Fault-Tolerant Quantum Communication Systems Using Clifford Hierarchy-based CSS Codes

Abstract Recent advances in quantum communication demand the development of a robust quantum infrastructure for secure data transmission across multimodal networks. Quantum communication transmits information using quantum states (qubits), which act as fundamental units and are vulnerable to noise, decoherence, and hardware imperfections in optical networks. This paper presents a fault-tolerant framework for quantum communication. It integrates Clifford hierarchy-based diagonal gates with Calderbank-Shor-Steane (CSS) codes to ensure error-resilient operation. The proposed scheme uses recursive algebraic structures, including transversal Clifford gates (T, CZ, CCZ). It also employs concatenated Reed-Muller code families to build logical operators that maintain fault tolerance under realistic channel conditions. The recursive algebraic structure of the Clifford hierarchy and the application of quantum Reed-Muller code families in this study provide reliable fault tolerant links and quantum key distribution (QKD) mechanisms for effective noise mitigation. Channel modeling is performed for both fiber-based and free-space optical links, incorporating depolarizing noise, photon loss, and detector dark counts to evaluate system reliability. The Steane and Reed-Muller codes effectively depolarize noise and minimize the logical error rate to an optimum level. Simulation results demonstrate that the proposed coding scheme reduces logical error rates by nearly an order of magnitude compared to unencoded qubits, maintains state fidelity above 0.9 under moderate loss conditions, and achieves secure key rates well beyond the 7% QBER threshold of the conventional BB84 protocol. The results extend the operational noise tolerance of QKD systems under realistic fiber-based conditions and highlight the framework’s adaptability to free-space optical channels. Overall, the developed framework bridges the gap between mathematical fault-tolerant code design and practical quantum communication architectures.