Variational determination of multi-qubit geometrical entanglement in NISQ computers

TL;DR

This paper introduces a variational method to estimate the geometric entanglement of multi-qubit states using only single-qubit operations, making it suitable for noisy intermediate-scale quantum (NISQ) devices.

Contribution

It presents a novel variational algorithm for measuring multi-qubit entanglement that is compatible with current NISQ hardware and demonstrates its effectiveness on IBM quantum devices.

Findings

Successfully implemented on IBM Quantum devices for 3-5 qubits.

Shows robustness and accuracy through simulations with random states.

Demonstrates scalability up to 25 qubits using matrix product states.

Abstract

Current noise levels in physical realizations of qubits and quantum operations limit the applicability of conventional methods to characterize entanglement. In this adverse scenario, we follow a quantum variational approach to estimate the geometric measure of entanglement of multiqubit pure states. The algorithm requires only single-qubit gates and measurements, so it is well suited for NISQ devices. This is demonstrated by successfully implementing the method on IBM Quantum devices for Greenberger-Horne-Zeilinger states of $3$, $4$, and $5$ qubits. Numerical simulations with random states show the robustness and accuracy of the method. The scalability of the protocol is numerically demonstrated via matrix product states techniques up to $25$ qubits.