The constituent parts of a quantum computer are inherently vulnerable to
errors. To this end we have developed quantum error-correcting codes to protect
quantum information from noise. However, discovering codes that are capable of
a universal set of computational operations with the minimal cost in quantum
resources remains an important and ongoing challenge. One proposal of
significant recent interest is the gauge color code. Notably, this code may
offer a reduced resource cost over other well-studied fault-tolerant
architectures using a new method, known as gauge fixing, for performing the
non-Clifford logical operations that are essential for universal quantum
computation. Here we examine the gauge color code when it is subject to noise.
Specifically we make use of single-shot error correction to develop a simple
decoding algorithm for the gauge color code, and we numerically analyse its
performance. Remarkably, we find threshold error rates comparable to those of
other leading proposals. Our results thus provide encouraging preliminary data
of a comparative study between the gauge color code and other promising
computational architectures.Comment: v1 - 5+4 pages, 11 figures, comments welcome; v2 - minor revisions,
new supplemental including a discussion on correlated errors and details on
threshold calculations; v3 - Author accepted manuscript. Accepted on
21/06/16. Deposited on 29/07/16. 9+5 pages, 17 figures, new version includes
resource scaling analysis in below threshold regime, see eqn. (4) and methods
sectio
