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Low-Overhead Fault-Tolerant Quantum Error Correction with the Surface-GKP Code

Noh, Kyungjoo and Chamberland, Christopher and Brandão, Fernando G. S. L. (2022) Low-Overhead Fault-Tolerant Quantum Error Correction with the Surface-GKP Code. PRX Quantum, 3 (1). Art. No. 010315. ISSN 2691-3399. doi:10.1103/PRXQuantum.3.010315.

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Fault-tolerant quantum error correction is essential for implementing quantum algorithms of significant practical importance. In this work, we propose a highly effective use of the surface Gottesman-Kitaev-Preskill (GKP) code, i.e., the surface code consisting of bosonic GKP qubits instead of bare two-level qubits. In our proposal, we use error-corrected two-qubit gates between GKP qubits and introduce a maximum-likelihood decoding strategy for correcting shift errors in the two-GKP-qubit gates. Our proposed decoding reduces the total CNOT failure rate of the GKP qubits, e.g., from 0.87% to 0.36% at a GKP squeezing of 12 dB, compared to the case where the simple closest-integer decoding is used. Then, by concatenating the GKP code with the surface code, we find that the threshold GKP squeezing is given by 9.9 dB under the the assumption that finite squeezing of the GKP states is the dominant noise source. More importantly, we show that a low logical failure rate p_L < 10⁻⁷ can be achieved with moderate hardware requirements, e.g., 291 modes and 97 qubits at a GKP squeezing of 12 dB as opposed to 1457 bare qubits for the standard rotated surface code at an equivalent noise level (i.e., p=0.36%). Such a low failure rate of our surface-GKP code is possible through the use of space-time correlated edges in the matching graphs of the surface-code decoder. Further, all edge weights in the matching graphs are computed dynamically based on analog information from the GKP error correction using the full history of all syndrome measurement rounds. We also show that a highly squeezed GKP state of GKP squeezing ≳12 dB can be experimentally realized by using a dissipative stabilization method, namely, the big-small-big method, with fairly conservative experimental parameters. Lastly, we introduce a three-level ancilla scheme to mitigate ancilla decay errors during a GKP state preparation.

Item Type:Article
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URLURL TypeDescription Paper
Noh, Kyungjoo0000-0002-6318-8472
Chamberland, Christopher0000-0003-3239-5783
Brandão, Fernando G. S. L.0000-0003-3866-9378
Additional Information:© 2022 Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. Received 13 August 2021; accepted 6 January 2022; published 28 January 2022. We would like to acknowledge the AWS EC2 resources, which were used for part of the simulations performed in this work.
Group:AWS Center for Quantum Computing, Institute for Quantum Information and Matter
Issue or Number:1
Record Number:CaltechAUTHORS:20210511-130157842
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:109083
Deposited By: Tony Diaz
Deposited On:11 May 2021 20:35
Last Modified:01 Feb 2022 17:42

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