Neural Network Decoder Lowers Quantum Error Rate with Learned Confidence Estimates

David Dentelski, affiliated with the Institute for Quantum Computing has found that the logit output of a pretrained graph neural network, designed for the rotated surface code, acts as a learned proxy for the complementary, or logical, gap typically used in minimum-weight perfect matching decoders. The findings reveal that post-selection using the graph neural network’s confidence metric achieves a lower logical error rate than using the conventional minimum-weight perfect matching gap. This is a key result because it shows neural network decoders can independently learn to assess decoding reliability, offering a valuable alternative when traditional gap estimates are impractical or inaccurate for specific noise models.

Graph neural networks predict quantum error correction reliability from error syndromes

A graph neural network (GNN) offers a novel approach to assessing decoding reliability in quantum error correction; instead of directly calculating the logical gap, the network learns this measure of confidence in the corrected quantum state from data, similar to a spellchecker confirming a fixed sentence. This pretrained network, designed for the rotated surface code, analysed patterns of detected errors, known as syndromes, and produced a ‘logit’ output representing the network’s confidence in its decoding decision. The technique bypasses computationally intensive comparisons of potential corrections across multiple logical sectors, providing a rapid, learned assessment of reliability directly from the syndrome.

Employing a graph neural network (GNN) allowed evaluation of decoding reliability, sidestepping the need to calculate the logical gap, which measures confidence in a corrected quantum state. Pretrained using the rotated surface code, the GNN analysed patterns of detected errors, termed syndromes, to produce a ‘logit’ output indicating decoding confidence. This approach avoids exhaustive comparisons of potential corrections, which become computationally expensive as the number of logical qubits increases, with complexity growing exponentially with qubit count.

Error rates dropped to a logical error rate lower than that achieved using minimum-weight perfect matching (MWPM) gap post-selection, representing a 14% improvement at a fixed acceptance rate; previously, comparable performance necessitated computationally expensive calculations of the logical gap. This advancement is particularly significant because calculating the logical gap becomes impractical with increasing qubit numbers and complex noise models, hindering scalable quantum error correction. Scientists demonstrated that the logit output from a graph neural network (GNN) decoder effectively replicates the function of the logical gap, providing a learned substitute for assessing decoding reliability.

A 14% reduction in logical error rate was confirmed compared to using the minimum-weight perfect matching (MWPM) gap for post-selection, while maintaining a consistent acceptance rate. Analysis of individual decoding instances revealed the GNN assigned higher confidence levels to a greater number of correctly decoded results, suggesting improved discrimination between correct and incorrect outputs. Furthermore, the magnitude of the GNN’s confidence score more closely aligned with the ideal posterior log-likelihood ratio, a key metric for assessing decoding reliability, than the MWPM gap did. These findings indicate the neural network learns to estimate confidence without needing detailed knowledge of detector error models or complex matching probabilities; however, this performance was achieved under specific, uniform circuit-level noise conditions and does not yet demonstrate durability across diverse, realistic quantum hardware.

Graph neural networks learn to emulate logical gap calculations for improved quantum error

Quantum computers promise revolutionary calculations, yet remain vulnerable to errors; correcting these errors requires discerning accurate results from noise, a task traditionally reliant on computationally intensive methods like minimum-weight perfect matching. This offers a compelling alternative, demonstrating a graph neural network can learn to assess decoding reliability, bypassing complex calculations. However, the current demonstration remains confined to a specific code, the rotated surface code, and a simplified noise model, raising questions about its adaptability.

It is important to acknowledge that this demonstration focused on a specific type of quantum code, the rotated surface code, and a simplified model of errors. Establishing that a neural network can independently learn to gauge decoding reliability, however, represents a significant step forward. This capability offers a valuable alternative when traditional methods, such as minimum-weight perfect matching, are impractical or ill-suited to complex noise patterns.

Artificial neural networks can independently assess the reliability of quantum error correction, offering a potential alternative to traditional, computationally demanding methods like minimum-weight perfect matching, as researchers have demonstrated. This new technique gauges decoding confidence, vital for discerning accurate results from the inherent noise in quantum systems. Establishing a reliable means of assessing decoding accuracy is a crucial step towards building practical quantum computers. The work demonstrates a graph neural network can learn to estimate the confidence of its own decoding decisions, effectively replicating the function of a traditionally calculated logical gap, which assesses how certain a decoder is about its correction of quantum errors. By training the network on patterns of detected errors, known as syndromes, researchers achieved a learned confidence metric that offers a potential advantage as quantum systems become more complex.

Researchers found that a graph neural network decoder successfully learned to estimate the reliability of its own decoding decisions, mirroring the function of a traditionally calculated logical gap. This is important because assessing decoding confidence is crucial for building practical quantum computers and discerning accurate results from noise. The network was trained using data from the rotated surface code and achieved a lower logical error rate when its confidence metric was used for post-selection. The authors demonstrated this approach offers a valuable alternative when traditional methods are unavailable or poorly suited to the noise model.