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 . 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  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 . 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 . Implementing these algorithms on reduced models with near-term quantum computers will also be addressed.
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