Hybrid Classical–Quantum Text Search Based on Hashing

The paper considers the problem of finding a given substring in a text. It is known that the complexity of a classical search query in an unordered database is linear in the length of the text and a given substring. At the same time, Grover’s quantum search provides a quadratic speed-up in the complexity of the query and gives the correct result with a high probability. We propose a hybrid classical–quantum algorithm (hybrid random–quantum algorithm, to be more precise) that implements Grover’s search to find a given substring in a text. As expected, the algorithm works (a) with a high probability of obtaining the correct result and (b) with a quadratic query acceleration compared to the classical one. What is new is that our algorithm uses the uniform hash family functions technique. As a result, our algorithm is much more memory efficient (in terms of the number of qubits used) compared to previously known quantum algorithms.