# Sequential minimal optimization for quantum-classical hybrid algorithms

## TL;DR

This paper introduces a new sequential minimal optimization method for quantum-classical hybrid algorithms that converges faster, is robust to errors, and requires no hyperparameter tuning, significantly improving optimization efficiency.

## Contribution

The paper presents a novel optimization method dividing the problem into solvable subproblems, enhancing convergence speed and robustness for quantum circuit parameter tuning.

## Key findings

- Outperforms existing optimization algorithms in speed and accuracy
- Converges independently of initial parameter choices
- Accelerates quantum-classical hybrid algorithms effectively

## Abstract

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.