  We develop a new numerical scheme which allows precise solution of coherent
tunneling problems, i.e., problems with exponentially small transition
amplitudes between quasidegenerate states. We explain how this method works for
the single-particle (tunneling in the double-well potential) and many-body
systems (e.g., vacuum-to-vacuum transitions), and gives directly the instanton
shape and tunneling amplitude. Most importantly, transition amplitudes may be
calculated to arbitrary accuracy (being limited solely by statistical errors)
no matter how small are their absolute values.
