Optimizing for an arbitrary perfect entangler: I. Functionals.

Abstract

Optimal control theory is a powerful tool for improving figures of merit in quantum 
information tasks. Finding the solution to any optimal control problem via numerical 
optimization depends crucially on the choice of the optimization functional. Here, we 
derive a functional that targets the full set of two-qubit perfect entanglers, gates 
capable of creating a maximally-entangled state out of some initial product state. The
functional depends on easily-computable local invariants and uniquely determines when 
a gate evolves into a perfect entangler. Optimization with our functional is most 
useful if the two-qubit dynamics allows for the implementation of more than one 
perfect entangler. We discuss the reachable set of perfect entanglers for a generic 
Hamiltonian that corresponds to several quantum information platforms of current interest.