Quantum Machine Learning

Quantum Machine Learning methods for Fourier-based distribution estimation with application in option pricing ArXiv ID: 2510.19494 “View on arXiv” Authors: Fernando Alonso, Álvaro Leitao, Carlos Vázquez Abstract The ongoing progress in quantum technologies has fueled a sustained exploration of their potential applications across various domains. One particularly promising field is quantitative finance, where a central challenge is the pricing of financial derivatives-traditionally addressed through Monte Carlo integration techniques. In this work, we introduce two hybrid classical-quantum methods to address the option pricing problem. These approaches rely on reconstructing Fourier series representations of statistical distributions from the outputs of Quantum Machine Learning (QML) models based on Parametrized Quantum Circuits (PQCs). We analyze the impact of data size and PQC dimensionality on performance. Quantum Accelerated Monte Carlo (QAMC) is employed as a benchmark to quantitatively assess the proposed models in terms of computational cost and accuracy in the extraction of Fourier coefficients. Through the numerical experiments, we show that the proposed methods achieve remarkable accuracy, becoming a competitive quantum alternative for derivatives valuation. ...

From Classical Rationality to Contextual Reasoning: Quantum Logic as a New Frontier for Human-Centric AI in Finance ArXiv ID: 2510.05475 “View on arXiv” Authors: Fabio Bagarello, Francesco Gargano, Polina Khrennikova Abstract We consider state of the art applications of artificial intelligence (AI) in modelling human financial expectations and explore the potential of quantum logic to drive future advancements in this field. This analysis highlights the application of machine learning techniques, including reinforcement learning and deep neural networks, in financial statement analysis, algorithmic trading, portfolio management, and robo-advisory services. We further discuss the emergence and progress of quantum machine learning (QML) and advocate for broader exploration of the advantages provided by quantum-inspired neural networks. ...

Quantum and Classical Machine Learning in Decentralized Finance: Comparative Evidence from Multi-Asset Backtesting of Automated Market Makers ArXiv ID: 2510.15903 “View on arXiv” Authors: Chi-Sheng Chen, Aidan Hung-Wen Tsai Abstract This study presents a comprehensive empirical comparison between quantum machine learning (QML) and classical machine learning (CML) approaches in Automated Market Makers (AMM) and Decentralized Finance (DeFi) trading strategies through extensive backtesting on 10 models across multiple cryptocurrency assets. Our analysis encompasses classical ML models (Random Forest, Gradient Boosting, Logistic Regression), pure quantum models (VQE Classifier, QNN, QSVM), hybrid quantum-classical models (QASA Hybrid, QASA Sequence, QuantumRWKV), and transformer models. The results demonstrate that hybrid quantum models achieve superior overall performance with 11.2% average return and 1.42 average Sharpe ratio, while classical ML models show 9.8% average return and 1.47 average Sharpe ratio. The QASA Sequence hybrid model achieves the highest individual return of 13.99% with the best Sharpe ratio of 1.76, demonstrating the potential of quantum-classical hybrid approaches in AMM and DeFi trading strategies. ...

On Quantum BSDE Solver for High-Dimensional Parabolic PDEs ArXiv ID: 2506.14612 “View on arXiv” Authors: Howard Su, Huan-Hsin Tseng Abstract We propose a quantum machine learning framework for approximating solutions to high-dimensional parabolic partial differential equations (PDEs) that can be reformulated as backward stochastic differential equations (BSDEs). In contrast to popular quantum-classical network hybrid approaches, this study employs the pure Variational Quantum Circuit (VQC) as the core solver without trainable classical neural networks. The quantum BSDE solver performs pathwise approximation via temporal discretization and Monte Carlo simulation, framed as model-based reinforcement learning. We benchmark VQCbased and classical deep neural network (DNN) solvers on two canonical PDEs as representatives: the Black-Scholes and nonlinear Hamilton-Jacobi-Bellman (HJB) equations. The VQC achieves lower variance and improved accuracy in most cases, particularly in highly nonlinear regimes and for out-of-themoney options, demonstrating greater robustness than DNNs. These results, obtained via quantum circuit simulation, highlight the potential of VQCs as scalable and stable solvers for highdimensional stochastic control problems. ...

Comparative Study of Long Short-Term Memory (LSTM) and Quantum Long Short-Term Memory (QLSTM): Prediction of Stock Market Movement ArXiv ID: 2409.08297 “View on arXiv” Authors: Unknown Abstract In recent years, financial analysts have been trying to develop models to predict the movement of a stock price index. The task becomes challenging in vague economic, social, and political situations like in Pakistan. In this study, we employed efficient models of machine learning such as long short-term memory (LSTM) and quantum long short-term memory (QLSTM) to predict the Karachi Stock Exchange (KSE) 100 index by taking monthly data of twenty-six economic, social, political, and administrative indicators from February 2004 to December 2020. The comparative results of LSTM and QLSTM predicted values of the KSE 100 index with the actual values suggested QLSTM a potential technique to predict stock market trends. ...

Statistics-Informed Parameterized Quantum Circuit via Maximum Entropy Principle for Data Science and Finance ArXiv ID: 2406.01335 “View on arXiv” Authors: Unknown Abstract Quantum machine learning has demonstrated significant potential in solving practical problems, particularly in statistics-focused areas such as data science and finance. However, challenges remain in preparing and learning statistical models on a quantum processor due to issues with trainability and interpretability. In this letter, we utilize the maximum entropy principle to design a statistics-informed parameterized quantum circuit (SI-PQC) for efficiently preparing and training of quantum computational statistical models, including arbitrary distributions and their weighted mixtures. The SI-PQC features a static structure with trainable parameters, enabling in-depth optimized circuit compilation, exponential reductions in resource and time consumption, and improved trainability and interpretability for learning quantum states and classical model parameters simultaneously. As an efficient subroutine for preparing and learning in various quantum algorithms, the SI-PQC addresses the input bottleneck and facilitates the injection of prior knowledge. ...

Empowering Credit Scoring Systems with Quantum-Enhanced Machine Learning ArXiv ID: 2404.00015 “View on arXiv” Authors: Unknown Abstract Quantum Kernels are projected to provide early-stage usefulness for quantum machine learning. However, highly sophisticated classical models are hard to surpass without losing interpretability, particularly when vast datasets can be exploited. Nonetheless, classical models struggle once data is scarce and skewed. Quantum feature spaces are projected to find better links between data features and the target class to be predicted even in such challenging scenarios and most importantly, enhanced generalization capabilities. In this work, we propose a novel approach called Systemic Quantum Score (SQS) and provide preliminary results indicating potential advantage over purely classical models in a production grade use case for the Finance sector. SQS shows in our specific study an increased capacity to extract patterns out of fewer data points as well as improved performance over data-hungry algorithms such as XGBoost, providing advantage in a competitive market as it is the FinTech and Neobank regime. ...

Improved Financial Forecasting via Quantum Machine Learning ArXiv ID: 2306.12965 “View on arXiv” Authors: Unknown Abstract Quantum algorithms have the potential to enhance machine learning across a variety of domains and applications. In this work, we show how quantum machine learning can be used to improve financial forecasting. First, we use classical and quantum Determinantal Point Processes to enhance Random Forest models for churn prediction, improving precision by almost 6%. Second, we design quantum neural network architectures with orthogonal and compound layers for credit risk assessment, which match classical performance with significantly fewer parameters. Our results demonstrate that leveraging quantum ideas can effectively enhance the performance of machine learning, both today as quantum-inspired classical ML solutions, and even more in the future, with the advent of better quantum hardware. ...