  We generalize the string method, originally designed for the study of
thermally activated rare events, to the calculation of quantum tunneling rates.
This generalization is based on the analogy between quantum mechanics and
statistical mechanics in the path-integral formalism. The quantum string method
first locates, in the space of imaginary-time trajectories, the minimal action
path (MAP) between two minima of the imaginary-time action. From the MAP, the
saddle-point (``bounce'') action associated with the exponential barrier
penetration probability is obtained and the pre-exponential factor (the ratio
of determinants) for the tunneling rate evaluated using stochastic simulation.
The quantum string method is implemented to calculate the zero-temperature
escape rates for the metastable zero-voltage states in the current-biased
Josephson tunnel junction model. In the regime close to the critical bias
current, direct comparison of the numerical and analytical results yields good
agreement. Our calculations indicate that for the nanojunctions encountered in
many experiments today, the (absolute) escape rates should be measurable at
bias current much below the critical current.
