  Superconducting qubits are among the most promising candidates for building
quantum computers. Despite significant improvements in qubit coherence,
achieving a fault-tolerant quantum 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.
