Deep Neural Network Probabilistic Decoder for Stabilizer Codes.

Area of Science:

• Quantum Information Science
• Machine Learning
• Coding Theory

Background:

• Error correcting codes are essential for reliable quantum computation.
• Traditional decoders face challenges with complex error correlations.
• Neural networks offer a powerful tool for pattern recognition and probability estimation.

Purpose of the Study:

• To develop a novel neural network-based decoder for quantum error correction.
• To leverage neural networks for efficient encoding of error probability distributions.
• To improve decoding performance by conditioning on error syndromes.

Main Methods:

• Implementing a neural network decoder applicable to any stabilizer code.
• Training the neural network to calculate conditional error probability distributions.
• Sampling from the predicted distribution to identify the most likely error.

Main Results:

• The neural network decoder successfully encodes conditional error probability distributions.
• Testing on the toric code demonstrated a higher error threshold than existing decoders.
• The decoder naturally identifies the most probable error and accounts for error correlations.

Conclusions:

• Neural network decoders represent a promising advancement in quantum error correction.
• This method offers improved performance by accurately modeling error probabilities and correlations.
• The algorithm's general applicability to stabilizer codes enhances its potential impact.