تقرير
Logical Operators and Fold-Transversal Gates of Bivariate Bicycle Codes
| العنوان: | Logical Operators and Fold-Transversal Gates of Bivariate Bicycle Codes |
|---|---|
| المؤلفون: | Eberhardt, Jens Niklas, Steffan, Vincent |
| سنة النشر: | 2024 |
| المجموعة: | Computer Science Mathematics Quantum Physics |
| مصطلحات موضوعية: | Quantum Physics, Computer Science - Information Theory |
| الوصف: | 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. Comment: 21 pages, comments welcome |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2407.03973 |
| رقم الأكسشن: | edsarx.2407.03973 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |