Quantum error correction for the toric code using deep reinforcement learning
Department of Physics, University of Gothenburg, SE-41296 Gothenburg, Sweden
| Published: | 2019-09-02, volume 3, page 183 |
| Eprint: | arXiv:1811.12338v3 |
| Doi: | https://doi.org/10.22331/q-2019-09-02-183 |
| Citation: | Quantum 3, 183 (2019). |
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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.
Featured image: Syndrome diagnosing the state of a quantum code for an error protected quantum memory. Arrows indicate the reinforcement learning action-value for a move that corresponds to a single qubit bit-flip operation.
Popular summary
In this paper we develop an error decoder based on artificial intelligence. We use deep reinforcement learning, which is the same framework that has recently achieved super-human performance in playing computer and board games. By exploration, experience is gathered and used to train an artificial neural network that can suggest the best error correction to perform for any given syndrome. 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 types of noise and error correcting codes.
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