Quantum search in sets with prior knowledge

TL;DR

This paper presents a modified quantum search algorithm that leverages prior knowledge of probability distributions to reduce the expected number of iterations needed for search, offering constant-factor improvements over standard quantum search.

Contribution

It introduces a novel modification to quantum search algorithms that utilizes prior distribution information to optimize search efficiency.

Findings

Expected number of iterations decreased with prior knowledge

Modified algorithm achieves constant-factor speedup

Applicable to sets with known probability distributions

Abstract

Quantum Search Algorithm made a big impact by being able to solve the search problem for a set with $N$ elements using only $O(\sqrt{N})$ steps. Unfortunately, it is impossible to reduce the order of the complexity of this problem, however, it is possible to make improvements by a constant factor. In this paper we pursued such improvements for search problem in sets with known probability distributions. We have shown that by using a modified version of quantum search algorithm, it is possible to decrease the expected number of iterations for such sets.