Print Email Facebook Twitter Variational Quantum Linear Solver for Finite Element Problems: a Poisson equation test case Title Variational Quantum Linear Solver for Finite Element Problems: a Poisson equation test case Author Cappanera, Enrico (TU Delft Aerospace Engineering) Contributor Gerritsma, M.I. (mentor) Möller, M. (graduation committee) Degree granting institution Delft University of Technology Programme Aerospace Engineering Date 2021-09-17 Abstract This research investigates the possibility of solving one dimensional Poisson's equation on quantum computers using the Variational Quantum Linear Solver (VQLS) as a simplified test case for fluid dynamics applications. In this work, Poisson's equation is discretized with the finite element method and the resulting matrix is decomposed as a linear combination of unitaries to be cast in VQLS. When using Pauli Gates as a basis, the matrix is inefficiently decomposed with an exponential number of terms in the number of qubits. On the other hand, using gates with higher entanglement allowed for an efficient decomposition but requires high qubit interconnectivity. Numerical experiments were carried out on a quantum simulator: iterations to success were larger than the best classical counterpart and scaled exponentially for increasing qubits numbers. Across all the experiments performed, scalability was an issue mainly because of the vanishing of the gradient in the cost function Subject VQLSVariational Quantum AlgorithmPoisson equationFinite Element MethodComputational Fluid dynamicsVariational Quantum Linear SolverUnitary DecompositionQiskitquantum measurement To reference this document use: http://resolver.tudelft.nl/uuid:deba389d-f30f-406c-ad7b-babb1b298d87 Embargo date 2021-09-17 Part of collection Student theses Document type master thesis Rights © 2021 Enrico Cappanera Files PDF MsC_Thesis_E_Cappanera_49 ... _Final.pdf 5.58 MB Close viewer /islandora/object/uuid:deba389d-f30f-406c-ad7b-babb1b298d87/datastream/OBJ/view