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| Format: | Preprint |
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2024
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| Accès en ligne: | https://arxiv.org/abs/2404.18302 |
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| _version_ | 1866916661167128576 |
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| author | Novak, Oskar Rengaswamy, Narayanan |
| author_facet | Novak, Oskar Rengaswamy, Narayanan |
| contents | Quantum subsystem codes have been shown to improve error-correction performance, ease the implementation of logical operations on codes, and make stabilizer measurements easier by decomposing stabilizers into smaller-weight gauge operators. In this paper, we present two algorithms that produce new subsystem codes from a "seed" CSS code. They replace some stabilizers of a given CSS code with smaller-weight gauge operators that split the remaining stabilizers, while being compatible with the logical Pauli operators of the code. The algorithms recover the well-known Bacon-Shor code computationally as well as produce a new $\left[\left[ 9,1,2,2 \right]\right]$ rotated surface subsystem code with weight-$3$ gauges and weight-$4$ stabilizers. We illustrate using a $\left[\left[ 100,25,3 \right]\right]$ subsystem hypergraph product (SHP) code that the algorithms can produce more efficient gauge operators than the closed-form expressions of the SHP construction. However, we observe that the stabilizers of the lifted product quantum LDPC codes are more challenging to split into small-weight gauge operators. Hence, we introduce the subsystem lifted product (SLP) code construction and develop a new $\left[\left[ 775, 124, 20 \right]\right]$ code from Tanner's classical quasi-cyclic LDPC code. The code has high-weight stabilizers but all gauge operators that split stabilizers have weight $5$, except one. In contrast, the LP stabilizer code from Tanner's code has parameters $\left[\left[ 1054, 124, 20 \right]\right]$. This serves as a novel example of new subsystem codes that outperform stabilizer versions of them. Finally, based on our experiments, we share some general insights about non-locality's effects on the performance of splitting stabilizers into small-weight gauges. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_18302 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | GNarsil: Splitting Stabilizers into Gauges Novak, Oskar Rengaswamy, Narayanan Quantum Physics Emerging Technologies Quantum subsystem codes have been shown to improve error-correction performance, ease the implementation of logical operations on codes, and make stabilizer measurements easier by decomposing stabilizers into smaller-weight gauge operators. In this paper, we present two algorithms that produce new subsystem codes from a "seed" CSS code. They replace some stabilizers of a given CSS code with smaller-weight gauge operators that split the remaining stabilizers, while being compatible with the logical Pauli operators of the code. The algorithms recover the well-known Bacon-Shor code computationally as well as produce a new $\left[\left[ 9,1,2,2 \right]\right]$ rotated surface subsystem code with weight-$3$ gauges and weight-$4$ stabilizers. We illustrate using a $\left[\left[ 100,25,3 \right]\right]$ subsystem hypergraph product (SHP) code that the algorithms can produce more efficient gauge operators than the closed-form expressions of the SHP construction. However, we observe that the stabilizers of the lifted product quantum LDPC codes are more challenging to split into small-weight gauge operators. Hence, we introduce the subsystem lifted product (SLP) code construction and develop a new $\left[\left[ 775, 124, 20 \right]\right]$ code from Tanner's classical quasi-cyclic LDPC code. The code has high-weight stabilizers but all gauge operators that split stabilizers have weight $5$, except one. In contrast, the LP stabilizer code from Tanner's code has parameters $\left[\left[ 1054, 124, 20 \right]\right]$. This serves as a novel example of new subsystem codes that outperform stabilizer versions of them. Finally, based on our experiments, we share some general insights about non-locality's effects on the performance of splitting stabilizers into small-weight gauges. |
| title | GNarsil: Splitting Stabilizers into Gauges |
| topic | Quantum Physics Emerging Technologies |
| url | https://arxiv.org/abs/2404.18302 |