Efficient Routing of Quantum LDPC Codes on Programmable 2D Toric Architectures
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Quantum Physics arXiv:2604.18714 (quant-ph) [Submitted on 20 Apr 2026] Title:Efficient Routing of Quantum LDPC Codes on Programmable 2D Toric Architectures Authors:Kun Liu, Takahiro Tsunoda, Sophia H. Xue, Evan McKinney, Zeyuan Zhou, Shifan Xu, Robert J. Schoelkopf, Yongshan Ding View a PDF of the paper titled Efficient Routing of Quantum LDPC Codes on Programmable 2D Toric Architectures, by Kun Liu and 7 other authors View PDF HTML (experimental) Abstract:Quantum low-density parity-check codes are promising candidates towards scalable fault-tolerant quantum computation. Among these, bivariate bicycle (BB) codes offer superior encoding rates and large code distance compared to surface codes. However, their requirement on long-range stabilizer measurements poses significant challenges for implementation on realistic hardware with limited connectivity, such as superconducting circuit platforms. In this work, we introduce a novel hardware-software co-design that leverages a programmable communication network architecture to address these limitations. Our approach utilizes a 2D toric network of oscillators as a flexible communication fabric linking qubits at each site. Such architecture significantly reduces the number of long-range couplers required from $O(n)$ to $O(\sqrt{n})$. Dual-rail qubits, along with native gates including Swap-Wait-Swap gates and beamsplitter SWAPs, ensure that long-range two-qubit gates can be executed with high fidelity and low latency. To further enhance performance, our qubit layout and routing algorithm utilize symmetries of the codes and enable maximum parallelism for long-range two-qubit gates, maintaining a low syndrome extraction cycle duration and scalability over the code length. We perform circuit-level simulation with realistic noise modeling based on experimental hardware parameters, observing an logical error rate per logical qubit per cycle of 3.06\% for $[[18, 4, 4]]$ BB code, 2.6$\times$ less than the existing experimental result. These findings provide a practical roadmap and identify key technological advancements needed to achieve low-overhead fault-tolerant quantum computing at scale. Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2604.18714 [quant-ph] (or arXiv:2604.18714v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2604.18714 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Kun Liu [view email] [v1] Mon, 20 Apr 2026 18:14:28 UTC (2,750 KB) Full-text links: Access Paper: View a PDF of the paper titled Efficient Routing of Quantum LDPC Codes on Programmable 2D Toric Architectures, by Kun Liu and 7 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-04 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?)