Microwave-activated entangling gates for fluxonium qubits

The main qubit transition of the superconducting fluxonium circuit in its flux sweet spot is characterized by a low frequency and very long coherence time, which reaches 500 μs [1]. At the same time, the transition between the first and second excited states of the fluxonium is comparable to those in transmons: it has an order of magnitude higher frequency and stronger coupling to a microwave field, but shorter lifetime. In this talk, we analyze and compare two-qubit gates between such qubits activated by driving different transitions in the two-qubit spectrum. In one scheme [2], the microwave drive is applied in resonance with a higher-frequency transition leading outside of the computational subspace. In the second scheme, which is similar to the cross-resonance gate with transmons [3], the microwave drive is applied at a low frequency to keep the system in the computational subspace. We calculate fidelity metrics for both gates with decoherence effects accounted for.
[1] Long B. Nguyen, et. al., Phys. Rev. X (2019).
[2] Konstantin N. Nesterov, et. al., Phys. Rev. A 98, 030301 (2018).
[3] Jerry M. Chow, et. al., Phys. Rev. Lett. 107, 080502 (2011).