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# Monte Carlo Tree Search based Hybrid Optimization of Variational Quantum Circuits

*Proceedings of Mathematical and Scientific Machine Learning*, PMLR 190:49-64, 2022.

#### Abstract

Variational quantum algorithms stand at the forefront of simulations on near-term and future fault-tolerant quantum devices. While most variational quantum algorithms involve only continuous optimization variables, the representation power of the variational ansatz can sometimes be significantly enhanced by adding certain discrete optimization variables, as is exemplified by the generalized quantum approximate optimization algorithm (QAOA). However, the hybrid discrete-continuous optimization problem in the generalized QAOA poses a challenge to the optimization. We propose a new algorithm called MCTS-QAOA, which combines a Monte Carlo tree search method with an improved policy gradient solver to optimize the discrete and continuous variables in the quantum circuit, respectively. We find that MCTS-QAOA has excellent noise-resilience properties, and can outperform prior algorithms in challenging instances of the generalized QAOA.