Posted

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 SS gates. In particular, we enumerate weight-8 self-dual bivariate bicycle codes with up to n200n \leq 200 physical qubits, realized on twisted tori that enhance code distance and improve stabilizer locality. Representative examples include codes with parameters [[n,k,d]][[n,k,d]]: [[16,4,4]][[16,4,4]], [[40,6,6]][[40,6,6]], [[56,6,8]][[56,6,8]], [[64,8,8]][[64,8,8]], [[120,8,12]][[120,8,12]], [[152,6,16]][[152,6,16]], and [[160,8,16]][[160,8,16]].

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