Optimal Toffoli-Depth Multi-Controlled Toffoli Decomposition in 2D Qubit Layout
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Quantum Physics arXiv:2606.15113 (quant-ph) [Submitted on 13 Jun 2026] Title:Optimal Toffoli-Depth Multi-Controlled Toffoli Decomposition in 2D Qubit Layout Authors:Anik Basu Bhaumik, Suman Dutta, Anupam Chattopadhyay View a PDF of the paper titled Optimal Toffoli-Depth Multi-Controlled Toffoli Decomposition in 2D Qubit Layout, by Anik Basu Bhaumik and 2 other authors View PDF Abstract:The multi-controlled Toffoli (MCT) gate is a key primitive in quantum arithmetic, oracle construction, and quantum cryptanalysis. Although recent work has established optimal Toffoli-depth MCT decompositions under all-to-all qubit connectivity, their realization on near-term quantum hardware with restricted qubit connectivity remains largely unexplored. While general-purpose quantum mappers can route arbitrary circuits, they do not explicitly exploit the repeated interaction patterns inherent in MCT decompositions. In our present paper, we study architecture-aware mappings of optimal Toffoli-depth MCT decompositions onto restricted two-dimensional qubit layouts. We begin with a structured geometric placements that preserve the parallelism of state-of-the-art Toffoli and MCT decompositions with no additional depth overhead. We further introduce a motif-based packing framework in which decomposition layers are represented by interaction motifs derived from basic Toffoli gates. By embedding these motifs vertex-disjointly into hardware graphs, we characterize the minimum-size topologies supporting the required qubit resources and derive explicit bounds on the resulting depth overhead under tight qubit budgets. Finally, we compare these bounds with routing-aware placement heuristics and empirically evaluate the effectiveness of embedding different motifs across a range of hardware topologies. Comments: Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2606.15113 [quant-ph] (or arXiv:2606.15113v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2606.15113 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Suman Dutta [view email] [v1] Sat, 13 Jun 2026 05:02:39 UTC (1,082 KB) Full-text links: Access Paper: View a PDF of the paper titled Optimal Toffoli-Depth Multi-Controlled Toffoli Decomposition in 2D Qubit Layout, by Anik Basu Bhaumik and 2 other authorsView PDFTeX Source view license Current browse context: quant-ph new | recent | 2026-06 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?)