Classically reversible logic gate coupled to a superconducting qubit: Qubit simulation (pt. 2)

We theoretically study a classically reversible logic gate coupled to a superconducting qubit for potential applications in quantum computing. The classical gate consists of a Josephson junction circuit interface between long Josephson junctions, and the input of the gate is a ballistically traveling fluxon (a topological sine-Gordon soliton). Depending on the gate definition, a fluxon can undergo different types of resonant elastic scattering, e.g., forward scattering as fluxon or antifluxon. Here we report on how the scattering outcome can depend on the state of a qubit that is embedded in the interface, thus potentially allowing the readout of the qubit from the fluxon dynamics. We specifically will show the effect for a fluxonium qubit galvanically coupled through a junction in the gate interface. This presents a large 4pi-phase difference seen by the qubit. Different fluxon scatterings are found in the classical dynamics of the coupled system for the fluxonium qubit states with macroscopically different phases. We will further use a quantized version of a quasiparticle model, originally developed for classical gates, and take into account few fluxonium levels. The newer analysis should allow us to predict state evolution of a qubit strongly coupled to a topological soliton.