A Neural Decoder for Topological Codes

Abstract

We present an algorithm for error correction in topological codes that exploits modern machine learning techniques. Our decoder is constructed from a stochastic neural network called a Boltzmann machine, of the type extensively used in deep learning. We provide a general prescription for the training of the network and a decoding strategy that is applicable to a wide variety of stabilizer codes with very little specialization. We demonstrate the neural decoder numerically on the well-known two dimensional toric code with phase-flip errors.

References in corpus (13)

• Surface codes: Towards practical large-scale quantum computation
• Solving the Quantum Many-Body Problem with Artificial Neural Networks
• Machine learning phases of matter
• Discovering Phase Transitions with Unsupervised Learning
• Experimental Quantum Computations on a Topologically Encoded Qubit
• Learning Thermodynamics with Boltzmann Machines
• Self-Learning Monte Carlo Method
• Accelerate Monte Carlo Simulations with Restricted Boltzmann Machines
• Efficient Algorithms for Maximum Likelihood Decoding in the Surface Code
• Error Threshold for Color Codes and Random 3-Body Ising Models
• Fault-tolerant error correction with the gauge color code
• Supervised Learning with Quantum-Inspired Tensor Networks
• Surface Code Threshold in the Presence of Correlated Errors

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