Local Predecoder to Reduce the Bandwidth and Latency of Quantum Error Correction
Samuel C. Smith, Benjamin J. Brown, Stephen D. Bartlett
Abstract
A fault-tolerant quantum computer will be supported by a classical decoding system interfacing with quantum hardware to perform quantum error correction. It is important that the decoder can keep pace with the quantum clock speed, within the limitations on communication that are imposed by the physical architecture. To this end, we propose a local ``predecoder,'' which makes greedy corrections to reduce the amount of syndrome data sent to a standard matching decoder. We study these classical overheads for the surface code under a phenomenological phase-flip noise model with imperfect measurements. We find substantial improvements in the run time of the global decoder and the communication bandwidth by using the predecoder. For instance, to achieve a logical-failure probability of $f={10}^{\ensuremath{-}15}$ using qubits with physical error rate $p={10}^{\ensuremath{-}3}$ and a distance $d=22$ code, we find that the bandwidth cost is reduced by a factor of 1000 and that the time taken by a matching decoder is sped up by a factor of 200. To achieve this target failure probability, the predecoding approach requires a 50% increase in the qubit count compared with the optimal decoder.