Self-dual bivariate bicycle codes with transversal Clifford gates

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]].