GPU-accelerated syndrome decoding for quantum LDPC codes below the 63 µs latency threshold

Abstract

This paper presents a GPU-accelerated decoder for quantum low-density parity-check (QLDPC) codes that achieves sub-63 µs latency, below the surface code decoder’s real-time threshold demonstrated on Google’s Willow quantum processor. While surface codes have demonstrated below-threshold performance, the encoding rates approach zero as code distances increase, posing challenges for scalability. Recently proposed QLDPC codes, such as those by Panteleev and Kalachev, offer constant-rate encoding and asymptotic goodness but introduce higher decoding complexity. To address such limitation, this work presents a parallelized belief propagation decoder leveraging syndrome information on commodity GPU hardware. Parallelism was exploited to maximize performance within the limits of target latency, allowing decoding latencies under 26 µs for [[784, 24, 24]] codes and as low as 16.9 µs for smaller codes, meeting the tight timing constraints of superconducting qubit cycles. These results show that real-time, scalable decoding of asymptotically good quantum codes is achievable using widely available commodity hardware, advancing the feasibility of fault-tolerant quantum computation beyond surface codes.