Logical Operators and Fold-Transversal Gates of Bivariate Bicycle Codes

• URL: http://arxiv.org/abs/2407.03973v1
• Date: Thu, 4 Jul 2024 14:49:35 GMT
• Title: Logical Operators and Fold-Transversal Gates of Bivariate Bicycle Codes
• Authors: Jens Niklas Eberhardt, Vincent Steffan,
• Abstract summary: 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.
• Score: 1.8416014644193066
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• Abstract: 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.

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