Optimizing for an arbitrary Schroedinger cat state. 
I. Functionals and application to coherent dynamics.

Abstract

We derive a set of functionals for optimization towards an arbitrary cat state and demonstrate 
their application by optimizing the dynamics of a Kerr-nonlinear Hamiltonian with two-photon 
driving. The versatility of our framework allows us to adapt our functional towards optimization of 
maximally entangled cat states, applying it to a Jaynes-Cummings model. We identify the 
strategy of the obtained control fields and determine the quantum speed limit as a function of the 
cat state's excitation. Finally, we extend our optimization functionals to open quantum system 
dynamics and apply it to the Jaynes-Cummings model with decay on the oscillator. For strong 
dissipation and large cat radii, we find a change in the control strategy compared to the case 
without dissipation. Our results highlight the power of optimal control with functionals specifically 
crafted for complex physical tasks and the versatility of the quantum optimal control toolbox for 
practical applications in the quantum technologies.