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

2025-08-11

AI Summary

Quantum low-density parity-check (QLDPC) codes face high real-time decoding latency, failing to meet the sub-microsecond error-correction deadline (≤63 μs) required by superconducting quantum processors; meanwhile, surface codes suffer from diminishing code rates with increasing distance, limiting scalability. Method: This work proposes the first GPU-accelerated parallel belief propagation (BP) decoding architecture for QLDPC codes, co-designed with GPU memory hierarchy and thread model to optimize syndrome processing and message updates. Results: On the [784, 24, 24] QLDPC code, it achieves an end-to-end decoding latency as low as 23.3 μs and averaging <50 μs—well below the 63 μs real-time threshold—while sustaining a constant code rate, thereby overcoming the scalability bottleneck of surface codes. This is the first hardware-feasible, real-time QLDPC decoder that simultaneously achieves ultra-low latency, high code rate, and practical deployability for large-scale fault-tolerant quantum computing.

Technology Category

• Machine Learning: Quantum Machine Learning
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding
• Search and Optimization: Learning to Search

Application Category

• Economics, Online Markets and Human Computation: LLM based quality controls for crowd work
• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines
• Security and Privacy: Large-scale security measurements

Abstract

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

Problem

• Achieve sub-63μs latency for QLDPC code decoding
• Overcome scalability limits of surface code encoding rates
• Enable real-time decoding on commodity GPU hardware

Innovation

• GPU-accelerated QLDPC decoder
• Sub-63μs latency achievement
• Parallelized belief propagation decoding