Efficient recursive encoders for quantum Reed-Muller codes towards Fault tolerance

Praveen Jayakumar, Priya J. Nadkarni, Shayan Srinivasa Garani · 2024 · arXiv

| 编号 QE072 | 主题 小码与早期码 | 链接 arXiv:2405.14549 |

摘要

摘要保留原文（英文）

摘要取自 arXiv / 出版方元数据，未作翻译，以保证与原文一致。

Transversal gates are logical gate operations on encoded quantum information that are efficient in gate count and depth, and are designed to minimize error propagation. Efficient encoding circuits for quantum codes that admit transversal gates are thus crucial to reduce noise and realize useful quantum computers. The class of punctured Quantum Reed-Muller codes admit transversal gates. We construct resource efficient recursive encoders for the class of quantum codes constructed from Reed-Muller and punctured Reed-Muller codes. These encoders on n qubits have circuit depth of O(log n) and gate count of O(n), improving upon prior encoders.

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