Optimal training of variational quantum algorithms without barren plateaus

TL;DR

This paper introduces adaptive quantum natural gradient methods to improve the training efficiency of variational quantum algorithms, avoiding barren plateaus and enhancing quantum state learning and control.

Contribution

It develops Gaussian kernel-based adaptive learning rates and a generalized quantum natural gradient, significantly improving VQA training stability and performance.

Findings

Outperforms existing optimization routines in VQA training

Avoids barren plateaus in certain quantum simulation tasks

Enhances quantum control protocol optimization

Abstract

Variational quantum algorithms (VQAs) promise efficient use of near-term quantum computers. However, training VQAs often requires an extensive amount of time and suffers from the barren plateau problem where the magnitude of the gradients vanishes with increasing number of qubits. Here, we show how to optimally train VQAs for learning quantum states. Parameterized quantum circuits can form Gaussian kernels, which we use to derive adaptive learning rates for gradient ascent. We introduce the generalized quantum natural gradient that features stability and optimized movement in parameter space. Both methods together outperform other optimization routines in training VQAs. Our methods also excel at numerically optimizing driving protocols for quantum control problems. The gradients of the VQA do not vanish when the fidelity between the initial state and the state to be learned is bounded from below. We identify a VQA for quantum simulation with such a constraint that thus can be trained free of barren plateaus. Finally, we propose the application of Gaussian kernels for quantum machine learning.