Density functionals, Kohn-Sham potentials, and Green’s functions from a quantum computer

Solving quantum chemistry problems on the quantum computer faces several hurdles in practical implementation [1]. Nevertheless, even incremental improvements in finding exact solutions for quantum chemistry can lead to real improvements in everyday life, so exploring the capabilities for quantum computers is worthwhile.  In this talk, I discuss how to export solutions from a quantum computer to a classical user as a machine learned model [2,3]. The quantities necessary for both pure-density functionals and Kohn-Sham potentials can be found, either quantity provably characterizes the quantum ground state with fewer parameters than the full wavefunction. The main goal in this proposal [4] is to avoid excessive measurement so the wavefunction can be recycled and the pre-factor for solving the quantum ground-state is reduced. Useful quantities for these and other theories can be extracted without full measurement using a quantum counting algorithm [5]. It will also be shown that finding the exact continued fraction representation of the Green’s function can be accomplished with exponentially less memory than existing classical techniques [6]. Implementing these algorithms on reduced models with near-term quantum computers will also be addressed.

[1] David Poulin, Matthew B Hastings, Dave Wecker, Nathan Wiebe, Andrew C Doherty, and Matthias Troyer, “The Trotter step size required for accurate quantum simulation of quantum chemistry” Quantum Information and Computation 15, 0361–0384 (2015).
[2] L. Li (李力), T.E. Baker, S.R. White, and K. Burke, “Pure density functional for strong correlations and the thermodynamic limit from machine learning” Phys. Rev. B 94, 245129 (2016)
[3] J. Hollingsworth, L. Li (李力), T.E. Baker, and K. Burke, “Can exact conditions improve machine-learned density functionals?” J. Chem. Phys. 148, 241743 (2018)
[4] T.E. Baker, and D. Poulin “Density functionals and Kohn-Sham potentials with minimal wavefunction preparations on a quantum computer” (2020) arXiv: 2008.05592
[5] Kristan Temme, Tobias J Osborne, Karl G Vollbrecht, David Poulin, and Frank Verstraete, “Quantum metropolis sampling,” Nature 471, 87 (2011).
[6] T.E. Baker “Computing Green’s functions on a quantum computer via Lanczos recursion” (2020) arXiv: 2008.05593