Reversible Fluxon Logic: Topological particles allow ballistic gates along 1D paths

Digital computing currently uses irreversible logic gates whose energy dissipation is fundamentally limited. Reversible logic gates can provide an energy-efficient alternative since they can operate with reversible processes that have no dissipation, such as with scattering processes involving elastic particles. The presented logic uses fluxons, topological solitons in Long Josephson Junctions (LJJs), as inputs into and outputs from logic gates. An advantage of using LJJs for connections is that they restrict scattering to 1D paths, in contrast to previous ballistic logic which is based on 2D scattering. Furthermore, we find through simulation that there is almost no energy loss in the scattering of fluxons between LJJs of designed unpowered circuit gates. To switch bit states, the fluxons are made to change polarity during operations -- fluxons in an input LJJ freely propagate into the gate circuit, excite a nonlinear oscillatory interface mode, and quickly scatter deterministically to an output LJJ as a fluxon or antifluxon. The numerically simulated soliton dynamics shows that over $97\%$ of the total energy is preserved as fluxon energy after gate operations. These phenomena are further analyzed with a collective coordinate ansatz, reducing the dynamics of many degrees of freedom to two coordinates which characterize fluxon and antifluxon type excitations in the input and the output LJJs. The solutions of the reduced model accurately describe the four possible energy-conserving scattering processes found in simulations of one-bit gate circuits (with two scattering directions and two output polarities). Calculated parameter tolerances indicate that the gates can be manufactured and tested. Results are shown for 1-bit gates as well as a fundamental 2-bit gate.