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

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 promising, since it can efficiently correct 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 with this architecture, an ancillary qubit is employed to stabilize GKP codewords in the cavity, a process which is sensitive to ancilla bit-flips but insensitive to ancilla phase-flips [1, 2]. A biased-noise ancilla, such as a Kerr-cat qubit, offers therefore a pathway to fault-tolerant error correction of the GKP code [3]. Building on our recent work demonstrating quantum control of an oscillator with a Kerr-cat qubit [4], we discuss our experimental progress toward fault-tolerant stabilization of the GKP code.

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

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

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

[4] Ding, Brock, et al., arXiv:2407.10940 (2024).