A quantum algorithm for string matching - Niroula, Pradeep; Nam, Yunseong (npj quantum information, 2021)
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 O ̃ ( 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.