2026/08/03 by Zhide Lu, Weikang Li, Dong-Ling Deng
Physics and Astronomy · #quant-ph
arxiv created 2026/08/03 · arxiv updated 2026/08/05
Suppressing errors is the central challenge for useful large-scale quantum computing. While quantum error correction promises a viable solution to this challenge, existing codes typically suffer from trade-offs among encoding efficiency, error threshold, and hardware feasibility. Here, we introduce Cornucopia codes, a family of practical, hardware-efficient quantum low-density parity-check codes that achieve an ultra-high encoding rate exceeding 1/2 while maintaining a pseudo-threshold exceeding 0.4% under the standard circuit-level noise model. Inspired by recent affine-permutation-based code constructions and the long-range connectivity available in reconfigurable neutral-atom arrays, we adopt a structured code geometry in which the code layout, atom rearrangement, and syndrome-extraction schedule are co-designed. This structure enables nonlocal syndrome measurements through simple, parallel atom rearrangements. A complete syndrome extraction cycle measures all X- and Z-type checks in parallel with 12 entangling layers, independent of the code size. The resulting threshold is comparable to those of the surface code and bivariate bicycle codes. In particular, a single code block [[2844,1426,18]] encodes 1,426 distance-18 logical qubits, achieving an extrapolated logical error rate of 2.6×10-16 (1.9×10-31) per logical qubit per cycle, assuming the physical error rate of 0.1% (0.01%). By comparison, a bivariate bicycle code implementation would require more than 68,000 physical qubits to encode the same number of logical qubits at a comparable logical error rate. These results bring demonstrations of ultra-low overhead quantum error correction within the reach of near-term quantum processors.