  Reversible logic can provide lower switching energy costs relative to all
irreversible logic, including those developed by industry in semiconductor
circuits, however, more research is needed to understand what is possible.
Superconducting logic, an exemplary platform for both irreversible and
reversible logic, uses flux quanta to represent bits, and the reversible
implementation may switch state with low energy dissipation relative to the
energy of a flux quantum. Here we simulate reversible shift register gates that
are ballistic: their operation is powered by the input bits alone. A storage
loop is added relative to previous gates as a key innovation, which bestows an
asynchronous property to the gate such that input bits can arrive at different
times as long as their order is clearly preserved. The shift register
represents bit states by flux polarity, both in the stored bit as well as the
ballistic input and output bits. Its operation consists of the elastic swapping
of flux between the stored and the moving bit. This is related to a famous
irreversible shift register, developed prior to the advent of superconducting
flux quanta logic (which used irreversible gates). In the base design of our
ballistic shift register (BSR) there is one 1-input and 1-output port, but we
find that we can make other asynchronous ballistic gates by extension. The gate
constitutes the first asynchronous reversible 2-input gate. Finally, for a
better insight into the dynamics, we introduce a collective coordinate model.
We find that the gate can be described as motion in two coordinates subject to
a potential determined by the input bit and initial stored flux quantum. Aside
from the favorable asynchronous feature, the gate is considered practical in
the context of energy efficiency, parameter margins, logical depth, and speed.
