Towards fault-tolerant stabilization of a GKP qubit using a Kerr-cat ancilla*

Bosonic quantum error correction (QEC) offers a hardware-efficient means of redundantly encoding a logical qubit within the large Hilbert space of a harmonic oscillator. The Gottesman-Kitaev-Preskill (GKP) code is particularly promising in the circuit QED architecture since it can efficiently correct for photon loss in the oscillator, which is the dominant source of intrinsic error in state-of-the-art superconducting microwave cavities.  In the recent realizations of the GKP code using this architecture, an ancillary qubit is employed to stabilize GKP codewords in the cavity, a process which has been shown to be sensitive to ancilla bit-flips but insensitive to ancilla phase-flips [1, 2].  Using a biased-noise ancilla therefore offers a pathway to fault-tolerant error correction of the GKP code [3].  Here, we discuss our experimental progress toward stabilizing the GKP code using a Kerr-cat ancilla.

Work supported by: ARO, AFOSR, NSF, DOE and YINQE.

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

[2] V.V. Sivak et al., Nature 616, 50-55 (2023).

[3] Puri et al., Phys. Rev. X 9, 041009 (2019)