Authors: Michael Goerz, Daniel M. Reich, Alireza Shabani, Birgitta Whaley, and Christiane P. Koch
We consider two transmon qubits  coupled via a cavity bus . The strong coupling of each qubit to the shared cavity modes provides an indirect interaction that can be used to implement a two-qubit gate. Describing the system numerically allows us to take into account an arbitrary number of qubit and cavity excitations. We use optimal control theory (OCT), specifically Krotov's method , to find microwave pulses that drive the full system in the desired way in the shortest possible amount of time. Modeling the system dynamics with a master equation in Lindblad form , we analyze the effect of decoherence on the feasibility of high-fidelity two-qubit gates. OCT can then specifically select pathways robust to the influence of decoherence.
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 D. M. Reich et. al., J. Chem. Phys. 136, 104103 (2012)
 M. Boissonneault et. al. Phys. Rev. A 85, 022305 (2012)
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