Biased Gottesman-Kitaev-Preskill repetition code
- URL: http://arxiv.org/abs/2212.11397v2
- Date: Fri, 1 Dec 2023 04:43:26 GMT
- Title: Biased Gottesman-Kitaev-Preskill repetition code
- Authors: Matthew P. Stafford, Nicolas C. Menicucci
- Abstract summary: Continuous-variable quantum computing architectures based upon the Gottesmann-Kitaev-Preskill (GKP) encoding have emerged as a promising candidate.
We study the code-capacity behaviour of a rectangular-lattice GKP encoding with a repetition code under an isotropic Gaussian displacement channel.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: Continuous-variable quantum computing architectures based upon the
Gottesmann-Kitaev-Preskill (GKP) encoding have emerged as a promising candidate
because one can achieve fault-tolerance with a probabilistic supply of GKP
states and Gaussian operations. Furthermore, by generalising to
rectangular-lattice GKP states, a bias can be introduced and exploited through
concatenation with qubit codes that show improved performance under biasing.
However, these codes (such as the XZZX surface code) still require weight-four
stabiliser measurements and have complex decoding requirements to overcome. In
this work, we study the code-capacity behaviour of a rectangular-lattice GKP
encoding concatenated with a repetition code under an isotropic Gaussian
displacement channel. We find a numerical threshold of $\sigma = 0.599$ for the
noise's standard deviation, which outperforms the biased GKP planar surface
code with a trade-off of increased biasing at the GKP level. This is all
achieved with only weight-two stabiliser operators and simple decoding at the
qubit level. Furthermore, with moderate levels of bias (aspect ratio $\leq
2.4$) and nine or fewer data modes, significant reductions in logical error
rates can still be achieved for $\sigma \leq 0.3$, opening the possibility of
using GKP-biased repetition codes as a simple low-level qubit encoding for
further concatenation.
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