Quantum error correction with the color-Gottesman-Kitaev-Preskill code
- URL: http://arxiv.org/abs/2112.14447v2
- Date: Thu, 30 Dec 2021 03:03:55 GMT
- Title: Quantum error correction with the color-Gottesman-Kitaev-Preskill code
- Authors: Jiaxuan Zhang, Jian Zhao, Yu-Chun Wu, and Guo-Ping Guo
- Abstract summary: The Gottesman-Kitaev-Preskill (GKP) code is an important type of bosonic quantum error-correcting code.
In this paper, we consider the concatenation of the single-mode GKP code with the two-dimension (2D) color code.
- Score: 5.780815306252637
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: The Gottesman-Kitaev-Preskill (GKP) code is an important type of bosonic
quantum error-correcting code. Since the GKP code only protects against small
shift errors in $\hat{p}$ and $\hat{q}$ quadratures, it is necessary to
concatenate the GKP code with a stabilizer code for the larger error
correction. In this paper, we consider the concatenation of the single-mode GKP
code with the two-dimension (2D) color code (color-GKP code) on the
square-octagon lattice. We use the Steane type scheme with a maximum-likelihood
estimation (ME-Steane scheme) for GKP error correction and show its advantage
for the concatenation. In our main work, the minimum-weight perfect matching
(MWPM) algorithm is applied to decode the color-GKP code. Complemented with the
continuous-variable information from the GKP code, the threshold of 2D color
code is improved. If only data GKP qubits are noisy, the threshold reaches
$\sigma\approx 0.59$ $(\bar{p}\approx13.3\%)$ compared with $\bar{p}=10.2\%$ of
the normal 2D color code. If measurements are also noisy, we introduce the
generalized Restriction Decoder on the three-dimension space-time graph for
decoding. The threshold reaches $\sigma\approx 0.46$ when measurements in the
GKP error correction are noiseless, and $\sigma\approx 0.24$ when all
measurements are noisy. Lastly, the good performance of the generalized
Restriction Decoder is also shown on the normal 2D color code giving the
threshold at $3.1\%$ under the phenomenological error model.
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