Beam search decoder for quantum LDPC codes
Min Ye, Dave Wecker, Nicolas Delfosse

TL;DR
This paper introduces a beam search heuristic decoder guided by belief propagation for quantum LDPC codes, offering improved speed-accuracy tradeoffs and significant reductions in logical error rates and runtime, suitable for trapped ion quantum architectures.
Contribution
The paper presents a novel beam search decoder for quantum LDPC codes that outperforms existing decoders in speed and accuracy, adaptable to all quantum LDPC codes.
Findings
A beam width of 64 reduces logical error rate by 17x.
A beam width of 8 matches BP-OSD error rate with 26.2x faster runtime.
A beam width of 32 achieves low error rate with sub-1ms runtime per syndrome extraction.
Abstract
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 bivariate bicycle (BB) code at noise rate 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 reduction in logical error rate. With a beam width of 8, we reach the same logical error rate as BP-OSD with a reduction in the 99.9 percentile runtime. We identify the beam search decoder…
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Taxonomy
TopicsQuantum Computing Algorithms and Architecture · Error Correcting Code Techniques · Radiation Effects in Electronics
