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QI: Fachverband Quanteninformation

QI 5: Quantum Computing and Algorithms II

QI 5.6: Vortrag

Dienstag, 10. März 2026, 10:45–11:00, BEY/0137

Quantum-inspired space-time PDE solver and dynamic mode decomposition — •Raghavendra Dheeraj Peddinti¹, Stefano Pisoni^1,2, Narsimha Rapaka³, Mohamed K. Riahi³, Egor Tiunov¹, and Leandro Aolita¹ — ¹Quantum Research Center, Technology Innovation Institute, Abu Dhabi, UAE — ²Hamburg University of Technology, Institute for Quantum Inspired and Quantum Optimization, Germany — ³Emirates Nuclear Technology Center, Khalifa University of Science and Technology, Abu Dhabi, UAE

Numerical solutions of partial differential equations (PDEs) are central to the understanding of dynamical systems. Space-time methods that treat the combined space-time domain simultaneously offer better stability and accuracy than standard time-stepping schemes. Interestingly, data-driven approaches, such as dynamic mode decomposition (DMD), also employ a combined space-time representation. However, the curse of dimensionality often limits the practical benefits of space-time methods. In this work, we investigate quantum-inspired methods for space-time approaches, both for solving PDEs and for making DMD predictions. We achieve this goal by treating both spatial and temporal dimensions within a single matrix product state (MPS) encoding. First, we benchmark our MPS space-time solver for both linear and nonlinear PDEs, observing that the MPS ansatz accurately captures the underlying spatio-temporal correlations while having significantly fewer degrees of freedom. Second, we develop an MPS-DMD algorithm for accurate long-term predictions of nonlinear systems, with runtime scaling logarithmically with both spatial and temporal resolution.

Keywords: tensor networks; numerical methods; quantum-inspired methods