Implementation of a conditional displacement gate using the second-order nonlinearity of a cubic transmon in a planar superconducting circuit*

The conditional displacement gate plays a crucial role in the framework of bosonic codes. Recently, it has been typically implemented by enhancing a weak cross-Kerr interaction through the irradiation of a pump tone into the resonator [1]. This cross-Kerr interaction is a valuable control resource but can also act as a bit-flip error propagation channel during conditional gate operations. To address this issue, we present results on the implementation of the conditional displacement gate by harnessing the second-order nonlinearity of the cubic transmon [2,3], which is integrated into a planar superconducting circuit. In this approach, the resonator state follows the shortest path in its phase space, effectively decoupling the cross-Kerr interaction during conditional gate operations. Using this gate, we also demonstrate the creation of cat states and squeezed vacuum states through modular measurements with post-selection.

[1] P. Campagne-Ibarcq et al., Nature 584, 368–372 (2020)

[2] A. Noguchi et al., Phys. Rev. A 102, 062408 (2019)

[3] A. Bermudez et al., Phys. Rev. A 85, 040302 (2012)