Towards Lattice Surgery Compilation for the Color Code Using Pipe Diagrams

Quantum Physics arXiv:2607.05501 (quant-ph) [Submitted on 6 Jul 2026] Title:Towards Lattice Surgery Compilation for the Color Code Using Pipe Diagrams Authors:Laura S. Herzog, Gilad Kishony, Robert Wille, Austin Fowler View a PDF of the paper titled Towards Lattice Surgery Compilation for the Color Code Using Pipe Diagrams, by Laura S. Herzog and 3 other authors View PDF HTML (experimental) Abstract:Pipe diagrams have emerged as a powerful framework for flexible lattice surgery compilation and spacetime optimization for the surface code. In contrast, analogous compilation techniques for color code architectures remain largely unexplored, despite the color code's favorable properties, including reduced qubit overhead and transversal single-qubit Clifford gates. In this work, we develop a pipe diagram representation for the triangular color code on the 6.6.6 lattice and establish its correspondence to ZX-diagrammatic descriptions of computation. We present distance-independent constructions of color code pipe diagrams together with explicit realizations of correlation surfaces, stabilizers, and syndrome extraction circuits. This framework enables both macroscopic optimization of logical computations in spacetime and microscopic compilation to executable syndrome extraction circuits. We demonstrate the potential for compact spacetime embeddings with the color code's geometry. These results provide a foundation for automated lattice surgery compilation and diagrammatic optimization in color code architectures. Subjects: Quantum Physics (quant-ph); Emerging Technologies (cs.ET) Cite as: arXiv:2607.05501 [quant-ph] (or arXiv:2607.05501v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2607.05501 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Laura Sofie Herzog [view email] [v1] Mon, 6 Jul 2026 18:00:02 UTC (2,777 KB) Full-text links: Access Paper: View a PDF of the paper titled Towards Lattice Surgery Compilation for the Color Code Using Pipe Diagrams, by Laura S. Herzog and 3 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-07 Change to browse by: cs cs.ET 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?)