Density functionals and Kohn-Sham potentials with minimal wavefunction preparations on a quantum computer

@article{Baker2020DensityFA,
  title={Density functionals and Kohn-Sham potentials with minimal wavefunction preparations on a quantum computer},
  author={Thomas E. Baker and David Poulin},
  journal={arXiv: Quantum Physics},
  year={2020}
}
One of the potential applications of a quantum computer is solving quantum chemical systems. It is known that one of the fastest ways to obtain somewhat accurate solutions classically is to use approximations of density functional theory. We demonstrate a general method for obtaining the exact functional as a machine learned model from a sufficiently powerful quantum computer. Only existing assumptions for the current feasibility of solutions on the quantum computer are used. Several known… 

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References

SHOWING 1-10 OF 271 REFERENCES

The calculation of atomic fields

  • L. H. Thomas
  • Physics
    Mathematical Proceedings of the Cambridge Philosophical Society
  • 1927
The theoretical calculation of observable atomic constants is often only possible if the effective electric field inside the atom is known. Some fields have been calculated to fit observed data but

Markov chains for exploring posterior

  • nealing,” Statistical science
  • 1993

A dimensional acceleration of gradient

  • 2016

Stanley Raimes, “Many-electron theory,

  • 1972

Rates of convergence and error

  • ues,” J. Chem. Phys
  • 1984

Lanczos recursion on a quantum computer for the Green's function and ground state

The technique of quantum counting is used to obtain coefficients from a Lanczos recursion from a single ground-state wavefunction on the quantum computer. This is used to compute the continued

Insights into one-body density matrices using deep learning.

Known physical properties of the 1-RDM are exploited in the simplest possible cases to perform feature engineering, where they inform the structure of the models from known mathematical relations, allowing us to integrate existing understanding into the machine learning methods.

Efficient learning of a one-dimensional density functional theory

This work studies a theory of spinless fermions on a one-dimensional lattice, implicitly represented by a neural network, which predicts, besides the ground-state energy and density distribution, density-density correlation functions and shows that the network results are of high quantitative accuracy.
...