Expressibility of the alternating layered ansatz for quantum computation

TL;DR

This paper investigates the expressibility of shallow alternating layered ansatz in quantum computing, demonstrating it matches the expressibility of hardware efficient ansatz while maintaining high trainability, thus enabling better circuit design.

Contribution

It proves that shallow alternating layered ansatz has comparable expressibility to hardware efficient ansatz, balancing expressibility and trainability for intermediate-scale quantum algorithms.

Findings

Shallow alternating layered ansatz has high expressibility.

It matches the expressibility of hardware efficient ansatz.

The ansatz maintains high trainability, solving the gradient vanishing problem.

Abstract

The hybrid quantum-classical algorithm is actively examined as a technique applicable even to intermediate-scale quantum computers. To execute this algorithm, the hardware efficient ansatz is often used, thanks to its implementability and expressibility; however, this ansatz has a critical issue in its trainability in the sense that it generically suffers from the so-called gradient vanishing problem. This issue can be resolved by limiting the circuit to the class of shallow alternating layered ansatz. However, even though the high trainability of this ansatz is proved, it is still unclear whether it has rich expressibility in state generation. In this paper, with a proper definition of the expressibility found in the literature, we show that the shallow alternating layered ansatz has almost the same level of expressibility as that of hardware efficient ansatz. Hence the expressibility and the trainability can coexist, giving a new designing method for quantum circuits in the intermediate-scale quantum computing era.