Bayesian Optimization of Variational Quantum Eigensolvers

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2023Publisher
Πανεπιστήμιο Κύπρου, Σχολή Θετικών και Εφαρμοσμένων Επιστημών / University of Cyprus, Faculty of Pure and Applied SciencesGoogle Scholar check
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The variational quantum eigensolver (VQE) is a hybrid quantum-classical algorithm used to
find the ground state of a Hamiltonian using variational methods. It has a wide range of
potential applications, from quantum chemistry to lattice gauge theories in the Hamiltonian
formulation. VQE relies on quantum computers to evaluate the energy of the system in terms
of circuit parameters, and it minimizes this parametrized energy with a classical optimization
routine. This work describes a Bayesian optimization (BO) algorithm specifically designed
to minimize the parametrized energy obtained with a quantum computer. BO based on
Gaussian process regression (GPR) is an algorithm for finding the global minimum of a
black-box cost function, e.g. the energy, with a very low number of iterations even when
using data affected by statistical noise.
Furthermore, the GPR procedure developed for this work proved to be very versatile as
we also used it to compute discrete integral transforms of noisy data. In particular, this
procedure was used to reconstruct parton distribution functions from lattice QCD data.
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