eprintid: 1494042 rev_number: 37 eprint_status: archive userid: 608 dir: disk0/01/49/40/42 datestamp: 2016-05-29 04:29:30 lastmod: 2021-10-04 01:39:34 status_changed: 2018-01-04 13:11:33 type: article metadata_visibility: show creators_name: Watson, FHE creators_name: Campbell, ET creators_name: Anwar, H creators_name: Browne, DE title: Qudit color codes and gauge color codes in all spatial dimensions ispublished: pub divisions: UCL divisions: B04 divisions: C06 divisions: F60 note: This version is the version of record. For information on re-use, please refer to the publisher’s terms and conditions. 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. date: 2015-08-07 date_type: published publisher: AMER PHYSICAL SOC official_url: http://doi.org/10.1103/PhysRevA.92.022312 oa_status: green full_text_type: pub language: eng primo: open primo_central: open_green verified: verified_manual elements_id: 1053632 doi: 10.1103/PhysRevA.92.022312 lyricists_name: Browne, Daniel lyricists_id: DEBRO32 actors_name: Waragoda Vitharana, Nimal actors_id: NWARR44 actors_role: owner full_text_status: public publication: Physical Review A volume: 92 number: 2 article_number: 022312 pages: 15 issn: 1094-1622 citation: 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 <https://doi.org/10.1103/PhysRevA.92.022312>. Green open access document_url: https://discovery.ucl.ac.uk/id/eprint/1494042/1/Browne_PhysRevA.92.022312.pdf