Simultaneous Purcell and shot-noise protection in a flux-noise resistant multi-mode superconducting qubit

Superconducting qubits are promising candidates for quantum computing thanks to their relatively long coherence times and high-fidelity controllability. However, coupling to readout & control circuitry and neighboring qubits, leading to Purcell decay, shot-noise induced dephasing and crosstalk, can severely limit the performance of the qubit. To protect the qubit from these effects, we propose a superconducting multi-mode circuit consisting of three superconducting islands coupled to a central island via Josephson junctions. The circuit exhibits two essential anharmonic modes, one of which is flux-insensitive and can be used as a protected mode by decoupling it from the readout resonator. The second mode is flux-tunable and serves as a mediator to control the dispersive coupling to the resonator. In this geometry it is possible to protect against Purcell decay and shot noise simultaneously without being limited by flux noise dephasing. We demonstrate the protection of the qubit mode by characterizing its coherence times as a function of the operating point of the secondary mode. Measurements of T₁ against flux show that the protected mode is not Purcell-limited. Reducing the dispersive shift to $19(4)$ kHz results in resistance of its T₂ time to resonator occupancy.