  We consider tunneling of vortices across a superconducting film that is both
narrow and short (and connected to bulk superconducting leads at the ends). We
find that in the superconducting state the resistance, at low values of the
temperature (T) and current, does not follow the power-law dependence on T
characteristic of longer samples but is exponential in 1/T. The coefficient of
1/T in the exponent depends on the length or, equivalently, the total
normal-state resistance of the sample. These conclusions persist in the
one-dimensional limit, which is similar to the problem of quantum phase slips
in an ultra-narrow short wire.
