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

The accumulation of physical errors prevents the execution of large-scale algorithms in current quantum computers. Quantum error correction 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...

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Bibliographic Details
Published in:Nature (London) 2024-03, Vol.627 (8005), p.778-782
Main Authors: Bravyi, Sergey, Cross, Andrew W, Gambetta, Jay M, Maslov, Dmitri, Rall, Patrick, Yoder, Theodore J
Format: Article
Language:English
Subjects:
Algorithms
Codes
Computers
Decoding
Error analysis
Error correcting codes
Error correction
Error correction & detection
Fault tolerance
Gates (circuits)
Graph theory
Low density parity check codes
Quantum computers
Quantum computing
Quantum phenomena
Qubits (quantum computing)
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Summary:The accumulation of physical errors prevents the execution of large-scale algorithms in current quantum computers. Quantum error correction 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 algorithm . 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 codes . Our approach achieves an error threshold of 0.7% for the standard circuit-based noise model, on par with the surface code 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.
ISSN:0028-0836
1476-4687
1476-4687
DOI:10.1038/s41586-024-07107-7