Three-Qubit Parasitic Interactions in Superconducting Circuits

Superconducting qubits have proven to be an excellent candidate for quantum computing. But because of the imperfections in the gate fidelity of these qubits, making a giant network with many coupled qubits is still a far fetched dream. A much needed in-depth study is required to understand the nature of qubit-qubit couplings, especially the so-called parasitic interactions in order to minimize the leakage and have a much-improved gate fidelity. We study the Hamiltonian of a circuit containing multiple superconducting qubits coupled via shared resonators. We derive, both analytically and numerically, the parasitic multi-Z interactions for such a system. We also provide possible parameter regimes to minimize the parasitic interactions in order to achieve higher fidelity gate implementations for larger circuits.