Analysis of DC-biased Josephson junctions for cat qubit stabilisation

Current implementations of qubits continue to exhibit too frequent errors to be scaled into useful quantum machines. An emerging approach is to encode quantum information in the two metastable states of an oscillator exchanging pairs of photons with its environment, a mechanism shown to provide protection against bit flips. In this talk, we propose a theoretical study of a novel circuit design for the implementation of this so called dissipative cat qubit. The proposed circuit replaces the perturbative effect of a microwave pump to mediate the two-photon exchange, by the natural periodic evolution of a DC voltage biased Josephson junction. Our design is predicted to showcase a two-photon exchange rate larger than that of the microwave pump-based cat qubit implementation while dynamically averaging the usually resonant parasitic terms such as Kerr and cross Kerr. In addition to addressing qubit stabilization, we propose to use injection locking to prevent long-term drifts of the cat qubit phase associated to DC voltage noise.