Logical Operators and Fold-Transversal Gates of Bivariate Bicycle Codes
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866929410308833280 |
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| author | Eberhardt, Jens Niklas Steffan, Vincent |
| author_facet | Eberhardt, Jens Niklas Steffan, Vincent |
| contents | Quantum low-density parity-check (qLDPC) codes offer a promising route to scalable fault-tolerant quantum computation with constant overhead. Recent advancements have shown that qLDPC codes can outperform the quantum memory capability of surface codes even with near-term hardware. The question of how to implement logical gates fault-tolerantly for these codes is still open. We present new examples of high-rate bivariate bicycle (BB) codes with enhanced symmetry properties. These codes feature explicit nice bases of logical operators (similar to toric codes) and support fold-transversal Clifford gates without overhead. As examples, we construct $[[98,6,12]]$ and $[[162, 8, 12]]$ BB codes which admit interesting fault-tolerant Clifford gates. Our work also lays the mathematical foundations for explicit bases of logical operators and fold-transversal gates in quantum two-block and group algebra codes, which might be of independent interest. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_03973 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Logical Operators and Fold-Transversal Gates of Bivariate Bicycle Codes Eberhardt, Jens Niklas Steffan, Vincent Quantum Physics Information Theory Quantum low-density parity-check (qLDPC) codes offer a promising route to scalable fault-tolerant quantum computation with constant overhead. Recent advancements have shown that qLDPC codes can outperform the quantum memory capability of surface codes even with near-term hardware. The question of how to implement logical gates fault-tolerantly for these codes is still open. We present new examples of high-rate bivariate bicycle (BB) codes with enhanced symmetry properties. These codes feature explicit nice bases of logical operators (similar to toric codes) and support fold-transversal Clifford gates without overhead. As examples, we construct $[[98,6,12]]$ and $[[162, 8, 12]]$ BB codes which admit interesting fault-tolerant Clifford gates. Our work also lays the mathematical foundations for explicit bases of logical operators and fold-transversal gates in quantum two-block and group algebra codes, which might be of independent interest. |
| title | Logical Operators and Fold-Transversal Gates of Bivariate Bicycle Codes |
| topic | Quantum Physics Information Theory |
| url | https://arxiv.org/abs/2407.03973 |