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dc.contributor.authorMotamedi, Arsalan 14:07:59 (GMT) 14:07:59 (GMT)
dc.description.abstractGibbs sampling from continuous real-valued functions is a challenging problem of interest in machine learning. Here we leverage quantum Fourier transforms to build a quantum algorithm for this task when the function is periodic. We use the quantum algorithms for solving linear ordinary differential equations to solve the Fokker--Planck equation and prepare a quantum state encoding the Gibbs distribution. We show that the efficiency of interpolation and differentiation of these functions on a quantum computer depends on the rate of decay of the Fourier coefficients of the Fourier transform of the function. We view this property as a concentration of measure in the Fourier domain, and also provide functional analytic conditions for it. Our algorithm makes zeroeth order queries to a quantum oracle of the function. Despite suffering from an exponentially long mixing time, this algorithm allows for exponentially improved precision in sampling, and polynomial quantum speedups in mean estimation in the general case, and particularly under geometric conditions we identify for the critical points of the energy function.en
dc.publisherUniversity of Waterlooen
dc.titleQuantum Algorithms for Interpolation and Samplingen
dc.typeMaster Thesisen
dc.pendingfalse and Astronomyen (Quantum Information)en of Waterlooen
uws-etd.degreeMaster of Scienceen
uws.contributor.advisorRonagh, Pooya
uws.contributor.advisorLaflamme, Raymond
uws.contributor.affiliation1Faculty of Scienceen

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