A walk through of time series analysis on quantum computers

TL;DR

This paper explores quantum approaches to time series analysis, including quantum analogues of classical preprocessing and forecasting models, highlighting potential for quantum machine learning in temporal data tasks.

Contribution

It introduces quantum versions of classical time series methods and discusses future tools for quantum temporal data analysis.

Findings

Quantum neural networks can predict Fourier coefficients of functions.

Quantum operators can perform classical data preprocessing tasks.

Discussion of future quantum algorithms for time series forecasting.

Abstract

Because of the rotational components on quantum circuits, some quantum neural networks based on variational circuits can be considered equivalent to the classical Fourier networks. In addition, they can be used to predict the Fourier coefficients of continuous functions. Time series data indicates a state of a variable in time. Since some time series data can be also considered as continuous functions, we can expect quantum machine learning models to do many data analysis tasks successfully on time series data. Therefore, it is important to investigate new quantum logics for temporal data processing and analyze intrinsic relationships of data on quantum computers. In this paper, we go through the quantum analogues of classical data preprocessing and forecasting with ARIMA models by using simple quantum operators requiring a few number of quantum gates. Then we discuss future directions and some of the tools/algorithms that can be used for temporal data analysis on quantum computers.