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Quantum Physics

arXiv:2308.07915 (quant-ph)
[Submitted on 15 Aug 2023 (v1), last revised 21 Feb 2024 (this version, v2)]

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

Authors:Sergey Bravyi, Andrew W. Cross, Jay M. Gambetta, Dmitri Maslov, Patrick Rall, Theodore J. Yoder
View a PDF of the paper titled High-threshold and low-overhead fault-tolerant quantum memory, by Sergey Bravyi and 5 other authors
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Abstract:Quantum error correction becomes a practical possibility only if the physical error rate is below a threshold value that depends on a particular quantum code, syndrome measurement circuit, and decoding algorithm. Here we present an end-to-end quantum error correction protocol that implements fault-tolerant memory based on a family of LDPC codes with a high encoding rate that achieves an error threshold of $0.8\%$ for the standard circuit-based noise model. This is on par with the surface code which has remained an uncontested leader in terms of its high error threshold for nearly 20 years. The full syndrome measurement cycle for a length-$n$ code in our family requires $n$ ancillary qubits and a depth-7 circuit composed of nearest-neighbor CNOT gates. The required qubit connectivity is a degree-6 graph that consists of two edge-disjoint planar subgraphs. As a concrete example, we show that 12 logical qubits can be preserved for nearly one million syndrome cycles using 288 physical qubits in total, assuming the physical error rate of $0.1\%$. We argue that achieving the same level of error suppression on 12 logical qubits with the surface code would require nearly 3000 physical qubits. Our findings bring demonstrations of a low-overhead fault-tolerant quantum memory within the reach of near-term quantum processors.
Comments: numerical results are revised after fixing a bug in the simulation software
Subjects: Quantum Physics (quant-ph); Emerging Technologies (cs.ET)
Cite as: arXiv:2308.07915 [quant-ph]
  (or arXiv:2308.07915v2 [quant-ph] for this version)
  https://doi.org/10.48550/arXiv.2308.07915
arXiv-issued DOI via DataCite
Journal reference: Nature 627, 778-782 (2024)
Related DOI: https://doi.org/10.1038/s41586-024-07107-7
DOI(s) linking to related resources

Submission history

From: Dmitri Maslov [view email]
[v1] Tue, 15 Aug 2023 17:55:12 UTC (1,838 KB)
[v2] Wed, 21 Feb 2024 00:30:47 UTC (237 KB)
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