<!--HTML-->Machine learning has enabled computers to learn from data and improve their performance on tasks, revolutionizing various industries by automating processes, uncovering insights, and enhancing decision-making. NISQ (Noisy Intermediate-Scale Quantum) refers to the current stage of quantum computing, characterized by quantum devices with a moderate number of qubits and significant noise. In the NISQ era, parametrized quantum circuits (PQC) are employed in machine learning as flexible quantum algorithms that can be executed on current noisy quantum devices. By introducing tunable parameters, these circuits can adapt to the limitations of NISQ devices, enabling quantum-enhanced solutions to classification and generative tasks while paving the way for practical applications of quantum machine learning. Time series arise from the abundance of sequential data in various fields, and time series analysis uncovers patterns, trends, and dependencies within the temporal data, enabling informed decision-making and predictions for a wide range of applications. In this project, we aim to replicate the findings of a paper that utilized parametrized quantum circuits (PQCs) to forecast time series data in the context of finance. By faithfully reproducing the original experiments, we seek to establish the reliability and applicability of PQCs for financial time series predictions. Building upon these results, we further investigate the impact of hyperparameters and explore novel circuit architectures to optimize the performance of quantum machine learning in time series forecasting.
<!--HTML-->Machine learning has enabled computers to learn from data and improve their performance on tasks, revolutionizing various industries by automating processes, uncovering insights, and enhancing decision-making. NISQ (Noisy Intermediate-Scale Quantum) refers to the current stage of quantum computing, characterized by quantum devices with a moderate number of qubits and significant noise. In the NISQ era, parametrized quantum circuits (PQC) are employed in machine learning as flexible quantum algorithms that can be executed on current noisy quantum devices. By introducing tunable parameters, these circuits can adapt to the limitations of NISQ devices, enabling quantum-enhanced solutions to classification and generative tasks while paving the way for practical applications of quantum machine learning. Time series arise from the abundance of sequential data in various fields, and time series analysis uncovers patterns, trends, and dependencies within the temporal data, enabling informed decision-making and predictions for a wide range of applications. In this project, we aim to replicate the findings of a paper that utilized parametrized quantum circuits (PQCs) to forecast time series data in the context of finance. By faithfully reproducing the original experiments, we seek to establish the reliability and applicability of PQCs for financial time series predictions. Building upon these results, we further investigate the impact of hyperparameters and explore novel circuit architectures to optimize the performance of quantum machine learning in time series forecasting.
Time-series forecasting is vital across sectors such as finance, energy, and environmental science, where accurate future predictions drive informed decision-making. Traditional statistical methods and deep learning models like LSTM and Transformers, while effective, often struggle with high-dimensional data and long-term dependencies. In this paper, we propose a hybrid quantum-classical model that utilizes Parameterized Quantum Circuits (PQCs) to capture complex temporal patterns in multivariate time-series data. Our architecture integrates a classical encoder, a quantum variational processor, and a classical decoder, trained end-to-end using gradient-based optimization. Experiments conducted on benchmark datasets—electricity load, stock prices, and weather forecasting—demonstrate that the hybrid model consistently outperforms classical baselines in terms of Mean Squared Error (MSE), Mean Absolute Error (MAE), and R² score. Robustness analysis confirms the model’s resilience to moderate quantum noise, while an ablation study highlights the performance gain from quantum components. This work showcases the potential of hybrid quantum-classical approaches on Noisy Intermediate-Scale Quantum (NISQ) devices and lays a foundation for scalable, real-world quantum machine learning applications.
Quantum computing represents a groundbreaking approach to high-performance computing. In recent years, quantum computers have progressed from single-qubit processors to systems boasting over 400 qubits. The presence of such a large number of qubits offers significant advantages, including enhanced computational speed—a capability beyond classical computing methods. However, the current stage of quantum computing is referred to as the noisy intermediate-scale quantum (NISQ) era. The existence of noise in this era presents challenges in testing quantum computing applications, leading to considerable variance in application results. Furthermore, the diverse noise characteristics observed across different machines exacerbate this issue, complicating the selection of the appropriate machine for application execution. In response to these challenges, we introduce our Predictive Quantum Machine Learning (PQML) tool. This tool is designed to predict outcomes when executing identical quantum machine learning applications—specifically, a critical suite of variational quantum algorithms—across various quantum computers during the NISQ era. This effort relies on data collected over a 12-month period. To the best of our knowledge, this study represents the first attempt to ensure reproducibility across quantum computers for complex circuits. Additionally, we have developed a model capable of forecasting the accuracy of quantum computers for variational quantum algorithms, with a particular emphasis on quantum machine learning as a case study.
Parameterized quantum circuits (PQC) have emerged as a quantum analogue of deep neural networks and can be trained for discriminative or generative tasks and can be trained with gradient-based optimization on near-term quantum devices [1], [2], [3]. In the current era of quantum computing, known as the noisy intermediate scale quantum (NISQ) era [4], these devices contain a moderate number of qubits (< 100), and algorithmic performance is strongly impacted by hardware noise. Additionally, the training of PQCs are hybrid algorithms, in which the computational workflow is split between quantum and classical computing platforms.
In the era of Noisy Intermediate-Scale Quantum devices, Variational Quantum Circuits in Quantum Machine Learning are gaining attention, advancing towards practical quantum computing applications on NISQ devices. Reinforcement Learning (RL), known for its humanlike, trial-and-error learning, excels in adapting to changing financial environments. In particular, classical algorithms such as Deep Deterministic Policy Gradient (DDPG) and Proximal Policy Optimization (PPO) show promise, while emerging quantum neural networks offer potential for improved function approximation, better generalization capabilities and reduced parameters. In light of these advancements, we introduce a quantum-enhanced version of the DDPG agent (QDDPG), aiming to leverage these quantum capabilities for more efficient financial decisionmaking processes. The quantum part of the model utilizes a parameterized quantum policy, which consists of a sequential reuploading variational circuit with trainable input scaling parameters. Our objective is to explore the practicality and potential benefits of QRL in finance, aiming to realize viable quantum computing applications on NISQ devices. The QDDPG model surpasses traditional analytic strategies in portfolio allocation, achieving higher returns with fewer parameters and a favourable Sharpe ratio. In a simple configuration using a RAW-parameterized quantum policy, the model achieves an average Sharpe ratio of 1.20 across 15 trained agents, compared to 0.96 for the minimum-variance strategy and 0.81 for the buy-and-hold baseline. Furthermore we investigate the impact of quantum noise, a significant challenge for NISQ devices. We analyze various types of noise, such as general depolarization, amplitude damping, phase damping, measurement noise, and shot noise, which uniquely affect quantum computations. Our study quantifies how these noise types influence the performance, reliability, and robustness of the QRL model. We study new techniques to harness quantum noise as hyperparameter to control the exploration-exploitation balance of the agent, using noise as regularization method and to stabilize the training of the agents. This comprehensive analysis aims to not only highlight the challenges posed by quantum noise but also to explore innovative methods to mitigate these effects and enhance the applicability of quantum algorithms in real-world applications.
The growing complexity, interdependencies, and rapid fluctuations inherent in modern financial markets create substantial challenges for accurate forecasting, portfolio optimization, and risk management. Conventional machine learning techniques, while powerful, often face limitations in capturing nonlinear relationships and processing high-dimensional datasets efficiently. Quantum machine learning (QML) has emerged as a promising paradigm that leverages quantum computing principles to enhance predictive modeling in finance. This study presents a comprehensive investigation into the application of QML methods—including variational quantum circuits, quantum kernel estimation, and quantum-enhanced support vector machines—for financial time-series prediction and asset price classification. We propose a hybrid quantum-classical framework that integrates quantum feature mapping with classical optimizers to improve model expressiveness and convergence. Empirical experiments are conducted using historical stock market data and synthetic datasets to benchmark QML approaches against established classical models such as long short-term memory networks and gradient boosting machines. The results demonstrate that QML techniques can achieve superior prediction accuracy and lower computational latency under certain data regimes, particularly when dealing with small-to-medium-sized datasets and high feature correlations. Additionally, the study examines scalability considerations, hardware constraints of near-term quantum devices, and the interpretability of quantum model outputs in financial decision-making contexts. The findings underscore the transformative potential of quantum machine learning as an innovative tool for advancing predictive analytics in finance and provide practical insights into how financial institutions can begin integrating QML capabilities into their workflows.
Financial markets generate complex, high-dimensional time series characterized by nonlinearity, noise, and structural uncertainty, posing persistent challenges for classical machine learning and statistical forecasting models. This paper examines quantum machine learning (QML) architectures for stock market forecasting, anomaly detection, and pattern recognition in financial time series. By leveraging quantum phenomena such as superposition, entanglement, and quantum-enhanced feature spaces, QML models offer new computational paradigms for capturing intricate market dynamics and latent structures. The study synthesizes recent advances in quantum neural networks, variational quantum circuits, and hybrid quantum–classical models, evaluating their applicability to predictive modeling and risk-sensitive detection tasks in finance. The paper argues that QML architectures have the potential to complement classical approaches by improving representational capacity and scalability for complex financial data, while also outlining current technical limitations and research directions necessary for practical deployment.