Exponential of a Matrix, a Nonlinear Problem and Quantum Gates

Willi-Hans Steeb, Yorick Hardy

Published 2013-11-11, updated 2014-10-03Version 2

We describe solutions of the matrix equation $\exp(z(A-I_n))=A$, where $z \in {\mathbb C}$. Applications in quantum computing are given. Both normal and nonnormal matrices are studied. For normal matrices, the Lambert W-function plays a central role.