  We show how to determine whether a given pattern p of length m occurs in a
given text t of length n in ${\tilde O}(\sqrt{n}+\sqrt{m})$\footnote{${\tilde
O}$ allows for logarithmic factors in m and $n/m$} time, with inverse
polynomial failure probability. This algorithm combines quantum searching
algorithms with a technique from parallel string matching, called {\em
Deterministic Sampling}.
