Halving the cost of QROM
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Quantum Physics arXiv:2605.20334 (quant-ph) [Submitted on 19 May 2026] Title:Halving the cost of QROM Authors:Danial Motlagh, Matthew Pocrnic View a PDF of the paper titled Halving the cost of QROM, by Danial Motlagh and Matthew Pocrnic View PDF Abstract:Table lookup, often referred to as quantum read only memory (QROM), is one of the most widely used subroutines in quantum algorithms, and constitutes the majority share of algorithmic overheads in most practical applications of quantum computers. It involves the coherent loading of $N$ bitstrings of length $b$ in superposition, and naively has a non-Clifford cost of $N$ Toffolis. It is known that given access to $b\, \lambda$ dirty qubits, one can reduce the Toffoli cost of QROM to $2\frac{N}{\lambda} + 4b(\lambda - 1)$. In this work, we first present an optimization to reduce this cost to $2\frac{N}{\lambda} + 2b(\lambda - 1) + 2\lambda-6$ by replacing the ``SelectSwap" architecture with ``SelectCopy". We then provide a further optimization for the qubit-constrained regime where the Toffoli cost is typically $\sim 2\frac{N}{\lambda}$, and reduce it to $\sim (1+\frac{1}{b})\frac{N}{\lambda}$, cutting the cost by approximately $50\%$ and effectively matching the performance of clean-qubit QROM using dirty qubits for practical values of $b$. Lastly, we provide a parametric family of methods that allow the interpolation of the prefactor of the $\frac{N}{\lambda} $ term from $2$ to ($\, 1+\frac{1}{b}\,$) to obtain the best cost for different qubit availability regimes. Comments: Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2605.20334 [quant-ph] (or arXiv:2605.20334v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2605.20334 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Matthew Pocrnic [view email] [v1] Tue, 19 May 2026 18:00:04 UTC (221 KB) Full-text links: Access Paper: View a PDF of the paper titled Halving the cost of QROM, by Danial Motlagh and Matthew PocrnicView PDFTeX Source view license Current browse context: quant-ph new | recent | 2026-05 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?)