Utilizing a three-level auxiliary for Conditional Displacement Gates during GKP Stabilization

The Gottesman-Kitaev-Preskill (GKP) code is a promising bosonic code for a scalable quantum computing architecture, and is tolerant to photon loss and displacement errors [1]. The GKP qubit defined by the code is generally controlled using the first two levels of an auxiliary qubit, such as a transmon, via echoed-conditional displacement (ECD) gates [2]. In order to perform error correction on the GKP qubit, conditional displacements of a size corresponding to the GKP lattice constant are required [3]. A decay of the auxiliary during this type of ECD can propagate to a logical error on the GKP qubit, thus limiting its lifetime. In this work, we propose a Conditional Displacement scheme utilizing the third level of the auxiliary qubit. Here, an auxiliary decay event does not propagate to a logical error on the GKP during stabilization, with detailed numerical simulations demonstrating significant improvements to the GKP logical lifetime.

[1] D. Gottesman, A. Kitaev, and J. Preskill, Phys. Rev. A 64, 012310 (2001)

[2] A. Eickbusch, V. Sivak, A. Z. Ding et al., Nat. Phys. 18, 1464–1469 (2022)

[3] B. Royer, S. Singh, and S. M. Girvin, Phys. Rev. Lett. 125, 260509 (2020)