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| Format: | Preprint |
| Veröffentlicht: |
2026
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| Online-Zugang: | https://arxiv.org/abs/2603.20294 |
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| _version_ | 1866911532676284416 |
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| author | Kulkarni, Raghu |
| author_facet | Kulkarni, Raghu |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_20294 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A 67%-Rate CSS Code on the FCC Lattice: [[192,130,3]] from Weight-12 Stabilizers Kulkarni, Raghu Quantum Physics 81P73, 94B60, 52C17 E.4; J.2; F.2.2 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. |
| title | A 67%-Rate CSS Code on the FCC Lattice: [[192,130,3]] from Weight-12 Stabilizers |
| topic | Quantum Physics 81P73, 94B60, 52C17 E.4; J.2; F.2.2 |
| url | https://arxiv.org/abs/2603.20294 |