Geometric properties of quantum entanglement and machine learning

Abstract

Objectives. Fast data analysis based on hidden patterns is one of the main issues for adaptive artificial intelligence systems development. This paper aims to propose and verify a method of such analysis based on the representation of data in the form of a quantum state, or, alternatively, in the form of a geometric object in a space allowing online machine learning.Methods. This paper uses Feynman formalism to represent quantum states and operations on them, the representation of quantum computing in the form of quantum circuits, geometric transformations, topological classification, as well as methods of classical and quantum machine learning. The Python programming language is used as a development tool. Optimization tools for machine learning are taken from the SciPy module. The datasets for analysis are taken from open sources. Data preprocessing was performed by the method of mapping features into numerical vectors, then the method of bringing the data to the desired dimension was applied. The data was then displayed in a quantum state. A proprietary quantum computing emulator is used (it is in the public domain).Results. The results of computational experiments revealed the ability of very simple quantum circuits to classify data without optimization. Comparative indicators of classification quality are obtained without the use of optimization, as well as with its use. Experiments were carried out with different datasets and for different values of the dimension of feature spaces. The efficiency of the models and methods of machine learning proposed in the work, as well as methods of combining them into network structures, is practically confirmed.Conclusions. The proposed method of machine learning and the model of quantum neural networks can be used to create adaptive artificial intelligence systems as part of an online learning module. Free online optimization learning process allows it to be applied in data streaming, that is, adapting to changes in the environment. The developed software does not require quantum computers and can be used in the development of artificial intelligence systems in Python as imported modules.