An Oracle Design for Grover’s Quantum Search Algorithm for Solving the Exact String Matching Problem

Grover’s quantum search algorithm is a template for doing quantum search in unstructured search spaces. The details of the oracle in Grover’s algorithm is abstracted for the purpose of analyzing the bound on the number of queries the algorithm must make in order to find the target element of the search space. In order for Grover’s quantum search algorithm to be usable in a specific unstructured search problem, one must provide details on the inner workings of the oracle.

Specifically, we present a high-level and basic design of the oracle using the quantum computing model specific to the exact string matching problem. We describe our design using the quantum circuit model of computing and show that the gate complexity of the circuit is linear with respect to the product of the length of the pattern and the size of the alphabet. We have suggested a quantum memory structure for storage and retrieval of the input text. The quantum circuit we presented requires scratch qubits linear to the product of the length of the pattern and the size of the alphabet to reduce the size of the scratch register without exponential increase in the count of elementary gates required for the computation.