Enhancing density functional theory using the variational quantum eigensolver
arxiv(2024)
摘要
Quantum computers open up new avenues for modelling the physical properties
of materials and molecules. Density Functional Theory (DFT) is the gold
standard classical algorithm for predicting these properties, but relies on
approximations of the unknown universal functional, limiting its general
applicability for many fundamental and technologically relevant systems. In
this work we develop a hybrid quantum/classical algorithm called quantum
enhanced DFT (QEDFT) that systematically constructs quantum approximations of
the universal functional using data obtained from a quantum computer.
We benchmark the QEDFT algorithm on the Fermi-Hubbard model, both numerically
and on data from experiments on real quantum hardware. We find that QEDFT
surpasses the quality of groundstate results obtained from Hartree-Fock DFT, as
well as from direct application of conventional quantum algorithms such as VQE.
Furthermore, we demonstrate that QEDFT works even when only noisy, low-depth
quantum computation is available, by benchmarking the algorithm on data
obtained from Google's quantum computer.
We further show how QEDFT also captures quintessential properties of strongly
correlated Mott physics for large Fermi-Hubbard systems using functionals
generated on much smaller system sizes. Our results indicate that QEDFT can be
applied to realistic materials and molecular systems, and has the potential to
outperform the direct application of either DFT or VQE alone, without the
requirement of large scale or fully fault-tolerant quantum computers.
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