Is this paper claiming to improve SAT solver step iteration time from O(m) to O(1) legit at all? If not, where is the error?

Quantum Physics arXiv:2308.03344 (quant-ph) [Submitted on 7 Aug 2023] Title:A Parallel and Distributed Quantum SAT Solver Based on Entanglement and Quantum Teleportation Authors:Shang-Wei Lin, Tzu-Fan Wang, Yean-Ru Chen, Zhe Hou, David Sanán, Yon Shin Teo View a PDF of the paper titled A Parallel and Distributed Quantum SAT Solver Based on Entanglement and Quantum Teleportation, by Shang-Wei Lin and 5 other authors View PDF Abstract:Boolean satisfiability (SAT) solving is a fundamental problem in computer science. Finding efficient algorithms for SAT solving has broad implications in many areas of computer science and beyond. Quantum SAT solvers have been proposed in the literature based on Grover's algorithm. Although existing quantum SAT solvers can consider all possible inputs at once, they evaluate each clause in the formula one by one sequentially, making the time complexity O(m) -- linear to the number of clauses m -- per Grover iteration. In this work, we develop a parallel quantum SAT solver, which reduces the time complexity in each iteration from linear time O(m) to constant time O(1) by utilising extra entangled qubits. To further improve the scalability of our solution in case of extremely large problems, we develop a distributed version of the proposed parallel SAT solver based on quantum teleportation such that the total qubits required are shared and distributed among a set of quantum computers (nodes), and the quantum SAT solving is accomplished collaboratively by all the nodes. We have proved the correctness of our approaches and demonstrated them in simulations. Subjects: Quantum Physics (quant-ph); Distributed, Parallel, and Cluster Computing (cs.DC) Cite as: arXiv:2308.03344 [quant-ph] (or arXiv:2308.03344v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2308.03344 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Shang-Wei Lin [view email] [v1] Mon, 7 Aug 2023 06:52:06 UTC (228 KB) Full-text links: Access Paper: View a PDF of the paper titled A Parallel and Distributed Quantum SAT Solver Based on Entanglement and Quantum Teleportation, by Shang-Wei Lin and 5 other authorsView PDFTeX Source view license Current browse context: quant-ph new | recent | 2023-08 Change to browse by: cs cs.DC 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?)