A microwave-activated controlled-phase gate between a transmon and a fluxonium*

In the quest for high qubit coherence, fluxonium qubits have emerged as promising candidates for

storing quantum information, reaching 1 ms coherence times. On the other hand, large

superconducting qubit devices based on transmon qubits have been built due to the relative

simplicity of the circuit and the ability to perform fast two-qubit gates compared to their coherence

times. We here analyze how two-qubit gates between a transmon and a fluxonium can be realized in

a possible hybrid architecture. The observation that the typical transmon frequencies are at least one

order of magnitude larger than those of the fluxonia leads immediately to the following question:

how can we couple qubits with such different frequencies? We show that this is possible by

microwave-activating the coupling by virtually exciting the fluxonium to its higher levels. In

particular, we consider a microwave-driven controlled-phase gate between capacitively-coupled

transmon and fluxonium qubits, similar to the approach proposed in [Ficheux et al, Phys. Rev. X 11,

021026, (2021)] for two fluxonia. We perform simulations of the gate, including relaxation and

dephasing noise, and show that the gate can be realized with high fidelity while allowing for low

leakage and low residual ZZ coupling.