Time series forecasting has always been a thought-provoking topic in the field of machine learning. Machine learning scientists define a time series as a set of observations recorded over consistent time steps. And, time series forecasting is a way of analyzing the data and finding how variables change over time and hence, predicting the future value. Time is of great essence in this forecasting as it shows how the data coordinates over the dataset and the final result. It also requires a large dataset to ascertain the regularity and reliability. Quantum computers may prove to be a better option for perceiving the trends in the time series by exploiting quantum mechanical phenomena like superposition and entanglement. Here, we consider one-step time series forecasting using variational quantum circuits, and record observations for different datasets.
Time series forecasting has always been a thought-provoking topic in the field of machine learning. Machine learning scientists define a time series as a set of observations recorded over consistent time steps. And, time series forecasting is a way of analyzing the data and finding how variables change over time and hence, predicting the future value. Time is of great essence in this forecasting as it shows how the data coordinates over the dataset and the final result. It also requires a large dataset to ascertain the regularity and reliability. Quantum computers may prove to be a better option for perceiving the trends in the time series by exploiting quantum mechanical phenomena like superposition and entanglement. Here, we consider one-step time series forecasting using variational quantum circuits, and record observations for different datasets.
Continuous Variable-based Quantum Computing (CVQC) has been developing at speed with a lot of promise in the field of quantum machine learning. It provides a direct and natural way to accommodate continuous values into the quantum computing framework. We carried out experiments on quantum simulators where we compared the results of time series forecasting on a type of continuous-variable quantum variational circuit, called CV-Quantum Neural Networks (CVQNN) for different types of time series like Energy Consumption data and stock price data. We compared their performance with a discrete variable-based variational quantum algorithm as well as with a classical Neural Network. Experiments showed that CVQNN can function just like a neural network but with a lesser number of parameters while tackling the two obstacles that are faced in qubit-based computing, which are, tackling continuous values and introducing controlled non-linearity into the circuits. We used the circuit for multi-step forecasting that performed better for a larger prediction window than one-step forecasting done iteratively on the predicted data. The resembling architecture of CVQNN with that of a neural network offers the flexibility of using a similar structure for both one-step and multi-step forecasting.
Time series forecasting is a critical problem with applications in various fields, such as finance, energy, and environmental science. While classical machine learning methods have shown significant progress in this domain, the advent of quantum machine learning introduces a new perspective to address the complexities of time series prediction. In this research, we propose a novel Quantum Neural Network (QNN) approach for time series forecasting, leveraging the unique capabilities of quantum computing to capture intricate temporal dependencies and exploit quantum parallelism. By encoding time series data into quantum states and designing quantum circuits for processing, the QNN aims to achieve improved predictive accuracy compared to classical neural networks. Through extensive experiments on diverse time series datasets, we demonstrate the potential of our QNN framework and discuss the future prospects of quantum-powered time series prediction in real-world applications.
Accurate load forecasting is critical for effective energy management, infrastructure planning, and ensuring the stability of modern power systems. With growing interest in Quantum Computing (QC), recent efforts have demonstrated the applicability of Quantum Machine Learning (QML) across various domains, including supervised and unsupervised learning. However, the use of QML models for Time Series Forecasting (TSF) remains relatively underexplored. In this work, we present a complete framework for TSF based on Variational Quantum Algorithms (VQAs), capable of both single-step and multi-step ahead forecasting. We use tensor product encoding to encode the classical input samples into quantum states, and use the data re-uploading strategy to introduce temporal dependencies across each layer of the quantum circuit. Within this framework, we systematically evaluate multiple Variational Quantum Circuit (VQC) architectures to assess their suitability for forecasting problem. Among the tested configurations, thenLocaland its modified variantQuReUpconsistently outperformed other quantum ansatz designs. Notably, in recursive multi-step forecasting scenarios, these models not only matched but surpassed the performance of a classical Artificial Neural Network (ANN). For example, thenLocalmodel achieved a 8% reduction in mean absolute error (MAE) over ANN for a 24-hour horizon. These results underscore the potential of VQAs for efficient and accurate TSF, particularly in scenarios requiring short to medium-term predictions. The proposed framework offers a promising foundation for future research, including extensions to diverse datasets and deployment on real quantum hardware to study the impact of quantum noise and scalability.
Quantum computing promises a paradigm shift in computational power. However, a major challenge is mitigating the inherent noise and errors in quantum circuits. As quantum computers operate, their fragile qubits are highly susceptible to environmental disturbances, leading to errors that affect the outcomes of repeated circuit executions. Understanding and predicting these errors is crucial for improving the accuracy and reliability of quantum computing systems. In this work, we analyze and predict the output patterns of a single qubit quantum circuit by treating the results of repeated executions as a time series. Specifically, we collect measurement data from multiple runs of a quantum circuit and construct a time series from these observations. By training a predictive model, we aim to forecast future outcomes, providing insights into the error behavior of the quantum circuit. Additionally, we analyze time series data from two different circuits executed on the same qubit to investigate potential relationships and assess whether one dataset can be used to predict the other. Our findings reveal key characteristics of quantum circuit outputs, including stationarity, autocorrelation, seasonality, trends, linearity, and causality. The analysis highlights intriguing behaviors within the dataset. Furthermore, we evaluate multiple time series prediction methods and determine that XGBoost (Extreme Gradient Boosting) outperforms other approaches, demonstrating its effectiveness in accurately predicting quantum computing outputs in subsequent runs.
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.
Abstract In this work, we explore the application of 1D quantum convolutional layers for time series forecasting, framing the problem within the context of machine learning and quantum circuit expressivity. By encoding multiple time steps as features into a quantum circuit, the forecasting task becomes intrinsically multidimensional. We leverage the recent theoretical results that describe Variational Quantum Circuits (VQCs) as multidimensional Fourier series, to design a more expressive 1D quantum convolutional neural network in which an enhanced performance is obtained by reuploading the data. We aim to relate the number of accessible coefficients in each architecture design with the obtained metrics. Our analysis incorporates key machine learning concepts such as expressivity and the presence of barren plateaus, evaluating their impact on generalization and training efficiency. Notably, we show that even with a limited number of trainable parameters, quantum circuits can approximate high-degree Fourier functions, underscoring their expressive capacity and computational efficiency. Our results demonstrate that more expressive ansatz, characterized by richer Fourier spectra, consistently yield improved predictive performance as the number of qubits increases. This study bridges theoretical insights from quantum physics with practical advances in machine learning model design for time series forecasting.