Engineering XY and ZZ interactions between two remote superconducting qubits via a multimode waveguide

Waveguides provide a flexible platform for long-range interactions between superconducting qubits. Here, we study how to engineer the effective XY and ZZ interactions between two qubits via qubit frequency assignments and multimode interference determined by the mode configuration and standing-wave parities of a finite multimode waveguide. For a single-mode waveguide, we find that XY and ZZ interactions cannot be simultaneously suppressed to zero and the residual qubit-qubit coupling always exists. For example, the XY interaction may be suppressed to a negligible level when two qubits and the waveguide mode satisfy the two-photon resonant condition, but the ZZ interaction cannot be switched off. For multimode configurations within the central dispersive window, the engineered interaction types are very different for odd and even numbers of modes. Even-mode configurations can readily produce strong XY interactions, whereas odd-mode configurations can strongly suppress the XY interaction while retaining a finite ZZ interaction. Full-Hamiltonian simulations of minimal two- and three-mode configurations confirm XY-dominated SWAP dynamics and ZZ-dominated CZ-type dynamics, respectively. These results establish a frequency assignment criterion of qubits and waveguide modes for selectively engineering long-range qubit-qubit interaction types induced by the waveguide with finite multimode.