Dissipative quantum dynamics and optimal control using
iterative time ordering: an application to superconducting
qubits

Abstract. 

We combine a quantum dynamical propagator that explicitly accounts 
for quantum mechanical time ordering with optimal control theory. 
After analyzing its performance with a simple model, we apply it
to a superconducting circuit under so-called Pythagorean control. 
Breakdown of the rotating-wave approximation is the main source of 
the very strong time-dependence in this example. While the propagator 
that accounts for the time ordering in an iterative fashion proves 
its numerical eciency for the dynamics of the superconducting circuit, 
its performance when combined with optimal control turns out to be rather
sensitive to the strength of the time-dependence. We discuss the kind 
of quantum gate operations that the superconducting circuit can implement 
including their performance bounds in terms of fidelity and speed.