Deep neural decoders for near term fault-tolerant experiments

TL;DR

This paper introduces deep neural decoders for quantum error correction that operate without prior noise knowledge, demonstrating their potential for near-term fault-tolerant quantum experiments through detailed analysis and comparison.

Contribution

It presents novel deep neural decoding algorithms for quantum error correction that do not require noise model knowledge, suitable for real-world experimental conditions.

Findings

Deep neural decoders perform well near the codes' pseudo-thresholds.

The methods are applicable to surface, Steane, and Knill codes.

Decoding runtimes are compatible with future quantum device gate times.

Abstract

Finding efficient decoders for quantum error correcting codes adapted to realistic experimental noise in fault-tolerant devices represents a significant challenge. In this paper we introduce several decoding algorithms complemented by deep neural decoders and apply them to analyze several fault-tolerant error correction protocols such as the surface code as well as Steane and Knill error correction. Our methods require no knowledge of the underlying noise model afflicting the quantum device making them appealing for real-world experiments. Our analysis is based on a full circuit-level noise model. It considers both distance-three and five codes, and is performed near the codes pseudo-threshold regime. Training deep neural decoders in low noise rate regimes appears to be a challenging machine learning endeavour. We provide a detailed description of our neural network architectures and training methodology. We then discuss both the advantages and limitations of deep neural decoders. Lastly, we provide a rigorous analysis of the decoding runtime of trained deep neural decoders and compare our methods with anticipated gate times in future quantum devices. Given the broad applications of our decoding schemes, we believe that the methods presented in this paper could have practical applications for near term fault-tolerant experiments.