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Quantum error correction for the toric code using deep reinforcement learning

Journal article
Authors Philip Andreasson
Joel Johansson
Simon Liljestrand
Mats Granath
Published in Quantum
Volume 3
Pages 183
ISSN 2521-327X
Publication year 2019
Published at Department of Physics (GU)
Pages 183
Language en
Links https://doi.org/10.22331/q-2019-09-...
Subject categories Low temperature physics, Nano Technology

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 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.

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