A 67%-Rate CSS Code on the FCC Lattice: [[192,130,3]] from Weight-12 Stabilizers

Quantum Physics [Submitted on 19 Mar 2026] A 67%-Rate CSS Code on the FCC Lattice: [[192,130,3]] from Weight-12 Stabilizers Raghu Kulkarni We construct a three-dimensional Calderbank-Shor-Steane (CSS) stabilizer code on the Face-Centered Cubic (FCC) lattice. Physical qubits reside on the edges of the lattice (coordination K=12); X-stabilizers act on octahedral voids and Z-stabilizers on vertices, both with uniform weight 12. Computational verification confirms CSS validity (H_{X}H_{Z}^{T}=0 over GF(2)) and reveals k=2L^{3}+2 logical qubits: k=130 at L=4 and k=434 at L=6, yielding encoding rates of 67.7% and 67.0% respectively. The minimum distance d=3 is proven exactly by exhaustive elimination of all weight-\le 2 candidates combined with constructive weight-3 non-stabilizer codewords. The code parameters are [[192, 130, 3]] at L=4 and [[648, 434, 3]] at L=6. This rate is 24x higher than the cubic 3D toric code (2.8% at d=4), though at a lower distance (d=3 vs. d=4); the comparison is across different distances. The high rate originates in a structural surplus: the FCC lattice has 3L^{3} edges but only L^{3}-2 independent stabilizer constraints, leaving k=2L^{3}+2 logical degrees of freedom. We provide a minimum-weight perfect matching (MWPM) decoder adapted to the FCC geometry, demonstrate a 10x coding gain at p=0.001 (and 63x at p=0.0005), and discuss implications for fault-tolerant quantum computing on neutral-atom and photonic platforms. Comments: 14 pages, 2 figures, 3 tables, 2 appendices with reproducible Python code Subjects: Quantum Physics (quant-ph) MSC classes: 81P73, 94B60, 52C17 ACM classes: E.4; J.2; F.2.2 Cite as: arXiv:2603.20294 [quant-ph]   (or arXiv:2603.20294v1 [quant-ph] for this version)   https://doi.org/10.48550/arXiv.2603.20294 Focus to learn more Submission history From: Raghu Kulkarni Mr [view email] [v1] Thu, 19 Mar 2026 02:57:55 UTC (98 KB) Access Paper: HTML (experimental) view license Current browse context: quant-ph < prev   |   next > new | recent | 2026-03 References & Citations INSPIRE HEP NASA ADS Google Scholar Semantic Scholar Export BibTeX Citation 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 Demos Related Papers About arXivLabs Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)