Tools in the Riemannian geometry of quantum computation

Tools in the Riemannian geometry of quantum computation An introduction is first given of recent developments in the Riemannian geometry of quantum computation in which the quantum evolution is represented in the tangent space manifold of the special unitary unimodular group 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Quantum Information Processing Springer Journals

Tools in the Riemannian geometry of quantum computation

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Publisher
Springer US
Copyright
Copyright © 2011 by Springer Science+Business Media, LLC (outside the USA)
Subject
Physics; Theoretical, Mathematical and Computational Physics; Mathematics, general; Quantum Physics; Physics, general; Computer Science, general
ISSN
1570-0755
eISSN
1573-1332
D.O.I.
10.1007/s11128-011-0290-6
Publisher site
See Article on Publisher Site

Abstract

An introduction is first given of recent developments in the Riemannian geometry of quantum computation in which the quantum evolution is represented in the tangent space manifold of the special unitary unimodular group 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.

Journal

Quantum Information ProcessingSpringer Journals

Published: Sep 16, 2011

References

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