On the importance of hyperparameters in initializing parameterized quantum circuits

TL;DR

This paper introduces an evolutionary algorithm to optimize hyperparameters for parameterized quantum circuits, improving initialization and convergence without exacerbating barren plateau issues.

Contribution

It presents a novel hyperparameter optimization method tailored for PQCs, enhancing initial parameter selection for better performance and faster convergence.

Findings

Algorithm consistently finds performant initial parameters.

Improved convergence speed in quantum circuit training.

Does not worsen barren plateau phenomena.

Abstract

There has been intensive research on increasing the utility and performance of Parameterized Quantum Circuits (PQCs) in the past couple of years. Owing to this research, there are now several inductive biases available to a quantum algorithms researchers to design a good circuit for their chosen task. In this paper, we focus on the problem of finding performant initial parameters for a given PQC. Different from previous research that focuses on finding the right \emph{distribution}, we focus on finding the \emph{hyperparameters} for any given distribution. To that end we introduce an evolutionary-search based algorithm that finds optimal hyperparameter given a PQC and quantum task. Our empirical results indicate that our algorithm consistently leads to selection of performant initial parameters tuned specifically to the ansatz and the quantum task leading to faster convergence and performance. More importantly, our algorithm does not \emph{negatively} affect the barren plateau phenomenon. In other words, the initial parameters suggested by algorithm do not worsen the gradient variance scaling for a given initializing distribution.