Vegapunk: Accurate and Fast Decoding for Quantum LDPC Codes with Online Hierarchical Algorithm and Sparse Accelerator

Quantum Low-Density Parity-Check (qLDPC) codes are a promising class of quantum error-correcting codes that exhibit constantrate encoding and high error thresholds, thereby facilitating scalable fault-tolerant quantum computation.However, real-time decoding of qLDPC codes remains a significant challenge due to the high connectivity of their check matrices, which typically requires solving large-scale linear systems with sparse structures.In particular, off-the-shelf qLDPC decoders are often subject to a tradeoff between accuracy and latency, thus yielding no accurate and realtime decoding.This paper presents Vegapunk, a software-hardware co-design framework that enables real-time qLDPC decoding with high accuracy.To improve decoding accuracy, we design an offline decoupling strategy leveraging Satisfiability Modulo Theories (SMT) optimizations to mitigate quantum degeneracy.To enable fast decoding, we introduce an online hierarchical decoding algorithm employing a greedy strategy.Furthermore, we show that our SMT-optimized strategy suffices to produce decoupled matrices with maximized sparsity, thus admitting a dedicated accelerator to fully exploit the sparsity and parallelism to achieve real-time qLDPC decoding.Experimental results demonstrate that Vegapunk enables real-time decoding (< 1𝜇𝑠) for the Bivariate Bicycle (BB) code up to [[784,24,24]] while exhibiting logical error rates on par with the state-of-the-art decoder, i.e., BP+OSD.