EPJ Quantum Technol. (2015) 2: 21
https://doi.org/10.1140/epjqt/s40507-015-0034-0

Research

Hybrid optimization schemes for quantum control

¹ Theoretische Physik, Universität Kassel, Heinrich-Plett-Str. 40, Kassel, D-34132, Germany
² Department of Chemistry, University of California, Berkeley, CA, 94720, USA

^* e-mail: christiane.koch@uni-kassel.de

Received: 21 May 2015
Accepted: 11 August 2015
Published online: 17 September 2015

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 geometric phase gate 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.