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Title: Exponential of a matrix, a nonlinear problem, and quantum gates

We describe solutions of the matrix equation exp(z(A − I{sub n})) = A, where z ∈ ℂ. Applications in quantum computing are given. Both normal and non-normal matrices are studied. For normal matrices, the Lambert W-function plays a central role.
Authors:
 [1] ;  [2]
  1. International School for Scientific Computing, University of Johannesburg, Auckland Park 2006 (South Africa)
  2. Department of Mathematical Sciences, University of South Africa, Johannesburg (South Africa)
Publication Date:
OSTI Identifier:
22403084
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Mathematical Physics; Journal Volume: 56; Journal Issue: 1; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; EQUATIONS; MATHEMATICAL SOLUTIONS; MATRICES; NONLINEAR PROBLEMS; QUANTUM COMPUTERS