Beam search decoder for quantum LDPC codes

We propose a decoder for quantum low density parity check (LDPC) codes based on a beam search heuristic guided by belief propagation (BP). Our beam search decoder applies to all quantum LDPC codes and achieves different speed-accuracy tradeoffs by tuning its parameters such as the beam width. We perform numerical simulations under circuit level noise for the $[[144, 12, 12]]$ bivariate bicycle (BB) code at noise rate $p=10^{-3}$ to estimate the logical error rate and the 99.9 percentile runtime and we compare with the BP-OSD decoder which has been the default quantum LDPC decoder for the past six years. A variant of our beam search decoder with a beam width of 64 achieves a $17\times$ reduction in logical error rate. With a beam width of 8, we reach the same logical error rate as BP-OSD with a $26.2\times$ reduction in the 99.9 percentile runtime. We identify the beam search decoder with beam width of 32 as a promising candidate for trapped ion architectures because it achieves a $5.6\times$ reduction in logical error rate with a 99.9 percentile runtime per syndrome extraction round below 1ms at $p=5 \times10^{-4}$. Remarkably, this is achieved in software on a single core, without any parallelization or specialized hardware (FPGA, ASIC), suggesting one might only need three 32-core CPUs to decode a trapped ion quantum computer with 1000 logical qubits.