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

Sergey Bravyi, Andrew W. Cross, Jay M. Gambetta, Dmitri Maslov (), Patrick Rall and Theodore J. Yoder
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Sergey Bravyi: IBM Quantum, IBM T.J. Watson Research Center
Andrew W. Cross: IBM Quantum, IBM T.J. Watson Research Center
Jay M. Gambetta: IBM Quantum, IBM T.J. Watson Research Center
Dmitri Maslov: IBM Quantum, IBM T.J. Watson Research Center
Patrick Rall: IBM Quantum, MIT-IBM Watson AI Laboratory
Theodore J. Yoder: IBM Quantum, IBM T.J. Watson Research Center

Nature, 2024, vol. 627, issue 8005, 778-782

Abstract: Abstract 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, we show that 12 logical qubits can be preserved for nearly 1 million syndrome cycles using 288 physical qubits in total, assuming the physical error rate of 0.1%, whereas the surface code would require nearly 3,000 physical qubits to achieve said performance. Our findings bring demonstrations of a low-overhead fault-tolerant quantum memory within the reach of near-term quantum processors.

Date: 2024
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DOI: 10.1038/s41586-024-07107-7

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