[Paper Review] Neural network decoder for near-term surface-code experiments

Boris Varbanov, Marc Serra-Peralta+2 more|arXiv (Cornell University)|Jul 6, 2023

Neural Networks and Applications4 citations

TL;DR

This paper proposes a recurrent neural network decoder for surface codes that outperforms minimum-weight perfect matching (MWPM) by better handling correlated errors like Y errors. Applied to experimental data from a transmon processor, the neural decoder reduces logical error rates by approximately 25% compared to MWPM, approaching maximum-likelihood performance while requiring no prior error model and enabling real-time decoding with low latency.

ABSTRACT

Neural-network decoders can achieve a lower logical error rate compared to conventional decoders, like minimum-weight perfect matching, when decoding the surface code. Furthermore, these decoders require no prior information about the physical error rates, making them highly adaptable. In this study, we investigate the performance of such a decoder using both simulated and experimental data obtained from a transmon-qubit processor, focusing on small-distance surface codes. We first show that the neural network typically outperforms the matching decoder due to better handling errors leading to multiple correlated syndrome defects, such as $Y$ errors. When applied to the experimental data of [Google Quantum AI, Nature 614, 676 (2023)], the neural network decoder achieves logical error rates approximately $25\%$ lower than minimum-weight perfect matching, approaching the performance of a maximum-likelihood decoder. To demonstrate the flexibility of this decoder, we incorporate the soft information available in the analog readout of transmon qubits and evaluate the performance of this decoder in simulation using a symmetric Gaussian-noise model. Considering the soft information leads to an approximately $10\%$ lower logical error rate, depending on the probability of a measurement error. The good logical performance, flexibility, and computational efficiency make neural network decoders well-suited for near-term demonstrations of quantum memories.

Motivation & Objective

• To develop a neural network decoder that improves logical error rate performance over conventional decoders like minimum-weight perfect matching (MWPM) in near-term surface-code experiments.
• To evaluate the decoder’s performance on both simulated and real experimental data from a transmon-qubit processor, including non-ideal error characteristics.
• To demonstrate the decoder’s adaptability by incorporating soft information from analog transmon qubit readouts without requiring prior knowledge of physical error rates.
• To achieve real-time, scalable decoding suitable for near-term quantum memory demonstrations using practical hardware constraints.

Proposed method

• The decoder uses a two-layer stacked Long Short-Term Memory (LSTM) network to process time-series syndrome measurement data from surface codes.
• The network is trained end-to-end using backpropagation with the Adam optimizer and dropout regularization to prevent overfitting.
• Training data includes simulated and experimental syndrome sequences with varying code distances (d=3,5,7), using both uniform and experimental circuit-level noise models.
• The decoder leverages soft measurement outcomes from transmon qubits by incorporating analog readout values as input features, improving robustness to noise.
• Hyperparameters such as learning rate, batch size, and dropout rate are tuned via cross-validation and early stopping to optimize generalization.
• Inference is performed in real time with low latency—0.7 to 1.1 seconds per QEC round for d=3 to d=7 codes, using batched inference on CPU/GPU.

Experimental results

Research questions

• RQ1 Can a neural network decoder achieve lower logical error rates than MWPM on experimental surface-code data, particularly when handling correlated errors like Y errors?
• RQ2 To what extent does incorporating soft information from analog transmon qubit readouts improve decoder performance compared to binary syndrome data?
• RQ3 How does the performance of a neural network decoder scale with increasing code distance, and what training strategies improve generalization on real hardware data?
• RQ4 Can a neural decoder achieve near-maximum-likelihood performance without requiring a priori knowledge of physical error rates?

Key findings

• On experimental data from Google Quantum AI’s 2023 surface-code experiment, the neural network decoder achieved a logical error rate approximately 25% lower than MWPM.
• The neural decoder outperformed MWPM by better handling correlated errors such as Y errors, which are poorly modeled by the independent X/Z error assumption of MWPM.
• Incorporating soft information from analog transmon readouts reduced the logical error rate by approximately 10%, depending on the measurement error probability.
• The decoder achieved near-maximum-likelihood performance, approaching the theoretical lower bound of logical error rates, despite being trained without access to the true physical error model.
• The training process was stable and generalizable, with early stopping and hyperparameter tuning preventing overfitting and ensuring consistent performance across code distances.
• The decoder demonstrated practical real-time performance, with inference taking only 0.7 to 1.1 seconds per QEC round for d=3 to d=7 codes, making it suitable for near-term quantum memory applications.