The Levy-Lieb embedding of density functional theory and its Quantum Kernel: Illustration for the Hubbard Dimer using near-term quantum algorithms

• URL: http://arxiv.org/abs/2207.08995v1
• Date: Tue, 19 Jul 2022 00:23:52 GMT
• Title: The Levy-Lieb embedding of density functional theory and its Quantum Kernel: Illustration for the Hubbard Dimer using near-term quantum algorithms
• Authors: C. D. Pemmaraju, Amol Deshmukh
• Abstract summary: We numerically implement the Levy-Lieb procedure for a paradigmatic lattice system, the Hubbard dimer. We demonstrate density variational minimization using the resulting hybrid quantum-classical scheme.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The constrained-search formulation of Levy and Lieb provides a concrete mapping from N-representable densities to the space of N-particle wavefunctions and explicitly defines the universal functional of density functional theory. We numerically implement the Levy-Lieb procedure for a paradigmatic lattice system, the Hubbard dimer, using a modified variational quantum eigensolver approach. We demonstrate density variational minimization using the resulting hybrid quantum-classical scheme featuring real-time computation of the Levy-Lieb functional along the search trajectory. We further illustrate a fidelity based quantum kernel associated with the density to pure-state embedding implied by the Levy-Lieb procedure and employ the kernel for learning observable functionals of the density. We study the kernel's ability to generalize with high accuracy through numerical experiments on the Hubbard dimer.

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