Quantum Computational Geodesics

Abstract

Recent developments in the differential geometry of quantum computation offer a new approach to the analysis of quantum computation. In the Riemannian geometry of quantum computation, the quantum evolution is described in terms of the special unitary group of n-qubit unitary operators with unit determinant. The group manifold is taken to be Riemannian. The objective of this report is to mathematically elaborate on characteristics of geodesics describing possible minimal complexity paths in the group manifold representing the unitary evolution associated with a quantum computation. For this purpose the Jacobi equation, generic lifted Jacobi equation, lifted Jacobi equation for varying penalty parameter, and the so-called geodesic derivative are reviewed. These tools are important for investigations of the global characteristics of geodesic paths in the group manifold, and the determination of optimal quantum circuits for carrying out a quantum computation.

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Document Details

Document Type
Technical Report
Publication Date
Jan 01, 2010
Accession Number
ADA513754

Entities

People

  • Howard E. Brandt

Organizations

  • United States Army Research Laboratory

Tags

DTIC Thesaurus Topics

  • Computations
  • Curvature
  • Differential Equations
  • Equations
  • Geodesics
  • Geometry
  • Identities
  • Lie Groups
  • Military Research
  • Personal Information Managers
  • Quantum Circuits
  • Quantum Computing
  • Quantum Information Science
  • Standards

Readers

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Technology Areas

  • Quantum Computing