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Cornucopia codes represent a significant theoretical advance in quantum error correction by achieving ultra-high encoding rates and low overhead specifically tailored for reconfigurable neutral-atom architectures. This work demonstrates that practical, large-scale fault tolerance may be reachable sooner than previously thought without relying on massive qubit counts typical of surface code implementations. The findings directly address the critical hardware-feasibility trade-offs required to transition quantum computing from experimental prototypes to useful systems.
Quantum error correction at ultra-low overhead
arXiv:2608.02773v1 Announce Type: new Abstract: 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 $2.6\times10^{-16}$ ($1.9\times10^{-31}$) 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.
Abstract: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 $2.6\times10^{-16}$ ($1.9\times10^{-31}$) 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.
arXiv:2608.02773 [quant-ph]
(or arXiv:2608.02773v1 [quant-ph] for this version)
https://doi.org/10.48550/arXiv.2608.02773 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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