  We consider the problem of finite resistance $R$ in superconducting films
with geometry of a strip of width $W$ near zero temperature. The resistance is
generated by vortex configurations of the phase field. In the first type of
process, quantum phase slip, the vortex worldline in 2+1 dimensional space-time
is space-like (i.e., the superconducting phase winds in time and space). In the
second type, vortex tunneling, the worldline is time-like (i.e., the phase
winds in the two spatial directions) and connects opposite edges of the film.
For moderately disordered samples, processes of second type favor a train of
vortices, each of which tunnels only across a fraction of the sample.
Optimization with respect to the number of vortices yields a tunneling distance
of the order of the coherence length $\xi$, and the train of vortices becomes
equivalent to a quantum phase slip. Based on this theory, we find the
resistance $\ln R \sim -g W/\xi$, where $g$ is the dimensionless normal-state
conductance. Incorporation of quantum fluctuations indicates a quantum phase
transition to an insulating state for $g \lesssim 1$.
