Evaluation of variational quantum states entanglement on a quantum computer by the mean value of spin

TL;DR

This paper investigates the geometric measure of entanglement in variational quantum states using the mean spin value, analyzing how entanglement depends on circuit parameters and graph properties, with experiments on IBM quantum hardware.

Contribution

It introduces a method to evaluate entanglement in variational quantum states via mean spin, linking entanglement to circuit parameters and graph structure, validated on a real quantum computer.

Findings

Entanglement depends on rotational gate angles and graph vertex degree.

The geometric measure of entanglement varies with circuit parameters.

Experimental results confirm theoretical predictions on IBM quantum hardware.

Abstract

The geometric measure of entanglement of variational quantum states is studied on the basis of its relation with the mean value of spin. We examine n-qubit quantum states prepared by a variational circuit with a layer formed by the rotational gates and two-qubit controlled phase gates. The variational circuit is a generalization of that used for preparing quantum Generative Adversarial Network states. The entanglement of a qubit with other qubits in the variational quantum states is determined by the angles of rotational gates that act on the qubit and qubits entangled with it by controlled phase gates and also their parameters. In the case of one layer variational circuit, the states can be associated with graphs with vertices representing qubits and edges corresponding to two-qubit gates. The geometric measure of entanglement of a qubit with other qubits in the quantum graph state depends on the properties of the vertex that represents it in the graph, namely it depends on the vertex degree. The dependence of the geometric measure of entanglement of variational quantum states on their parameters is quantified on IBM's quantum computer.