In a paper published in the journal Nature, researchers developed a recurrent, transformer-based neural network to decode the surface code, a leading quantum error correction code. Their decoder outperformed state-of-the-art decoders on real-world data from Google's sycamore quantum processor.
Study: Learning high-accuracy error decoding for quantum processors. Image Credit: Sunshine Seeds/Shutterstock.com
The decoder maintained its advantage on simulated data with realistic noise, adapting to complex error distributions after training on synthetic and experimental data. This work demonstrated machine learning's (ML) potential to improve quantum error correction beyond human-designed algorithms.
Related Work
Past work has explored the potential of quantum computation to outperform classical computation, with applications in material science, ML, and optimization. Achieving fault-tolerant quantum computation requires correcting errors on physical devices, often through redundancy using logical qubits.
The surface code, known for its high error tolerance, is a promising strategy. However, decoding methods must address complex noise effects like leakage and cross-talk, with research focusing on adapting decoders to real-world conditions for effective quantum error correction.
Advancing Quantum Error Correction
ML techniques have been increasingly applied to quantum error correction, with neural networks playing a central role. Early research focused on simpler qubit-level error models, but recent studies have tackled more complex circuit-level noise. Some advancements, such as recurrent and convolutional networks, have been trained to decode surface and color codes under realistic conditions, including both Pauli and beyond-Pauli noise. However, while some approaches achieved promising results with surface codes, they fell short of the performance of maximum likelihood decoders under experimental conditions.
AlphaQubit, a recurrent-transformer-based neural network, significantly outperformed previous decoders, including ML-based ones, in decoding Sycamore surface code experiments. Trained in two stages, it incorporates analogue inputs for improved accuracy and scales well to more considerable code distances.
On simulated data, it surpassed matching with weighted path metric-correlated (MWPM-Corr), maintaining accuracy even with complex noise models. AlphaQubit achieved superior error suppression, scalability, and generalization for real-world quantum devices and future applications.
Neural Network Surface Code
A neural network architecture has been developed to decode the surface code under realistic hardware-level noise. The network uses a per-stabilizer decoder state representation, storing syndrome history for each stabilizer. Convolutions allow spatial information sharing, with dilation enabling longer-range communication.
Self-attention mechanisms update stabilizer state vectors, ensuring efficient interconnection. The pooling and readout network aggregates stabilizer information to predict logical errors and is trained using experimental data and cross-entropy optimization.
Due to limited experimental data, a two-stage training approach is utilized. First, the network is pre-trained on synthetic data generated from a generic noise model, such as circuit depolarizing noise. In the second stage, the model is fine-tuned with experimental data from a physical device.
This method achieves state-of-the-art decoding performance on current quantum hardware. The pre-trained and fine-tuned decoder outperforms traditional methods, demonstrating improved accuracy on larger-scale quantum devices across different code distances.
Providing stabilizer measurements directly as inputs, rather than stabilizer detection events, proved beneficial. Traditionally, stabilizer readouts are binary (si,n ∈ {0, 1}), with detection events derived by XORing consecutive measurements. This change captures the same information as the event inputs but allows soft measurement inputs.
Posterior probabilities for each stabilizer measurement are treated as Bernoulli random variables. The ‘soft XOR’ mechanism transforms these probabilities into detection events, ensuring the same information content while enabling smoother data integration.
Training with soft information is challenging, especially when soft data-qubit measurements are recomputed via SoftXOR, as it may allow the model to deduce the logical state. To prevent this, data-qubit measurements are thresholded in the final memory round, ensuring alignment with traditional non-soft readout experiments and avoiding inference of the logical label.
The Pauli+ simulator models quantum devices by incorporating effects like cross-talk, leakage, and soft I/Q readouts to generate data at various code distances. It uses metrics such as logical error rates (LER) and fitting techniques to analyze decoder performance, with experiments involving multiple rounds of error correction. The AlphaQubit neural network, designed for surface code decoding, leverages recurrent architectures and attention mechanisms to process stabilizer measurements and events, optimizing quantum error correction across varying code distances.
In the SI1000 pretraining, the model trains on fixed-length experiments with intermediate measurements used as auxiliary labels. A noise curriculum is applied, starting with low noise and increasing during training to stabilize and improve accuracy.
Half of the experimental data is used for fine-tuning training, with early stopping based on a development set. Pauli+ pretraining involves simplified leakage simulation with I/Q noise, followed by fine-tuning using a Pauli+ simulator. Models are trained with cross-entropy loss to minimize error.
Conclusion
To sum up, AlphaQubit, a neural network decoder, outperformed the best tensor-network decoders, setting a new benchmark in error suppression for surface codes. It showed excellent scalability and accuracy, even at large code distances, though challenges remain in data efficiency and throughput.
The decoder’s ability to generalize across rounds and code distances demonstrated its potential for fault-tolerant quantum computation. AlphaQubit highlighted the promise of ML in advancing practical quantum computing despite the need for further improvements.
Journal Reference
Bausch, J., et al. (2024). Learning high-accuracy error decoding for quantum processors. Nature, 1-7. DOI: 10.1038/s41586-024-08148-8, https://www.nature.com/articles/s41586-024-08148-8
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