Comparative studies of optimizer performance in a variational quantum eigensolver

Quantum computation holds the seminal key to overcoming inherent limitations of classical computing, potentially unlocking profound advancements across every scientific and industrial frontier. Currently and in the near future, variational quantum eigensolver (VQE) is one of the most promising algorithms in solving multi-body problems. Under the VQE framework, the classical optimizer plays a critical role in estimating expectation values. However, it is not well studied how different optimizers perform in a quantum circuit. The answer to this question helps make VQE applicable to larger systems. In this work, we scrutinize 12 optimizers on their convergence performances in VQE calculations by varying the number of qubits, depths of the quantum circuit, initial guesses, and number of measurements. It is found that gradient-based methods generally outperform the derivative-free methods. The optimizers involving stochastic processes usually fail to locate the minimum. The step length is far from trivial to reach the convergence. In addition, the Powell method is the most promising to alleviate the barren plateau problem.