  New computing technologies are being sought near the end of CMOS transistor
scaling, meanwhile superconducting digital, i.e., single-flux quantum (SFQ),
logic allows incredibly efficient gates which are relevant to the impending
transition. In this work we present a proposed reversible logic, including gate
simulations and schematics under the name of Reversible Fluxon Logic (RFL). In
the widest sense it is related to SFQ-logic, however it relies on (some
approximately) reversible gate dynamics and promises higher efficiency than
conventional SFQ which is logically irreversible. Our gates use fluxons, a type
of SFQ which has topological-particle characteristics in an undamped Long
Josephson junction (LJJ). The collective dynamics of the component Josephson
junctions (JJs) enable ballistic fluxon motion within LJJs as well as good
energy preservation of the fluxon for JJ-circuit gates. For state changes, the
gates induce switching of fluxon polarity during resonant scattering at an
interface between different LJJs. Related to the ballistic nature of fluxons in
LJJ, the gates are powered, almost ideally, only by data fluxon momentum in
stark contrast to conventionally damped logic gates which are powered
continuously with a bias. At first the fundamental Identity and NOT gates are
introduced. Then 2-bit gates are discussed, including the IDSN gate which
actually allows low fluxon-number inputs for more than 4 input states. A
digital CNOT, an important milestone for 2-bit reversible superconducting
gates, is planned as a central result. It uses a store and launch gate to stop
and then later route a fluxon. This use of the store and launch gate allows a
clocked CNOT gate and synchronization within. The digital CNOT gate could
enable high efficiency relative to conventional irreversible gates and shows
the utility of the IDSN as a reversible gate primitive.
