  Reversible logic gates were previously implemented in superconducting
circuits as adiabatic-reversible gates, which are powered with a sufficiently
slow clock. In contrast, we are studying ballistic-reversible gates, where
fluxons serve to both encode the information and power the gates. No power is
applied to the gate apart from the energy of the input fluxons, and the two
possible flux polarities represent the bit states. Undamped long Josephson
junctions (LJJs), where fluxons move at practically constant speed from
inertia, form the input and output channels of the gates. LJJs are connected in
the gates by circuit interfaces, which are designed to allow the ballistic
scattering from input to output fluxon states, using the temporary excitation
of a localized mode. The duration of the resonant scattering determines the
operation time of the gate, approximately a few Josephson plasma periods. Due
to the coherent conversions between fluxon and localized modes the ballistic
gates can be very efficient: in our simulations only a few percent of the
fluxon's energy are dissipated in the gate operation. Ballistic-reversible
gates can be combined with other, non-ballistic gate circuits to extend the
range of gate functionalities. Here we describe how the CNOT can be built as a
structure that includes the IDSN (Identity-else-Same-gives-NOT) and
Store-and-Launch (SNL) gates. The IDSN is a 2-bit ballistic gate, which we
describe and analyze in terms of equivalent 1-bit circuits. The SNL is a
clocking gate, that allows the storage of a bit and the clocked launch of a
fluxon on a bit-state dependent output path. In the CNOT the SNL gates provide
the necessary routing and fluxon synchronization for the input to the IDSN
gate.
