Lanczos recursion on a quantum computer for the Green's function*

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 fraction representation of an interacting Green's function, useful for condensed matter, particle physics, and other areas. The wavefunction does not need to be re-prepared at each iteration. The quantum algorithm represents an exponential reduction in memory required over classical methods.

Using similar methods, the pure-density functional and Kohn-Sham potentials can also be determined from the quantum computer [1].

[1] T.E. Baker and D. Poulin, “Density functionals and Kohn-Sham potentials with minimal wavefunction preparations on a quantum computer” (2020) arXiv: 2008.05592