Sparse Mamba Decoder for Quantum Error Correction: Efficient Defect-Centric Processing of Surface Code Syndromes

TL;DR

The paper introduces the Sparse Mamba Decoder, a defect-centric neural decoder for quantum error correction that processes only active detection events, achieving significant speedups and comparable or better accuracy than existing methods.

Contribution

It presents a novel defect-centric neural decoding approach with linear complexity, improving speed and efficiency in quantum error correction over dense decoders.

Findings

Reduces logical error rate by up to 49% at small code distances.

Runs 95-467x faster than near-MLD decoders on benchmarks.

Maintains nearly constant latency across various code distances.

Abstract

Quantum error correction (QEC) is essential for building fault-tolerant quantum computers, requiring decoders that are simultaneously accurate, fast, and scalable. Most state-of-the-art neural decoders achieve high accuracy but process the full dense syndrome array of size $O(d^2 R) $regardless of the actual error rate, where d is the code distance and R is the number of measurement rounds. At physically relevant error rates (p ~ 0.1%), fewer than 5% of syndrome entries contain active detection events -- yet existing decoders process the entire syndrome volume. We introduce the Sparse Mamba Decoder (SMD), a defect-centric neural decoder that processes only the k active detection events using a 13-dimensional feature representation per defect and a Mamba state-space backbone, achieving $O(k)$ complexity. Across depolarizing, uniform circuit-level, SI1000, and Google Sycamore experimental benchmarks, SMD reduces the MWPM logical error rate by up to 49% at $d \le 5$ under SI1000 noise, runs 95-467x faster than the Tesseract near-MLD decoder and 232-463x faster than Belief Matching, and maintains nearly constant latency (24-57 us) across d = 3-9 under uniform circuit-level noise. On the Sycamore experimental dataset, the SMD ensemble matches or slightly surpasses the dense Mamba decoder of Varbanov et al. All results are obtained on commodity NVIDIA GPUs with 7.5-16M parameters, without specialized accelerators.