Purcell protection and crosstalk reduction using multimode superconducting circuits

Superconducting qubits are promising candidates for quantum computation due to their long coherence times and high-fidelity control. However, coupling to readout circuits and neighboring qubits can limit qubit performance through Purcell decay and crosstalk. To protect the qubit from these effects, we propose a multimode superconducting circuit composed of three superconducting islands coupled to a central island via Josephson junctions. When the capacitance to the center island is small, the circuit accommodates two modes in the 1-10 GHz frequency range with a large cross-Kerr interaction: one mode decouples from other circuit elements and is used as a protected logical mode; the other mode is used to mediate couplings to the readout resonator and other qubits. Replacing one of the junctions with a SQUID makes the mediating mode flux tunable. By simultaneously driving the tunable modes of adjacent multimode circuits, we introduce conditional phases on the logical modes, resulting in a CPHASE gate. Numerical simulations of coherent dynamics suggest gate fidelities of 99.9 % for a gate time of 100 ns, up to single qubit rotations.