Matrix Product State Based Quantum Generative Adversarial Networks for Financial Time Series Modelling

This thesis develops a quantum-inspired framework for modelling financial time series by using Quantum Generative Adversarial Networks (QGANs) based on Ma trix Product States (MPS). Traditional financial models often struggle to capture the complex, high-dimensional characteristics of market data, leading to short comings in predicting or simulating financial phenomena accurately. To overcome these limitations, we explore a simulated quantum-inspired framework that lever ages the computational advantages of quantum systems. In our approach, MPS are used to represent quantum states efficiently while controlling entanglement through the so-called bond dimension. This controlled representation allows the QGAN to explore a high-dimensional state space with improved precision com pared to classical GANs. We simulate these networks to assess their performance in reproducing the subtle statistical features inherent in financial time series. We show that tensor-network techniques can...Show moreThis thesis develops a quantum-inspired framework for modelling financial time series by using Quantum Generative Adversarial Networks (QGANs) based on Ma trix Product States (MPS). Traditional financial models often struggle to capture the complex, high-dimensional characteristics of market data, leading to short comings in predicting or simulating financial phenomena accurately. To overcome these limitations, we explore a simulated quantum-inspired framework that lever ages the computational advantages of quantum systems. In our approach, MPS are used to represent quantum states efficiently while controlling entanglement through the so-called bond dimension. This controlled representation allows the QGAN to explore a high-dimensional state space with improved precision com pared to classical GANs. We simulate these networks to assess their performance in reproducing the subtle statistical features inherent in financial time series. We show that tensor-network techniques can replicate key statistical features of finan cial time series, providing both a foundation for future experiments on quantum hardware and advancing quantum machine-learning methodologies.Show less

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Matrix Product State Based Quantum Generative Adversarial Networks for Financial Time Series Modelling