A quantum algorithm for string matching

Algorithms that search for a pattern within a larger data-set appear ubiquitously in text and image processing. Here, we present an explicit, circuit-level implementation of a quantum pattern-matching algorithm that matches a search string (pattern) of length M inside a longer text of length N. Our algorithm has a time complexity of $$\tilde{O}(\sqrt{N})$$ , while the space complexity remains modest at O(N + M). We report the quantum gate counts relevant for both pre-fault-tolerant and fault-tolerant regimes.