Alternating Layered Variational Quantum Circuits Can Be Classically Optimized Efficiently Using Classical Shadows

TL;DR

This paper presents a new training algorithm for alternating layered variational quantum circuits that leverages classical shadows, significantly reducing training costs and enabling efficient classical optimization with strong performance guarantees.

Contribution

The authors introduce an exponentially more efficient training method for alternating layered VQAs using classical shadows, facilitating classical optimization of quantum circuits.

Findings

Achieved 2-3 orders of magnitude reduction in training cost.

Demonstrated effective classical optimization of quantum autoencoders.

Provided rigorous performance guarantees for the proposed method.

Abstract

Variational quantum algorithms (VQAs) are the quantum analog of classical neural networks (NNs). A VQA consists of a parameterized quantum circuit (PQC) which is composed of multiple layers of ansatzes (simpler PQCs, which are an analogy of NN layers) that differ only in selections of parameters. Previous work has identified the alternating layered ansatz as potentially a new standard ansatz in near-term quantum computing. Indeed, shallow alternating layered VQAs are easy to implement and have been shown to be both trainable and expressive. In this work, we introduce a training algorithm with an exponential reduction in training cost of such VQAs. Moreover, our algorithm uses classical shadows of quantum input data, and can hence be run on a classical computer with rigorous performance guarantees. We demonstrate 2--3 orders of magnitude improvement in the training cost using our algorithm for the example problems of finding state preparation circuits and the quantum autoencoder.