Error correction for depolarising noise on a quantum system using deep RL

Abstract

We implement a quantum error correction algorithm for the depolarized noise model on the topological toric code using deep reinforcement learning. An action-value Q-function encodes the discounted value of applying any of the three pauli operators ( x, y, z) to a specific qubit given the entire set of excitations on the torus. The Q-network is defined by a convolutional neural network (CNN), with one fully connected layer at the end. Considering the translational invariance of the torics code we can center every qubit and therefore naturally simplify the state space representation independently of the number of excitation pairs. We train the agent using experience replay and store the state from the algorithm to use it for mini-batch updates of the Q-network. We conclude that this approach, considering all three pauli operators, outperforms the Minimum Weight Perfect Matching (MWPM) algorithm and for small error rates is close to the asymptotic solution for very low error probabilites.