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Qudit color codes and gauge color codes in all spatial dimensions

Watson, FHE; Campbell, ET; Anwar, H; Browne, DE; (2015) Qudit color codes and gauge color codes in all spatial dimensions. Physical Review A , 92 (2) , Article 022312. 10.1103/PhysRevA.92.022312. Green open access

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Abstract

The surface code is one of the most promising candidates for combating errors in large scale fault-tolerant quantum computation. A fault-tolerant decoder is a vital part of the error correction process—it is the algorithm which computes the operations needed to correct or compensate for the errors according to the measured syndrome, even when the measurement itself is error prone. Previously decoders based on minimum-weight perfect matching have been studied. However, these are not immediately generalizable from qubit to qudit codes. In this work, we develop a fault-tolerant decoder for the surface code, capable of efficient operation for qubits and qudits of any dimension, generalizing the decoder first introduced by Bravyi and Haah [Phys. Rev. Lett. 111, 200501 (2013)]. We study its performance when both the physical qudits and the syndromes measurements are subject to generalized uncorrelated bit-flip noise (and the higher-dimensional equivalent). We show that, with appropriate enhancements to the decoder and a high enough qudit dimension, a threshold at an error rate of more than 8% can be achieved.

Type: Article
Title: Qudit color codes and gauge color codes in all spatial dimensions
Open access status: An open access version is available from UCL Discovery
DOI: 10.1103/PhysRevA.92.022312
Publisher version: http://doi.org/10.1103/PhysRevA.92.022312
Language: English
Additional information: This version is the version of record. For information on re-use, please refer to the publisher’s terms and conditions.
UCL classification: UCL
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Physics and Astronomy
URI: https://discovery.ucl.ac.uk/id/eprint/1494042
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