  We propose a novel Reinforcement Learning (RL) method for optimizing quantum
circuits using graph-theoretic simplification rules of ZX-diagrams. The agent,
trained using the Proximal Policy Optimization (PPO) algorithm, employs Graph
Neural Networks to approximate the policy and value functions. We demonstrate
the capacity of our approach by comparing it against the best performing
ZX-Calculus-based algorithm for the problem in hand. After training on small
Clifford+T circuits of 5-qubits and few tenths of gates, the agent consistently
improves the state-of-the-art for this type of circuits, for at least up to
80-qubit and 2100 gates, whilst remaining competitive in terms of computational
performance. Additionally, we illustrate its versatility by targeting both
total and two-qubit gate count reduction, conveying the potential of tailoring
its reward function to the specific characteristics of each hardware backend.
Our approach is ready to be used as a valuable tool for the implementation of
quantum algorithms in the near-term intermediate-scale range (NISQ).
