Clock-offset recovery with sublinear complexity enables synchronization on low-level hardware for quantum key distribution

We introduce iQSync, a clock-offset recovery method designed for implementation on low-level hardware, such as field-programmable gate arrays or microcontrollers, for quantum key distribution (QKD). iQSync requires minimal memory, only a simple instruction set (e.g., no floating-point operations), and can be evaluated with sublinear time complexity, typically involving no more than a few thousand iterations of a simple loop. Furthermore, iQSync allows for a precise clock-offset recovery within a few seconds, even for large offsets, and is well suited for scenarios with high channel loss and low signal-to-noise ratio, irrespective of the prepare-and-measure QKD protocol used. We implemented the method on our QKD platform, demonstrating its performance and conformity with analytically derived success probabilities for channel attenuations exceeding <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"><a:mn>70</a:mn><a:mspace width="0.2em"/><a:mi>dB</a:mi></a:math>.