# Recommendation systems with quantum k-NN and Grover's algorithms for data processing

## TL;DR

This paper presents a quantum recommendation system utilizing quantum k-NN and Grover's algorithms, detailing its construction, complexity, correctness verification, and numerical behavior analysis.

## Contribution

It introduces a novel quantum recommendation system framework combining quantum k-NN and Grover's algorithms with detailed circuit construction and correctness analysis.

## Key findings

- Quantum algorithms can effectively implement recommendation systems.
- The proposed system's complexity and success probability are analytically evaluated.
- Numerical examples demonstrate the system's behavior in specific cases.

## Abstract

In this article, we discuss the implementation of a quantum recommendation system that uses a quantum variant of the k-nearest neighbours algorithm and the Grover algorithm to search for a specific element in unstructured database. In addition to the presentation of the recommendation system as an algorithm, the article also shows a main steps in construction of a suitable quantum circuit for realisation of a given recommendation system. The computational complexity of individual calculation steps during recommendation system was also indicated. The verification correctness of a proposed recommendation system was also analysed, indicating an algebraic equation describing the probability of success of the recommendation. The article also shows numerical examples presenting the behaviour of the recommendation system for two selected cases.