Tools in the Riemannian geometry of quantum computation
type: Item
instance of: scholarly article
title: Tools in the Riemannian geometry of quantum computation
zbMATH Open document ID: 1260.81043
author: Howard E. Brandt
published in: Quantum Information Processing
publication date: 2012-09-20T00:00:00Z
review text: This paper represents a review of recent developments in the Riemannian geometry of quantum computation. A series of differential geometry concepts that were used to this end are presented and their relation with the topic is analyzed. More precisely, 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, and tools for calculating the geodesic derivative are presented. The role of geodesic derivative in facilitating 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 is also discussed. In my opinion, the article provides a very deep and useful view of the possible applications that well established concepts from differential geometry may have in the emerging field of quantum computing.
reviewed by: Florin Manea
Mathematics Subject Classification ID: 81P68
Mathematics Subject Classification ID: 81-02
Mathematics Subject Classification ID: 68Q12
Mathematics Subject Classification ID: 53B21
zbMATH DE Number: 6084525
zbMATH Keywords: quantum computing
zbMATH Keywords: quantum circuits
zbMATH Keywords: quantum complexity
zbMATH Keywords: differential geometry
zbMATH Keywords: Riemannian geometry
zbMATH Keywords: geodesics
zbMATH Keywords: Lax equation
zbMATH Keywords: Jacobi fields
MaRDI profile type: Publication
full work available at URL: s11128-011-0290-6
OpenAlex ID: W2059646813
Wikidata QID: Q115381355
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DOI: 10.1007/S11128-011-0290-6
description: scientific article; zbMATH DE number 6084525