Toward a quantum computing algorithm to quantify classical and quantum correlation of system states

TL;DR

This paper introduces a variational hybrid quantum-classical algorithm designed to quantify classical and quantum correlations in quantum states, suitable for NISQ devices, by mapping density matrices to a pure state representation and optimizing measurement operators.

Contribution

The paper presents a novel VHQC algorithm that efficiently measures correlations in quantum states using a new density matrix mapping and variational optimization, compatible with NISQ technology.

Findings

Algorithm outputs match exact calculations for tested states.

The method effectively quantifies correlations in various density matrices.

Compatible with current noisy quantum devices.

Abstract

Optimal measurement is required to obtain the quantum and classical correlations of a quantum state, and the crucial difficulty is how to acquire the maximal information about one system by measuring the other part; in other words, getting the maximum information corresponds to preparing the best measurement operators. Within a general setup, we designed a variational hybrid quantum-classical (VHQC) algorithm to achieve classical and quantum correlations for system states under the Noisy-Intermediate Scale Quantum (NISQ) technology. To employ, first, we map the density matrix to the vector representation, which displays it in a doubled Hilbert space, and it's converted to a pure state. Then we apply the measurement operators to a part of the subsystem and use variational principle and a classical optimization for the determination of the amount of correlation. We numerically test the performance of our algorithm at finding a correlation of some density matrices, and the output of our algorithm is compatible with the exact calculation.