The Kerr cat: spectral kissing and phase-flip robustness*

Schrödinger cat states, superpositions of coherent states in an oscillator, can be stabilized by a driven effective Hamiltonian thanks to the interplay between Kerr nonlinearity and single-mode squeezing [1]. The pair of resulting degenerate Kerr-cat states form a qubit whose coherence along one Bloch sphere axis increases exponentially with the average photon number, while decreasing only linearly along the other axes. The qubit protection arises from the progressive pairwise kissing of consecutive levels as the average photon number is increased--a quantum manifestation of robust period doubling in this system. We experimentally observe the pairwise kissing via spectroscopy and the associated increase in the period-doubled coherent state lifetime, which exceeds 1 ms, a factor of 440 improvement over the bare lifetime of the constituent SNAIL-transmon circuit. Furthermore, we achieve quantum nondemolition readout fidelities > 99% and retain universal quantum control [2]. Our system experimentally realizes a hardware-efficient repitition code leaving the Kerr-cat qubit poised for use in further quantum error correction schemes.

[1] Grimm, A., Frattini, N.E., Puri, S. et al. Stabilization and operation of a Kerr-cat qubit. Nature 584, 205–209 (2020).

[2] Frattini, N.E., Cortiñas, R.G., Venkatraman, J. et al. The squeezed Kerr oscillator: spectral kissing and phase-flip robustness. Arxiv 2209.03934 (2022).