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| Home > Publications database > Investigating scaling properties for quantum annealing to solve the Fermi-Hubbard model using the kinetic energy part as the driving Hamiltonian |
| Conference Presentation (After Call) | FZJ-2024-06526 |
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2024
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Please use a persistent id in citations: doi:10.34734/FZJ-2024-06526
Abstract: Quantum annealing can help in finding the ground state of Hamiltonians describing many body systems. One such Hamiltonian is the Fermi-Hubbard Hamiltonian. We investigate the scaling complexity for the quantum annealing process carried out using the kinetic energy part of the Hubbard model as driving Hamiltonian for ground state calculations. The way we do this is by studying the gaps between the ground state and the 1st relevant excited state that participates in the diabatic evolution for a 1-dimensional system. The behavior of these gaps with increasing system size could hint at polynomial scaling of required annealing time for finding the ground state of the Hubbard Hamiltonian. We also try to extend this idea to a Hubbard model ladder to learn more about the scaling behavior of gaps relevant to adiabatic evolution. Further, we discuss about initial state preparation for the quantum annealing strategy under study. Information on the complexity coupled with an efficient way of preparing the initial state could bolster our hopes for using adiabatic quantum computation for solving correlated many-body Hamiltonians.
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