Improving the efficieny of window decoding in QLDPC codes

Quantum low-density parity-check (QLDPC) codes, such as bivariate bicycle (BB) codes, are strong candidates that offer lower qubit overhead than surface codes for achieving quantum advantage in fault-tolerant quantum computing. However, for these codes to be practical, we need real-time decoding to prevent backlog, produce sufficiently low logical error rates, and be cost-effective.

A leading proposal to meet the real-time decoding requirements for long-running quantum computations is to decode windows of parity check data as they are generated, known as window decoding. In sliding window decoding, sequential data are passed forward in time, but this could lead to an exponential slowdown. Parallel window decoding techniques can meet these high-throughput requirements by removing these linear dependency chains but still introduce latency due to high reaction times. The SWIPER technique for window decoding addresses this through speculative decoding, reducing the latency in parallel window decoding. However, existing techniques use a fixed window size of $2d$ (which includes the window and buffer region) for a code of distance $d$, limiting the maximum amount of parallelism. In this work, we propose and analyze techniques for dynamically fine-tuning the size of each window based on the syndrome data, which increases throughput by enabling greater potential parallelism. We also propose efficient methods to exchange information along the window boundaries using soft information rather than hard decisions, which lead to a loss of past information.