A local pre-decoder to reduce the bandwidth and latency of quantum error correction

TL;DR

This paper introduces a local pre-decoder for quantum error correction that significantly reduces bandwidth and latency, enabling faster and more efficient fault-tolerant quantum computing with manageable qubit overhead.

Contribution

It proposes a local pre-decoder that makes greedy corrections to decrease syndrome data sent to the global decoder, improving runtime and communication efficiency in surface code error correction.

Findings

Bandwidth cost reduced by a factor of 1000

Decoder runtime sped up by a factor of 200

Requires 50% more qubits for target failure probability

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 `pre-decoder', 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 runtime of the global decoder and the communication bandwidth by using the pre-decoder. For instance, to achieve a logical failure probability of $f = 10^{-15}$ using qubits with physical error rate $p = 10^{-3}$ and a distance $d=22$ code, we find that the bandwidth cost is reduced by a factor of $1000$, and the time taken by a matching decoder is sped up by a factor of $200$. To achieve this target failure probability, the pre-decoding approach requires a $50\%$ increase in the qubit count compared with the optimal decoder.