Variational quantum algorithms to estimate rank, quantum entropies, fidelity and Fisher information via purity minimization

TL;DR

This paper introduces variational quantum algorithms that estimate key quantum properties like rank, entropies, fidelity, and Fisher information by minimizing quantum purity, with strategies to address gradient vanishing issues.

Contribution

The paper presents novel VQAs for estimating quantum properties using purity minimization, including adaptations for state learning and fractional inverses.

Findings

Algorithms effectively estimate quantum properties.

Strategies mitigate vanishing gradient problems.

Applicable to mixed quantum states.

Abstract

Variational quantum algorithms (VQAs) that estimate values of widely used physical quantities such as the rank, quantum entropies, the Bures fidelity and the quantum Fisher information of mixed quantum states are developed. In addition, variations of these VQAs are also adapted to perform other useful functions such as quantum state learning and approximate fractional inverses. The common theme shared by the proposed algorithms is that their cost functions are all based on minimizing the quantum purity of a quantum state. Strategies to mitigate or avoid the problem of exponentially vanishing cost function gradients are also discussed.