Circuit quantum electrodynamics (cQED) serves as a promising platform for scalable quantum computation, where precise microwave control of qubits lays the foundation for achieving high-fidelity quantum gates. Despite recent progress in developing various quantum gates, controlling artificial qubits remains a considerable challenge due to intricate Hamiltonian systems and the fragile nature of quantum states. Therefore, further research is needed to improve qubit gates and protect quantum states from qubit decoherence. This thesis presents two studies: 1) controlling cQED systems through black-box optimization to achieve state-of-the-art gate fidelity, 2) stabilizing an entangled two-qubit state indefinitely via engineering dissipation channels. The first study establishes the feasibility of direct black-box optimization as a method to discover novel qubit gates from simple initial conditions. We develop robust quantum optimization algorithms to efficiently learn novel qubit gates and evaluate these algorithms through simulations and experiments. Our findings show the potential to learn high-fidelity qubit gates without depending on the specifics of the system Hamiltonian. In the second study, our objective is to realize entanglement stabilization through quantum reservoir engineering. By coupling two qubits near resonance with a leaky resonator acting as a reservoir, we induce a strong correlated decay of the qubits. We experimentally demonstrate the subradiant effect of an entangled Bell state and, through simulation, reveal the robustness of this system in stabilizing a high-fidelity Bell state.