Suppressing spectator errors between fluxonium qubits in a cross resonance architecture

We propose a simple architecture for a quantum processor comprising capacitively coupled fluxonium qubits where two qubit gates utilize the cross resonance (CR) effect. This design is efficient because an entangling ZX interaction can be activated by microwave driving one qubit at the frequency of its detuned coupled neighbor. In our architecture, we find realistic parameters for a CNOT gate with a duration of 200 ns while keeping the residual ZZ coupling below 100 kHz. However, the static capacitive coupling hybridizes the bare fluxonium states leading to coherent over or under rotations that depend on the state of neighboring spectators. We find that inductive driving reduces the magnitude of these spectator errors because the persistent current states used to encode the qubit are more localized than the plasmon states. In particular, inductive driving leads to a change in the CR-rate of only 0.2% per spectator qubit compared to a change of 0.5% when capacitively driven. To further suppress these spectator errors, we employ a range of mitigation strategies including: dynamical decoupling, fast flux pulses, and driving the control and target qubits in alternating layers.