Journal Article

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

Yoder, Theodore J., Gambetta, Jay M., Bravyi, Sergey, Maslov, Dmitri, Cross, Andrew W., Rall, Patrick

2024

Overview

The accumulation of physical errors 1 – 3 prevents the execution of large-scale algorithms in current quantum computers. Quantum error correction 4 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 5 . 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 6 . Our approach achieves an error threshold of 0.7% for the standard circuit-based noise model, on par with the surface code 7 – 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. 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 shows the possibility of low-overhead fault-tolerant quantum memory within the reach of near-term quantum processors.

• Publisher: Nature Publishing Group UK,Nature Publishing Group
• Subject: 639/705/117 / 639/766/483/481 / 639/766/483/640 / Algorithms / Codes / Computers / Decoding / Error correcting codes / Error correction / Error correction & detection / Fault tolerance / Gates (circuits) / Graph theory / Humanities and Social Sciences / Low density parity check codes / multidisciplinary / Quantum computers / Quantum computing / Quantum phenomena / Qubits (quantum computing) / Science / Science (multidisciplinary)