Introducing the kernel descent optimizer for variational quantum algorithms

Area of Science:

• Quantum Computing
• Optimization Algorithms

Background:

• Variational quantum algorithms are a promising approach for achieving quantum advantage on current noisy intermediate-scale quantum (NISQ) devices.
• Efficiently minimizing the objective functions of these algorithms is crucial for their practical application.

Purpose of the Study:

• Introduce kernel descent, a novel algorithm for minimizing functions in variational quantum algorithms.
• Compare the performance of kernel descent against existing optimization methods.
• Demonstrate the effectiveness of kernel descent through extensive experiments.

Main Methods:

• Kernel descent iteratively computes classical local approximations of the objective function.
• It utilizes reproducing kernel Hilbert space techniques to construct these local approximations.
• Classical optimization steps are performed on these approximations.

Main Results:

• Kernel descent demonstrates superior performance compared to gradient descent.
• Kernel descent outperforms quantum analytic descent in specific scenarios.
• Extensive experiments validate the effectiveness of the kernel descent algorithm.

Conclusions:

• Kernel descent offers an effective new method for optimizing variational quantum algorithms.
• The use of reproducing kernel Hilbert space techniques provides a distinct advantage.
• This algorithm shows promise for advancing the application of NISQ devices.