Robust String Matching in O ( √ N + M ) Quantum Queries Chris

Finding a match of an M item pattern against an N item text is a common computing task, useful in string matching and image matching. The best classical (i.e., non-quantum) string matching algorithms, which are Θ(N +M) time and query complexity, are improved in many cases in this paper using Grover’s quantum searching algorithm. Specifically, given quantum oracles that return the j symbol in the text or pattern in constant time, we demonstrate a quantum string matching algorithm which returns a pattern match if it exists with query complexity O( √ N + M) and time complexity O( √ N logN + M log(MN) ). Variations of this algorithm allow wildcard matches, can return the number of matches, can return the nearest match in case of no exact matches, as well as the first or last such match, each with a slight change in complexity. We are also better than the best quantum string matching algorithms in many cases.