Entanglement of fluxonium qubits without leaving the computational space

The superconducting fluxonium circuit in its flux sweet spot possesses unique spectral properties. Its main qubit transition has low frequency and exceptionally long lifetime reaching 500 us [1], while the transition between its first and second excited states has an order of magnitude higher frequency and stronger coupling to a microwave field, which has been utilized in a fast controlled-Z gate [2, 3]. On the other hand, strong anharmonicity of the fluxonium also simplifies qubit control by driving transitions in the computational subspace to perform two-qubit gates. The first example discussed here is a controlled-X gate reminiscent of the cross-resonance gate in transmons [4]. It is activated by driving at the frequency of the target qubit and requires two independent controls. The second example is a swapping gate operation in the 00-11 subspace activated by a high-power drive at half the frequency of the 00-11 two-photon transition, which can be compared to bSWAP gate with transmons [5].

[1] L. B. Nguyen, et. al., Phys. Rev. X 9, 041041 (2019).
[2] K. N. Nesterov, et. al., Phys. Rev. A 98, 030301 (2018).
[3] Q. Ficheux, et.al., arXiv:2011.02634 (2020).
[4] J. M. Chow, et. al., Phys. Rev. Lett. 107, 080502 (2011).
[5] S. Poletto, et. al., Phys. Rev. Lett. 109, 240505 (2012).