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.

21 pages, 13 figures. Updated algorithms, added baseline simulations, and revised several proofs for greater rigor

Quantum Physics (quant-ph); Information Theory (cs.IT)

arXiv:2507.10395 [quant-ph]

(or arXiv:2507.10395v2 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2507.10395 Focus to learn more arXiv-issued DOI via DataCite

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