Fault-tolerant quantum error correction for constant-excitation stabilizer codes under coherent noise

Abstract Collective coherent (CC) noise poses challenges for fault-tolerant error correction (FTEC), as it is not captured by conventional stochastic noise models. Constant-excitation (CE) codes are inherently immune to CC errors, but a fault-tolerant framework for operating these codes under circuit-level noise has not yet been established. Here, we develop an FTEC framework for CE CSS codes based on dual-rail concatenation. We show that conventional transversal CNOT gates violate the CE constraint and develop CE-preserving logical CNOT gates together with modified Shor- and Steane-type syndrome extraction schemes using zero-controlled NOT gates and CE-compatible ancilla states. We further develop an extended stabilizer simulation algorithm that tracks both stochastic and CC noise. Using this framework, we identify small distance-3 CE CSS codes demonstrate that the [[14, 1, 3]] code maintains robust performance under coherent noise. Our results establish a fault-tolerant framework for CE codes under circuit-level noise and demonstrate their potential for quantum processors affected by CC noise.