Expressibility of linear combination of ansatz circuits

TL;DR

This paper introduces a method to enhance the expressibility of variational quantum circuits by linearly combining ansatzes, avoiding increased circuit depth and reducing noise, with a new measurement strategy and gradient calculation.

Contribution

The paper proposes a novel approach using linear combinations of ansatzes to improve expressibility without increasing circuit depth, along with a measurement strategy that reduces reliance on two-qubit gates.

Findings

Numerical simulations confirm the effectiveness of the proposed method.

The approach reduces quantum noise compared to deeper circuits.

A new measurement strategy eliminates the need for Hadamard tests.

Abstract

Variational Quantum Eigensolver is considered promising for medium-scale noisy quantum computers. Expressibility is an important metric for measuring the capability of a variational quantum Ansatz circuit. A commonly used method to increase expressibility is to increase the circuit depth. However, increasing the circuit depth also introduces more noise. We propose to use a linear combination of ansatzes to improve the expressibility of variational circuits, thus avoiding the increase of circuit depth. Concurrently, we introduce a novel measurement strategy that circumvents the necessity for the Hadamard test, thereby significantly diminishing the reliance on two-qubit gates, which are presently the predominant contributors to quantum noise. We also provide a corresponding gradient calculation method, which makes it convenient to update the parameters. Compared with the method of increasing the circuit depth, our method of improving expressibility is more practical. Numerical simulations demonstrate the effectiveness of our method.