Scalable Neural Decoders for Practical Real-Time Quantum Error Correction

TL;DR

In memory experiments using Sycamore hardware data, the Mamba decoder matches the performance of its Transformer-based counterpart, providing that its superior efficiency does not come at the cost of performance.

Abstract

Real-time, scalable, and accurate decoding is a critical component for realizing a fault-tolerant quantum computer. While Transformer-based neural decoders such as \textit{AlphaQubit} have demonstrated high accuracy, the computational complexity of their core attention mechanism, which scales as $\mathcal{O}(d^4)$ with code distance $d$, results in decoding speeds insufficient for practical real-time applications. In this work, we introduce and evaluate a \textit{Mamba}-based decoder, a state-space model with $\mathcal{O}(d^2)$ complexity. In memory experiments using Sycamore hardware data, our Mamba decoder matches the performance of its Transformer-based counterpart, providing that its superior efficiency does not come at the cost of performance. Crucially, in simulated real-time scenarios that account for decoder-induced noise, the Mamba decoder significantly outperforms the Transformer, exhibiting a higher error threshold of $0.0104$ compared to $0.0097$. These results demonstrate that Mamba decoders offer a compelling balance between speed and accuracy, making them a promising architecture for scalable, real-time quantum error correction.

Figures (5)

• Figure 1: The overall recurrent architecture of the neural decoder. At each cycle $n$, stabilizer measurement embeddings $S_n$ are processed by an RNN core, updating the decoder's hidden state from $h_n$ to $h_{n+1}$. The final state is passed to a readout network to predict $P_{L}$, the probability of a logical error. Further details on the architecture and notations are provided in the Methods section.
• Figure 2: (a) Logical error per round on the Sycamore dataset for various decoders at code distances 3 and 5. (b) A comparison of inference time for a Mamba block versus a Multi-Head Attention (MHA) block as code distance increases, measured on a local RTX 4090 GPU.
• Figure 3: (a) Experimental scheme for real-time decoding simulation. The evaluation runs for $8d+4$ cycles, structured as four repetitions of a $2d+1$ cycle block. After each block, decoding noise is injected to simulate the impact of decoder latency before a correction $\mathcal{R}$ is applied. (b) Comparison of Mamba and Transformer decoders in terms of Logical Error per Round (LER) under real-time decoding scenarios, evaluated at code distances of 3, 5, and 7. Performance is shown with decoder-induced noise, whose strength is scaled according to each decoder's computational complexity. For reference, LERs obtained without decoder-induced noise are shown in the inset.
• Figure 4: Analysis of the effective error threshold under real-time decoding with decoder-induced noise. The plots show the Logical Error Per Round (LER) as a function of the Physical Error Rate ($p$) for code distances $d=3$ and $d=5$. The effective error threshold is the crossover point where the LER for $d=5$ (orange line) becomes higher than the LER for $d=3$ (blue line). (a) The Transformer-based decoder, showing a threshold of 0.0097. (b) The Mamba-based decoder, showing a higher threshold of 0.0104.
• Figure 5: (a) Stabilizer Embedder: Raw stabilizer measurements and detection events are passed through linear layers and combined with positional encodings before being processed by a ResNet to create an embedding $S_n$ for each cycle. (b) RNN Core: The core processes the sequence of embeddings recurrently. At each step, the previous decoder's hidden state $h_n$ is combined with the current syndrome embedding $S_n$ and passed through three Syndrome Mixer layers to produce the updated state $h_{n+1}$. A scaled skip connection is used. (c) Syndrome Mixer: This is the central processing unit. The input is first processed by a Mixer Block, which can be either a Multi-Head Attention module (for the Transformer architecture) or a Mamba module. The output is then passed through a gated dense block and reshaped into a 2D grid to be processed by dilated convolutions, capturing spatial correlations. (d) Readout Network: The final decoder's hidden state $h_N$ is processed by a series of convolutional and dense layers to produce the final prediction for the logical error probability, $P_L$.