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.
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.
The work presented in this thesis is focused on quantum computing and in particular on the interplay between quantum devices and machine learning. This interaction gives birth to a relatively recent area of study, called Quantum Machine Learning (QML), which currently represents a hot research field. This work was carried out in collaboration with an important company with home in Turin, DATA Reply S.r.l., whose main focuses are Big Data, Artificial Intelligence, Machine Learning and Quantum Computing. We start by introducing the fundamental concepts of quantum mechanics, presenting the topic in a formal way from a mathematical point of view while keeping things as simple as possible, as long as they allow us to understand quantum computing basics. After an overview on motivations, possible employments of quantum devices and an analysis of risks and benefits of their development, we proceed to explain quantum computing main concepts, such as qubits and quantum gates. The introduced formalism is the so-called Discrete Variable (DV) formalism, which is the most prominent choice in literature for describing quantum systems. However, as extensively explained during the course of this work, this approach presents several drawbacks: one of the main goals of this thesis is to introduce the alternative formalism of Continuous Variables (CV) and investigate how it can contribute to improve this research area. Currently, one of the preferred tools for quantum machine learning algorithms are the Variational - or Parametrized - circuits: they allow to train the quantum devices in the same way as a classical neural network and allow to address ML problems, both supervised and unsupervised. After a detailed description of these tools, we proceed to introduce PennyLane, a Python library for QML which is very well suited for dealing with variational circuits. In the core part of this work, we concentrate on some QML examples, in particular we analyze some applications in which using the CV formalism turns out to be the most convenient choice. Integration, more specifically Monte Carlo integration, is one of those fields which the CV formalism suits best; in a similar way, Gaussian process regression in its continuous variables version provides a great advantage, namely an exponential speedup, as long as some hypothesis are satisfied. We only provide a brief overview of these applications, since we opted to leave more room to experiments involving variational classifiers and quantum neural networks. Three use cases are analyzed, all involving the CV formalism. The first one is a variational classifier, employed in a supervised setting for the classification of a simple dataset. The second one is a quantum neural network, used to solve a problem of function fitting. The results and the chosen hyperparameters are presented, together with a formal explanation of the theoretical concepts behind them. The last use case, the most complex and detailed one, focuses on a time series forecasting task, carried out with a quantum neural network, and also presents a comparison with the classical approach.
We explore the efficacy of the novel use of parametrised quantum circuits (PQCs) as quantum neural networks (QNNs) for forecasting time series signals with simulated quantum forward propagation. The temporal signals consist of several sinusoidal components (deterministic signal), blended together with trends and additive noise. The performance of the PQCs is compared against that of classical bidirectional long short-term memory (BiLSTM) neural networks. Our results show that for time series signals consisting of small amplitude noise variations (up to 40 per cent of the amplitude of the deterministic signal) PQCs, with only a few parameters, perform similar to classical BiLSTM networks, with thousands of parameters, and outperform them for signals with higher amplitude noise variations. Thus, QNNs can be used effectively to model time series having, at the same time, the significant advantage of being trained significantly faster than a classical machine learning model in a quantum computer.
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.
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 Time series prediction is essential for human activities in diverse areas. A common approach to this task is to harness recurrent neural networks (RNNs). However, while their predictions are quite accurate, their learning process is complex and, thus, time and energy consuming. Here, we propose to extend the concept of RRNs by including continuous-variable quantum resources in it and to use a quantum-enhanced RNN to overcome these obstacles. The design of the continuous-variable quantum RNN (CV-QRNN) is rooted in the continuous-variable quantum computing paradigm. By performing extensive numerical simulations, we demonstrate that the quantum network is capable of learning-time dependence of several types of temporal data and that it converges to the optimal weights in fewer epochs than a classical network. Furthermore, for a small number of trainable parameters, it can achieve lower losses than its classical counterpart. CV-QRNN can be implemented using commercially available quantum-photonic hardware.