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