We propose a sequential minimal optimization method for quantum-classical
hybrid algorithms, which converges faster, is robust against statistical error,
and is hyperparameter-free. Specifically, the optimization problem of the
parameterized quantum circuits is divided into solvable subproblems by
considering only a subset of the parameters. In fact, if we choose a single
parameter, the cost function becomes a simple sine curve with period $2\pi$,
and hence we can exactly minimize with respect to the chosen parameter.
Furthermore, even in general cases, the cost function is given by a simple sum
of trigonometric functions with certain periods and hence can be minimized by
using a classical computer. By repeatedly performing this procedure, we can
optimize the parameterized quantum circuits so that the cost function becomes
as small as possible. We perform numerical simulations and compare the proposed
method with existing gradient-free and gradient-based optimization algorithms.
We find that the proposed method substantially outperforms the existing
optimization algorithms and converges to a solution almost independent of the
initial choice of the parameters. This accelerates almost all quantum-classical
hybrid algorithms readily and would be a key tool for harnessing near-term
quantum devices.

本文提出了一种适用于量子经典混合算法的顺序最小优化方法，解决了参数量子电路上的优化问题，比现有的基于梯度和无梯度优化算法更快更稳健，可用于优化近期量子设备的性能。