High-threshold and low-overhead fault-tolerant quantum memory

S. Bravyi et al. · 2023 · Nature

| 编号 QE120 | 主题 qLDPC 码 | 链接 arXiv:2308.07915 |

摘要

摘要保留原文（英文）

摘要取自 arXiv / 出版方元数据，未作翻译，以保证与原文一致。

The accumulation of physical errors1–3 prevents the execution of large-scale algorithms in current quantum computers. Quantum error correction4 promises a solution by encoding k logical qubits onto a larger number n of physical qubits, such that the physical errors are suppressed enough to allow running a desired computation with tolerable fidelity. Quantum error correction becomes practically realizable once the physical error rate is below a threshold value that depends on the choice of quantum code, syndrome measurement circuit and decoding algorithm5. We present an end-to-end quantum error correction protocol that implements fault-tolerant memory on the basis of a family of low-density parity-check codes6. Our approach achieves an error threshold of 0.7% for the standard circuit-based noise model, on par with the surface code7–10 that for 20 years was the leading code in terms of error threshold. The syndrome measurement cycle for a length-n code in our family requires n ancillary qubits and a depth-8 circuit with CNOT gates, qubit initializations and measurements. The required qubit connectivity is a degree-6 graph composed of two edge-disjoint planar subgraphs. In particular,

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