On Grover's Search Algorithm from a Quantum Information Geometry Viewpoint

TL;DR

This paper offers an information geometric perspective on Grover's quantum search algorithm, using the Wigner-Yanase metric to analyze quantum distinguishability and characterizing the algorithm's dynamics as a geodesic on a quantum state manifold.

Contribution

It introduces a novel geometric framework for understanding Grover's algorithm, connecting quantum search dynamics with geodesic paths in quantum information geometry.

Findings

Grover's algorithm dynamics correspond to geodesics on a quantum state manifold.

Quantum distinguishability is quantified using the Wigner-Yanase metric.

Potential deviations from Grover's algorithm are discussed within this geometric framework.

Abstract

We present an information geometric characterization of Grover's quantum search algorithm. First, we quantify the notion of quantum distinguishability between parametric density operators by means of the Wigner-Yanase quantum information metric. We then show that the quantum searching problem can be recast in an information geometric framework where Grover's dynamics is characterized by a geodesic on the manifold of the parametric density operators of pure quantum states constructed from the continuous approximation of the parametric quantum output state in Grover's algorithm. We also discuss possible deviations from Grover's algorithm within this quantum information geometric setting.