Exponential of a Matrix, a Nonlinear Problem and Quantum Gates

Abstract

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.

one more example added, comments are welcome

References in corpus (1)

• The Lambert W Function, Laguerre Polynomials, and the Zeros of the QCD Partition Function