Benchmarking Adaptive Quantum Circuit Optimization Algorithms for Quantum Chemistry

In the noisy near-term quantum computing era variational quantum algorithms are promising to explore the boundaries of quantum advantage. One prevalent instance is the variational quantum eigensolver (VQE) employed in quantum chemistry to approximate ground-state energies of molecules. The performance of VQE depends on the design of the parametrized quantum circuit, as well as the optimization algorithm used to optimize those parameters. Circuit optimization methods have been developed to generate quantum circuits to reach accurate approximations to the ground-states. In this work, we conduct an empirical comparison between two prominent adaptive quantum circuit optimization algorithms, namely qubit-ADAPT-VQE and a reinforcement learning (RL) based method, on the problem of finding the ground state energy of Lithium Hydride (LiH). In our experiment, we focus on the circuit depth generated by each circuit optimization method and the number of two-qubit quantum gates in the best-found circuit.