Abstract
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 tod=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.
Highlights
Much of the spectacular advances in machine learning using artificial neural networks has been in the domain of supervised learning were deep convolutional networks excel at categorizing objects when trained with big annotated data sets[1,2,3]
The use of deep reinforcement learning may be less obvious in general as the type of topics addressed by RL typically involve some sort of ”intelligent” best strategy search, contrary to the deterministic or statistical models used in physics
In this paper we study a type of problem where artificial intelligence is applicable, namely the task of finding a best strategy for error correction of a topological quantum code; the potential basic building blocks of a quantum computer
Summary
Much of the spectacular advances in machine learning using artificial neural networks has been in the domain of supervised learning were deep convolutional networks excel at categorizing objects when trained with big annotated data sets[1,2,3]. The toric code will be harder to implement experimentally but provides a well understood standard model It provides a simplification from the fact that on a torus only the relative positions of syndrome defects are relevant which reduces the state space complexity that decoder agent has to master. By focusing on this minimal problem we find that we can make a rigorous benchmark on the RL decoder showing near optimal performance. Given that deep reinforcement learning is arguably the most promising AI framework it holds prospect for future versatile self-trained decoders that can adapt to different error scenarios and code architectures. We conclude and append details of the asymptotic fail rate for small error rates as well as the neural network architecture and the RL and network hyperparameters
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