Fast qubit-based frequency recovery algorithm for quantum key distribution

Abstract: Clock synchronization serves as a foundational subsystem in quantum key distribution (QKD). The recently proposed Qubit-based synchronization (Qubit4Sync) has opportunities in eliminating additional cost, noise, and potential side channels. It offers a promising alternative to dedicated synchronization hardware. However, the current frequency recovery process in Qubit4Sync requires high data throughput and computational speed, limiting practical use. To overcome these issues, we developed a fast frequency recovery algorithm that increases the recovery rate by orders of magnitude and remains robust under bad signal-to-noise ratio (SNR). This enables Qubit4Sync to operate effectively in mainstream gated-mode QKD systems. We further establish a theoretical model for frequency recovery, showing that our algorithm is robust against disturbances like dead time, jitter, and afterpulse. A frequency-domain SNR calculation method is also provided to guide parameter design for specific experimental conditions. This work opens the door to practical Qubit4Sync deployment in general QKD systems.