Near-optimal high-rate surgery from linear PCPPs

Quantum Physics arXiv:2609.26973 (quant-ph) [Submitted on 22 Sep 2026] Title:Near-optimal high-rate surgery from linear PCPPs Authors:Alexander Cowtan, Benjamin Ide View a PDF of the paper titled Near-optimal high-rate surgery from linear PCPPs, by Alexander Cowtan and Benjamin Ide View PDF HTML (experimental) Abstract:A central problem for surgery with quantum Low-Density Parity Check (LDPC) codes is the design of auxiliary systems which measure large sets of logical operators in parallel, while preserving sparsity and fault distance. We introduce a very general method for designing surgery gadgets which are 'high rate', meaning that the number of operators measured in parallel is large in comparison to the size of the auxiliary system. Given an arbitrary initial $[[ n, k, d ]]$ quantum LDPC Calderbank-Shor-Steane (CSS) code, and an arbitrary subcode of size $\mu \leq n$ that contains $t \leq k$ logical qubits, the method produces a sparse high-rate surgery gadget with size $\mu (\log\mu)^{O(\log\log \mu)}=\mu^{1+o(1)}$ which measures all $t$ logicals in the subcode. The space overhead is asymptotically optimal up to subpolynomial factors, as the lower bound is $\Omega(\mu)$. This gadget is produced in time polynomial in $\mu$. When logical measurement is performed using these surgery gadgets, the phenomenological fault distance is at least $d$ when performed for $d$ rounds. Our main result comes from relating surgery gadgets with relative cosystolic expansion to linear Probabilistically Checkable Proofs of Proximity (PCPPs), which allow a randomised verifier to probabilistically verify the input to a linear circuit, using only oracle access to the input and a claimed proof. Comments: Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2609.26973 [quant-ph] (or arXiv:2609.26973v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2609.26973 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Alexander Cowtan [view email] [v1] Tue, 22 Sep 2026 19:09:42 UTC (40 KB) Full-text links: Access Paper: View a PDF of the paper titled Near-optimal high-rate surgery from linear PCPPs, by Alexander Cowtan and Benjamin IdeView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-09 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?)