Hybrid Optimization Schemes for Quantum Control.

Abstract

Optimal control theory is a powerful tool for solving control problems in quantum 
mechanics, ranging from the control of chemical reactions to the implementation of 
gates in a quantum computer. Gradient-based optimization methods are able to find high
fidelity controls, but require considerable numerical effort and often yield highly 
complex solutions. We propose here to employ a two-stage optimization scheme to 
significantly speed up convergence and achieve simpler controls. The control is 
initially parametrized using only a few free parameters, such that optimization in 
this pruned search space can be performed with a simplex method. The result, 
considered now simply as an arbitrary function on a time grid, is the starting point 
for further optimization with a gradient-based method that can quickly converge to 
high fidelities. We illustrate the success of this hybrid technique by optimizing a 
holonomic phasegate for two superconducting transmon qubits coupled with a shared 
transmission line resonator, showing that a combination of Nelder-Mead simplex and 
Krotov’s method yields considerably better results than either one of the two methods 
alone.