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Technical University of Crete
Technical University of Crete
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| URI: | http://purl.tuc.gr/dl/dias/A837B96D-6862-4B48-BF10-2E8C4F7C1B2F | ||
| Year | 2025 | ||
| Type of Item | Diploma Work | ||
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| Bibliographic Citation | Georgios Kokkinis, "NN assisted quantum numerical simulation of Burgers’ equation", Diploma Work, School of Electrical and Computer Engineering, Technical University of Crete, Chania, Greece, 2025 https://doi.org/10.26233/heallink.tuc.103711 | ||
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This thesis develops a numerical study of the one-dimensional viscous Burgers’ equation, of Computational Fluid Dynamics (CFD), within the discipline of Quantum Computation specialized in the area of Quantum Simulations. Extensions of quantum simulation methodology to non-linear partial differential equationsof classical CFD, is a recent novel strand of applications that intends to develop quantum computational algorithms for solving applied PDEs within the reach of near-term quantum devices. The choice of Burgers’ equation is motivated by its attractive technical features (balanced occurrence of quadratic non-linearityand quadratic order derivative, shock way formation and propagation), and its physical significance and ubiquity.Utilizing recently available theoretical advantages, a method addressing the quantum simulation task a quantum-classical hybrid approach is developed: On the quantum side, a quantum circuit simulating ideally the equation is constructed; On the classical side, a classical neural network (specifically a physics informedneural network, PINN) is introduced to correct possible errors in the ideal solution via its optimizer functionality. The QCirc-PINN hybrid simulator departs from the well paved way of variational-algorithm (VQA) solution methodology for PDEs by combining QCirc and its noise affected ideal solution (i.e. faulty solution) with a PINN operationally acting as a correction backend of the simulator. Functionally,the QCirc splits into two modules: one implementing the non-linear term via unitarized non-local qubit gates and one for implementing higher-order derivatives. The latter employs standard elements of simple harmonic oscillator phase-space techniqces to accomplish its aims. The construction is amenable to accuratesimulation by few qubits, so that the whole QCirc-PINN hybrid simulator can be implemented by available state of the art multi-qubit architectures. This work summarizes the prospect of QCirc-PINN simulator that will enable addressing the solutions of various extensions of Burgers’ equation within the broaderframework of Quantum Computational Fluid Dynamics QCFD in combination with the PINN modalities.
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