Abstract
The purpose of this paper is to mathematically investigate characteristics of a geodesic equation describing locally minimum complexity paths in the special unitary group manifold representing the unitary evolution of n qubits associated with a quantum computation. The geodesic equation is a nonlinear differential matrix equation of the Lax type. A simple local initial-value solution is elaborated for the case of three qubits.
Acknowledgement
This work was supported by the Director's Research Initiative at the US Army Research Laboratory.