Low-Overhead Fault-Tolerant Quantum Error Correction with the Surface-GKP Code
Abstract
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.
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.Attached Files
Published - PRXQuantum.3.010315.pdf
Submitted - 2103.06994.pdf
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Additional details
- Eprint ID
- 109083
- Resolver ID
- CaltechAUTHORS:20210511-130157842
- Created
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2021-05-11Created from EPrint's datestamp field
- Updated
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2022-02-01Created from EPrint's last_modified field
- Caltech groups
- AWS Center for Quantum Computing, Institute for Quantum Information and Matter