Matching algorithms can be used for identifying errors in quantum systems, being the most famous the Blossom algorithm. Recent works have shown that small distance quantum error correction codes can be efficiently decoded by employing machine learning techniques based on neural networks (NN). Various NN-based decoders have been proposed to enhance the decoding performance and the decoding time. Their implementation differs in how the decoding is performed, at logical or physical level, as well as in several neural network related parameters. In this work, we implement and compare two NN-based decoders, a low level decoder and a high level decoder, and study how different NN parameters affect their decoding performance and execution time. Crucial parameters such as the size of the training dataset, the structure and the type of the neural network, and the learning rate used during training are discussed. After performing this comparison, we conclude that the high level decoder based on a Recurrent NN shows a better balance between decoding performance and execution time and it is much easier to train. We then test its decoding performance for different code distances, probability datasets and under the depolarizing and circuit error models.
Quantum error correction (QEC) is crucial for achieving fault-tolerant quantum computing by addressing errors in noisy qubits. The surface code, a leading QEC framework, traditionally employs the Minimum Weight Perfect Matching (MWPM) decoder. We present a step-by-step methodology that formulates surface code decoding as a supervised machine learning classification problem within a two-level framework, where low-level modules address physical qubit errors and highlevel modules correct logical errors. We implement Feedforward Neural Networks (FFNN) and Graph Neural Networks (GNN), which are individually employed to perform low-level physical qubit error correction and high-level logical error correction for rotated surface codes of distances
d=3,d=5, and
d=7. Under depolarizing noise, both FFNN and GNN achieve lower logical error rates than MWPM, with GNN yielding up to 28% improvement at
d=7. GNN achieves pseudothresholds of 0.1084, 0.1311, and 0.1441 for
d=3,d=5, and
d=7, surpassing MWPM's 0.0914, 0.1024, and 0.1126. Crossover points further indicate GNN's robustness at higher noise levels (e.g., 0.1632 vs. 0.1291 for MWPM). By learning error distributions in a two-level setting, both FFNN and GNN outperform MWPM, demonstrating their potential as scalable, high-performance decoders for near-term quantum devices.
Quantum error correction is essential to achieve fault-tolerant quantum computation in the presence of noisy qubits. Among the most promising approaches to quantum error correction is the surface code, thanks to a scalable two-dimensional architecture, only nearest-neighbor interactions, and a high error threshold. Decoding the surface code, i.e. finding the most likely error chain given a syndrome measurement outcome is a computationally complex task. Traditional decoders rely on classical algorithms, which, especially for larger systems, can be slow and may not always converge to the optimal solution. This thesis presents a novel approach to decoding the surface code using graph neural networks. By mapping the syndrome measurements to a graph and performing graph classification, we find that the graph neural networks can predict the most likely error configuration with high accuracy. Our results show that the GNN-based decoder outperforms the classic minimum weight perfect matching (MWPM) decoder in terms of accuracy. With a phenomenological noise model with depolarizing noise and perfect syndrome measurements, our networks beat MWPM up to code-size 15 across all relevant error rates. Furthermore, the GNN is capable of surpassing MWPM under circuit-level noise up to code size 7. We also show that training the network on repetition code data from a recent experiment [Google Quantum AI, Nature 614, 676 (2023)] produces per-step error rates comparable to those achieved with a matching decoder specifically adapted to the error rates of the physical qubits. This indicates that graph neural network decoders are capable of learning the underlying error distribution on the qubits. Our findings advance the field of quantum error correction and provide a promising new direction for the development of efficient decoding algorithms.