Capturing dynamics with noisy quantum computers

Dechant, D.S. (2026)

Doctoral Thesis

Quantum computing represents a fundamentally new computational paradigm, capable of addressing problems that are intractable for classical computers. Despite the promise, current quantum devices are small, noisy, unreliable, and costly, making theoretical analysis and classical simulations essential for understanding their capabilities and limitations. A key focus of quantum computing is modeling dynamics (how the state of a system evolves over time), which can be described mathematically through differential equations or time series. In this thesis, we investigate the application of quantum computing to capturing such dynamics from several complementary perspectives.
First, we show that by rescaling input data appropriately and incorporating derivative information into training, quantum models can achieve stronger and more accurate approximations, allowing them to capture the dynamical behavior of systems.
Second, we analyze quantum algorithms for solving differential equations for errors arising from both classical numerical methods and quantum shot noise, enabling precise estimates of computational resources.
Third, we introduce a quantum state tomography approach that mitigates shot noise in the reconstruction of quantum states from measurement data by incorporating physical constraints through semidefinite programming.
Finally, we show that quantum generative models, such as quantum generative adversarial networks, can generate synthetic time series that accurately capture both the statistical distributions and temporal correlations of real-world financial data; tasks that are difficult for classical models to achieve.
Overall, these results highlight both the opportunities and limitations of noisy quantum computers in modeling and simulating complex dynamical systems.

• Quantum algorithms
• Quantum computing
• Quantum information
• Partial differential equations
• Quantum state tomography
• Quantum generative adversarial networks
• Quantum machine learning

• All authors: Dechant, D.S.
• Supervisor: Tura, J.; Dunjko, V.
• Committee: Molen, S.J. van der; Beenakker, C.W.J.; Nieuwenburg, E.P.L. van; Kliesch, M.; Liu, N.
• Qualification: Doctor (dr.)
• Awarding Institution: Leiden Institute of Physics (LION), Faculty of Science, Leiden University
• Date: 2026-02-17