Zijian Liang, Yu-An Chen (Oct 08 2025).
Abstract: Bivariate bicycle codes are promising candidates for high-threshold, low-overhead fault-tolerant quantum memories. Meanwhile, color codes are the most prominent self-dual CSS codes, supporting transversal Clifford gates that have been demonstrated experimentally. In this work, we combine these advantages and introduce a broad family of self-dual bivariate bicycle codes. These codes achieve higher encoding rates than surface and color codes while admitting transversal CNOT, Hadamard, and
S gates. In particular, we enumerate weight-8 self-dual bivariate bicycle codes with up to
n≤200 physical qubits, realized on twisted tori that enhance code distance and improve stabilizer locality. Representative examples include codes with parameters
[[n,k,d]]:
[[16,4,4]],
[[40,6,6]],
[[56,6,8]],
[[64,8,8]],
[[120,8,12]],
[[152,6,16]], and
[[160,8,16]].