computer remains a major challenge, largely due to imperfect gate fidelity. A key source of this infidelity is the parasitic interaction between coupled qubits, which this thesis addresses in two- and three-qubit circuits. This parasitic interaction causes a bending between computational and non-computational levels, leading to a parasitic ZZ interaction. The thesis first investigates the possibility of zeroing the ZZ interaction in two qubit combinations: a pair of interacting transmons, and a hybrid pair of a transmon coupled to a capacitively shunted flux qubit (CSFQ). The theory developed is used to accurately simulate experimental results from our collaborators, who measured a CSFQ-transmon pair with and without a cross-resonance (CR) gate. The strong agreement between theory and experiment motivated further study of a CR gate that achieves 99.9% fidelity in the absence of static ZZ interaction. Since the CR pulse adds an additional ZZ component to the static part, a new strategy called dynamical ZZ freedom is proposed to zero the total ZZ interaction. This strategy can be applied in all-transmon circuits to enable perfect entanglement. Based on these findings, a new two-qubit gate, the parasitic-free (PF) gate, is proposed. Additionally, the thesis explores how to utilize the ZZ interaction to enhance the performance of a controlled-Z gate. Lastly, the impact of a third qubit on two-qubit gate performance is examined, with several examples illustrating the properties of two-body ZZ and three-body ZZZ interactions in circuits with more than two qubits.