We propose a couple of oracle construction methods for quantum pattern matching. in turn show that one the construct can be used with Grover's search algorithm exact and partial matching, deterministically. The other also points to matched indices, but primarily provides means generate Hamming distance between searched all possible sub strings input string, probabilistic way.

An important subtask of the pattern discovery process is pattern matching, where the pattern sought is already known and we want to determine how often and where it occurs in a sequence. In this paper we review the most practical techniques to find patterns of different kinds. We show how regular expressions can be searched for with general techniques, and how simpler patterns can be dealt with...