Introducing the Kernel Descent Optimizer for Variational Quantum Algorithms

TL;DR

Kernel descent is a new optimization algorithm for variational quantum algorithms that uses reproducing kernel Hilbert space techniques, outperforming some existing methods in certain scenarios on NISQ devices.

Contribution

Introduces kernel descent, a novel optimization method employing RKHS techniques for variational quantum algorithms, with demonstrated advantages over gradient-based methods.

Findings

Kernel descent outperforms gradient descent in specific scenarios.

Kernel descent outperforms quantum analytic descent in certain cases.

Extensive experiments validate the effectiveness of kernel descent.

Abstract

In recent years, variational quantum algorithms have garnered significant attention as a candidate approach for near-term quantum advantage using noisy intermediate-scale quantum (NISQ) devices. In this article we introduce kernel descent, a novel algorithm for minimizing the functions underlying variational quantum algorithms. We compare kernel descent to existing methods and carry out extensive experiments to demonstrate its effectiveness. In particular, we showcase scenarios in which kernel descent outperforms gradient descent and quantum analytic descent. The algorithm follows the well-established scheme of iteratively computing classical local approximations to the objective function and subsequently executing several classical optimization steps with respect to the former. Kernel descent sets itself apart with its employment of reproducing kernel Hilbert space techniques in the construction of the local approximations, which leads to the observed advantages.