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

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.

18 pages and 0 figures. To appear in Physica A

References in corpus (8)

• Quantum Computation as Geometry
• From Information Geometry to Quantum Theory
• From Information Geometry to Newtonian Dynamics
• Can chaotic quantum energy levels statistics be characterized using information geometry and inference methods?
• Quantifying The Complexity Of Geodesic Paths On Curved Statistical Manifolds Through Information Geometric Entropies and Jacobi Fields
• Information-Geometric Indicators of Chaos in Gaussian Models on Statistical Manifolds of Negative Ricci Curvature
• Optimal computation with non-unitary quantum walks
• Information Geometry, Inference Methods and Chaotic Energy Levels Statistics

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