We introduce a prototype FPGA decoder implementing the recently discovered Relay-BP algorithm and targeting memory experiments on the [[144,12,12]] bivariate bicycle quantum low-density parity check code. The decoder is both fast and accurate, achieving a belief propagation iteration time of 24ns. It matches the logical error performance of a floating-point implementation despite using reduced precision arithmetic. This speed is sufficient for an average per cycle decoding time under 1μs assuming circuit model error probabilities are less than 3×10−3. This prototype decoder offers useful insights on the path toward decoding solutions for scalable fault-tolerant quantum computers.
@article{arxiv.2510.21600,
title = {Real-time decoding of the gross code memory with FPGAs},
author = {Thilo Maurer and Markus Bühler and Michael Kröner and Frank Haverkamp and Tristan Müller and Drew Vandeth and Blake R. Johnson},
journal= {arXiv preprint arXiv:2510.21600},
year = {2025}
}