Biased Gottesman-Kitaev-Preskill repetition code
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| author | Stafford, Matthew P. Menicucci, Nicolas C. |
| author_facet | Stafford, Matthew P. Menicucci, Nicolas C. |
| contents | 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 $σ= 0.599$ 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 $σ\leq 0.3$, opening the possibility of using GKP-biased repetition codes as a simple low-level qubit encoding for further concatenation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2212_11397 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Biased Gottesman-Kitaev-Preskill repetition code Stafford, Matthew P. Menicucci, Nicolas C. Quantum Physics 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 $σ= 0.599$ 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 $σ\leq 0.3$, opening the possibility of using GKP-biased repetition codes as a simple low-level qubit encoding for further concatenation. |
| title | Biased Gottesman-Kitaev-Preskill repetition code |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2212.11397 |