  Quantum tunneling of the superconducting order parameter gives rise to the
phase slippage process which controls the resistance of ultra-thin
superconducting wires at sufficiently low temperatures. If the quantum phase
slip rate is high, superconductivity is completely destroyed by quantum
fluctuations and the wire resistance never decreases below its normal state
value. We present a detailed microscopic theory of quantum phase slips in
homogeneous superconducting nanowires. Focusing our attention on relatively
short wires we evaluate the quantum tunneling rate for phase slips, both the
quasiclassical exponent and the pre-exponential factor. In very thin and dirty
metallic wires the effect is shown to be clearly observable even at $T \to 0$.
Our results are fully consistent with recent experimental findings [A.
Bezryadin, C.N. Lau, and M. Tinkham, Nature {\bf 404}, 971 (2000)] which
provide direct evidence for the effect of quantum phase slips.
