Optimized Many-Hypercube Codes toward Lower Logical Error Rates and Earlier Realization

Quantum Physics arXiv:2512.00561 (quant-ph) [Submitted on 29 Nov 2025] Title:Optimized Many-Hypercube Codes toward Lower Logical Error Rates and Earlier Realization Authors:Hayato Goto View a PDF of the paper titled Optimized Many-Hypercube Codes toward Lower Logical Error Rates and Earlier Realization, by Hayato Goto View PDF HTML (experimental) Abstract:Many-hypercube codes [H. Goto, Sci. Adv. 10, eadp6388 (2024)], concatenated ${[[n,n-2,2]]}$ quantum error-detecting codes ($n$ is even), have recently been proposed as high-rate quantum codes suitable for fault-tolerant quantum computing. However, the original many-hypercube codes with ${n=6}$ have large code block sizes at high concatenation levels (216 and 1296 physical qubits per block at levels 3 and 4, respectively), making not only experimental realization difficult but also logical error rates high. Toward earlier experimental realization and lower logical error rates, here we investigate smaller many-hypercube codes obtained by concatenating $[[6,4,2]]$ and/or $[[4,2,2]]$ codes, where, e.g., $D_{6,4,4}$ denotes the many-hypercube code using $[[6,4,2]]$ at level 1 and $[[4,2,2]]$ at levels 2 and 3. As a result, we found a surprising fact: $D_{6,4,4}$ ($D_{6,6,4,4}$) can achieve lower block error rates than $D_{4,4,4}$ ($D_{4,4,4,4}$), despite its higher encoding rate. Focusing on level 3, we also developed efficient fault-tolerant encoders realizing about 60% overhead reduction while maintaining or even improving the performance, compared to the original design. Using them, we numerically confirmed that $D_{6,4,4}$ also achieves the best performance for logical controlled-NOT gates in a circuit-level noise model. These results will be useful for early experimental realization of fault-tolerant quantum computing with high-rate quantum codes. Comments: Subjects: Quantum Physics (quant-ph); Hardware Architecture (cs.AR) Cite as: arXiv:2512.00561 [quant-ph] (or arXiv:2512.00561v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2512.00561 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Hayato Goto [view email] [v1] Sat, 29 Nov 2025 17:11:50 UTC (1,009 KB) Full-text links: Access Paper: View a PDF of the paper titled Optimized Many-Hypercube Codes toward Lower Logical Error Rates and Earlier Realization, by Hayato GotoView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2025-12 Change to browse by: cs cs.AR 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?) Links to Code Toggle Papers with Code (What is Papers with Code?) 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?)