  One of the fundamental challenges in enabling fault-tolerant quantum
computation is realising fast enough quantum decoders. We present a new
two-stage decoder that accelerates the decoding cycle and boosts accuracy. In
the first stage, a partial decoder based on belief propagation is used to
correct errors that occurred with high probability. In the second stage, a
conventional decoder corrects any remaining errors. We study the performance of
our two-stage decoder with simulations using the surface code under
circuit-level noise. When the conventional decoder is minimum-weight perfect
matching, adding the partial decoder decreases bandwidth requirements,
increases speed and improves logical accuracy. Specifically, we observe partial
decoding consistently speeds up the minimum-weight perfect matching stage by
between $2$x-$4$x on average depending on the parameter regime, and raises the
threshold from $0.94\%$ to $1.02\%$.

Quantum Physics