Demonstration of a conditional displacement gate via a SNAIL coupler towards bosonic encoding

The conditional displacement (CD) gate plays a crucial role in the implementation of bosonic codes. Our team previously proposed a CD gate utilizing the second-order nonlinearity of a cubic transmon, enabling the resonator state to follow the shortest path in phase space[1]. However, similar to conventional schemes based on the cross-Kerr interaction[2], this approach still suffered from residual cross-Kerr effect, where the energy relaxation of the auxiliary qubit propagates as a phase error to the storage resonator holding the bosonic state, limiting the achievable gate fidelity.

In this work, we introduce a SNAIL coupler[3] between the transmon and the storage resonator to control the nonlinearity. By exploiting the SNAIL’s design flexibility, we optimized the second-order nonlinearity under specific flux-bias conditions and suppressed unwanted residual interactions. In addition, we employed a planar resonator that we developed to achieve both high coherence and scalability. Using this system, we demonstrated a CD gate driven by the engineered second-order nonlinearity. The planar-only bosonic architecture demonstrated here provides a promising path toward scalable quantum error correction based on superconducting circuits.

[1] S. Shirai et al., in preparation

[2] V. V. Sivak et al., Nature 616, 50 (2023)

[3] B. J. Chapman et al., PRX QUANTUM 4, 020355 (2023)