Institute Seminar | Thomas E. Baker | 2021.10.13 | 2/2 Discussion
Channel: CASUS.science
Date: 25/11/2021

TITLE: Lanczos recursion on a quantum computer for the Green’s function and wavefunctions

BIO
Thomas has focused on a variety of theoretical physics topics from classical physics to density functional theory and quantum computing. He often uses tensor networks as a computational tool. For his doctoral work, Thomas used the density matrix renormalization group (DMRG) to investigate the exact properties of density functional theory. It could be demonstrated that the pure-density functional could be learned by machine learning techniques. Recently Thomas has been using tensor networks to model superconducting circuits and also working on algorithms for quantum computing – the topic of his talk at CASUS.

ABSTRACT
A state-preserving quantum counting algorithm is used to obtain coefficients of a Lanczos recursion from a single ground-state wave function on the quantum computer [1]. This is used to compute the continued fraction representation of an interacting Green’s function for use in condensed matter, particle physics, and other areas. The wave function does not need to be re-prepared at each iteration. The quantum algorithm represents an exponential reduction in memory over known classical methods. An extension of the method to determining excitations is also possible [2]. Similar techniques can be used to determine the density functional and will be discussed [3].

References
[1] T.E. Baker, “Lanczos recursion on a quantum computer for the Green’s function and ground state” Phys. Rev. A 103, 032404 (2021) link
[2] T.E. Baker, “Block Lanczos method for excited states on a quantum computer” arXiv: 2109.14114 link
[3] T.E. Baker and D. Poulin, “Density functionals and Kohn-Sham potentials with minimal wavefunction preparations on a quantum computer”, Phys. Rev. Research 2, 043238 (2020) link

LICENSE:
CC BY-SA 4.0

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