Abstract
Conventional fault-tolerant quantum error-correction schemes require a number of extra qubits that grow linearly with the code’s maximum stabilizer generator weight. For some common distance-three codes, the recent “flag paradigm” uses just two extra qubits. Chamberland and Beverland [Quantum 2, 53 (2018)] provide a framework for flag error correction of arbitrary-distance codes. However, their construction requires conditions that only some code families are known to satisfy. We give a flag error-correction scheme that works for any stabilizer code, unconditionally. With fast qubit measurement and reset, it uses ≤d+1 extra qubits for a distance-d code.Received 24 January 2020Accepted 29 June 2020DOI:https://doi.org/10.1103/PRXQuantum.1.010302Published 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.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasQuantum error correctionQuantum memoriesQuantum Information
Highlights
In quantum error correction, errors are diagnosed by measuring the code’s check operators
Our protocol might be optimal in the number of ancilla qubits, but it is open to prove this
Good memory allows ancillas to be reset without introducing excessive noise on waiting qubits, and good connectivity allows the data and for each F ∈ v of a given pair (k, v), denote by SF the set that contains all the valid X data corrections for F, in form of binary strings
Summary
Errors are diagnosed by measuring the code’s check operators. Conventional fault-tolerant error-correction schemes [1,2,3,4] need as many ancillas as the maximum stabilizer generator weight. (Detectability requires that each stabilizer generator is measured with a flag circuit that signals whenever s < d/2 faults result in more than s data errors. Provided new flag error-correction schemes that apply to arbitrary distance-three and -five codes, and require, respectively, O(log w) and O(w) ancilla qubits, where w is the maximum stabilizer generator weight. Their schemes are nonadaptive but allow slow qubit reset; each ancilla qubit is measured only once per stabilizer generator
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