Optimized controlled-Z gates for two superconducting qubits coupled through a resonator

Superconducting qubits are promising candidates for building a quantum computer. A continued challenge for fast yet accurate gates is to minimize the effects of decoherence. Here we apply numerical methods to design fast entangling gates, specifically the controlled-Z, in an architecture where two qubits are coupled via a resonator. We find that the gates can be sped up by a factor of two and reach any target fidelity. We also discuss how systematic errors arising from experimental conditions affect the pulses and how to remedy them, providing a strategy for the experimental implementation of our results. We discuss the shape of the pulses, their spectrum and symmetry.