-directional Multi-solution Scalable Grover Search Algorithm Authors: Debanjan Konar , Zain Hafeez , Vaneet Aggarwal View a PDF of the paper titled A Bi-directional Multi-solution Scalable Grover Search Algorithm, by Debanjan Konar and 1 other authors View PDF HTML (experimental) Abstract: Grover's search algorithms, including various Partial Grover Searches (PGS), suffer from scaling issues when multiple solutions are sought, as the number of iterations scales with the number of solutions or marked states, making implementation more computationally expensive. Inspired by recent PGS algorithms for multi-solution searchers, this article proposes a scalable Grover quantum search algorithm, referred to as Bi-directional Multi-solution scalable Grover Search (BMGS), to efficiently search for an arbitrary number of solutions from an unstructured database. We introduced a novel multi-segment bidirectional search tactic with PGS across multiple equal segments of each state, starting from an initial state and multiple marked states in parallel, obviating the need for merge operations. We have shown in this work that for each solution our novel approach requires at most $\sqrt{\mathcal{N}}\left (1- \sqrt{\frac{1}{b^{\lfloor\frac{r}{dk}\rfloor}}}\right)$ iterations (here, $\mathcal{N}=2^r$ elements, $k=\log_2 b$, $d$ is the number of equal segments on $r$ qubits, and $b$ is the branching factor). Our proposed BMGS algorithm is benchmarked against state-of-the-art Depth First Grover Search (DFGS) and PGS implementations for an arbitrary number of solutions, ranging from $2$ to $20$ qubits, as a proof of concept. We also show that our BMGS requires fewer iterations for shallow quantum circuits and achieves an optimal $\mathcal{O}$($\sqrt{s\mathcal{N}}$) average complexity for $s$ solutions, when $dk < r$. The Qiskit Python implementation of the proposed BMGS algorithm is available on GitHub\footnote{ this https URL }. Comments: 29 pages Accepted in Quantum Information Processing, Springer Nature Journal, 2026 Subjects: Quantum Physics (quant-ph) ; Artificial Intelligence (cs.AI) Cite as: arXiv:2404.15616 [quant-ph] (or arXiv:2404.15616v2 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2404.15616 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Debanjan Konar PhD [ view email ] [v1] Wed, 24 Apr 2024 03:11:10 UTC (398 KB) [v2] Sat, 15 Aug 2026 09:30:19 UTC (2,120 KB) Full-text links: Access Paper: View a PDF of the paper titled A Bi-directional Multi-solution Scalable Grover Search Algorithm, by Debanjan Konar and 1 other authors View PDF HTML (experimental) TeX Source view license Current browse context: quant-ph < prev | next > new | recent | 2024-04 Change to browse by: cs cs.AI References & Citations INSPIRE HEP NASA ADS Google 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? ) We gratefully acknowledge support from our major funders , member institutions , , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from

Related documents

• Landscape-Similarity-Guided Optimization in Divide-and-Conquer QAOA#1011048
• DreamQAS: Learning a Decision-Useful World Model for VQE-Efficient Quantum Architecture Search#422252
• Quantum element-wise transforms#1143797
• Evaluation-efficient quantum architecture search with ZX-calculus-based topological reuse#1077027
• From Pattern Detection to Composition Analysis in Quantum Software#444700