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arXiv:1912.12919 · Physical Review Research

Deep Q-learning decoder for depolarizing noise on the toric code

David Fitzek, Mattias Eliasson, Anton Frisk Kockum, Mats Granath

Published May 26, 2020• 38 citations
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Abstract

This paper presents an artificial intelligence-based decoder for quantum error correction of the toric code. A neural network is trained, using reinforcement learning, to suggest error-correcting operations on the physical qubits to best avoid logical errors. By learning to take advantage of the correlations between bit-flip and phase-flip errors, it can outperform the standard matching decoder for depolarizing noise.

DOI
10.1103/physrevresearch.2.023230

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This paper presents an artificial intelligence-based decoder for quantum error correction of the toric code. A neural network is trained, using reinforcement learning, to suggest error-correcting operations on the physical qubits to best avoid logical errors. By learning to take advantage of the correlations between bit-flip and phase-flip errors, it can outperform the standard matching decoder for depolarizing noise.
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We implement a quantum error correction algorithm for bit-flip errors on the topological toric code using deep reinforcement learning. An action-value Q-function encodes the discounted value of moving a defect to a neighboring site on the square grid (the action) depending on the full set of defects on the torus (the syndrome or state). The Q-function is represented by a deep convolutional neural network. Using the translational invariance on the torus allows for viewing each defect from a central perspective which significantly simplifies the state space representation independently of the number of defect pairs. The training is done using experience replay, where data from the algorithm being played out is stored and used for mini-batch upgrade of the Q-network. We find performance which is close to, and for small error rates asymptotically equivalent to, that achieved by the Minimum Weight Perfect Matching algorithm for code distances up to d=7 . Our results show that it is possible for a self-trained agent without supervision or support algorithms to find a decoding scheme that performs on par with hand-made algorithms, opening up for future machine engineered decoders for more general error models and error correcting codes.
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.
Quantum error correction technology is an important solution to solve the noise interference generated during the operation of quantum computers. In order to find the best syndrome of the stabilizer code in quantum error correction, we need to find a fast and close to the optimal threshold decoder. In this work, we build a convolutional neural network (CNN) decoder to correct errors in the toric code based on the system research of machine learning. We analyze and optimize various conditions that affect CNN, and use the RestNet network architecture to reduce the running time. It is shortened by 30%–40%, and we finally design an optimized algorithm for CNN decoder. In this way, the threshold accuracy of the neural network decoder is made to reach 10.8%, which is closer to the optimal threshold of about 11%.The previous threshold of 8.9%–10.3% has been slightly improved, and there is no need to verify the basic noise.
Quantum error correction (QEC) is indispensable for the realization of fault-tolerant quantum computers. Surface codes are a leading QEC architecture due to their high error thresholds and planar design. The core challenge lies in the decoding process: inferring latent physical errors from syndrome measurements and applying appropriate corrections. Although there are classical decoders, their performance can degrade with complex noise or be computationally demanding. This paper investigates an advanced Deep Reinforcement Learning (DRL) approach, employing a Dueling Double Deep Q-Network (DQN), to decode X-type Pauli errors on ad=3\mathbf{d}=\mathbf{3}d=3rotated surface code. The DRL agent leverages syndrome history to discern temporal error correlations and utilizes a multi-round correction strategy, enabling iterative refinement of corrective actions within an environment that simulates both physical qubit errors and syndrome measurement noise. After 30,000 training episodes with a 5 % physical error rate and 1 % measurement noise, the agent achieved a 0.00 % logical error rate in the extended test, an average episode reward of 0.38, and successfully cleared syndromes in 63 % of the test cases, demonstrating robust learning of a safe decoding policy. The persistent challenge of high training loss, despite good policy performance, is discussed, offering insights into value function approximation in complex QEC environments.
We investigate the use of Quantum Neural Networks for discovering and implementing quantum error-correcting codes. Our research showcases the efficacy of Quantum Neural Networks through the successful implementation of the Bit-Flip quantum error-correcting code using a Quantum Autoencoder, effectively correcting bit-flip errors in arbitrary logical qubit states. Additionally, we employ Quantum Neural Networks to restore states impacted by Amplitude Damping by utilizing an approximative 4-qubit error-correcting codeword. Our models required modification to the initially proposed Quantum Neural Network structure to avoid barren plateaus of the cost function and improve training time. Moreover, we propose a strategy that leverages Quantum Neural Networks to discover new encryption protocols tailored for specific quantum channels. This is exemplified by learning to generate logical qubits explicitly for the bit-flip channel. Our modified Quantum Neural Networks consistently outperformed the standard implementations across all tasks.