SPECIAL ISSUE: The Korepin Festschrift From Statistical Mechanics to Quantum Information Science A Collection of Articles Written in Honor of the 60th Birthday of Vladimir KorepinNo Access

ASPECTS OF THE RIEMANNIAN GEOMETRY OF QUANTUM COMPUTATION

HOWARD E. BRANDT

HOWARD E. BRANDT

U.S. Army Research Laboratory, Adelphi, USA

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https://doi.org/10.1142/S0217979212430047Cited by:2 (Source: Crossref)

Abstract

A review is given of some aspects of the Riemannian geometry of quantum computation in which the quantum evolution is represented in the tangent space manifold of the special unitary unimodular group SU(2ⁿ) for n qubits. The Riemannian right-invariant metric, connection, curvature, geodesic equation for minimal complexity quantum circuits, Jacobi equation and the lifted Jacobi equation for varying penalty parameter are reviewed. Sharpened tools for calculating the geodesic derivative are presented. The geodesic derivative may facilitate the numerical investigation of conjugate points and the global characteristics of geodesic paths in the group manifold, the determination of optimal quantum circuits for carrying out a quantum computation, and the determination of the complexity of particular quantum algorithms.

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