GPU-Accelerated Syndrome Decoding for Quantum LDPC Codes below the 63 $\mu$s Latency Threshold

TL;DR

This paper demonstrates a GPU-based belief propagation decoder for quantum LDPC codes that achieves sub-63 microseconds latency, enabling real-time, scalable quantum error correction on commodity hardware.

Contribution

It introduces a parallelized belief propagation decoding method for quantum LDPC codes that meets strict latency requirements using GPU acceleration.

Findings

Decoding latency under 50 microseconds for large codes

Achieved 23.3 microseconds latency for smaller codes

Decoding performance suitable for superconducting qubit cycles

Abstract

This paper presents a GPU-accelerated decoder for quantum low-density parity-check (QLDPC) codes that achieves sub-$63$ $\mu$s 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 $50$ $\mu$s for [[$784$, $24$, $24$]] codes and as low as $23.3$ $\mu$s 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.