%0 Journal Article
%A Kaicher, Michael P.
%A Jäger, Simon B.
%A Dallaire-Demers, Pierre-Luc
%A Wilhelm, Frank K.
%T Roadmap for quantum simulation of the fractional quantum Hall effect
%J Physical review / A
%V 102
%N 2
%@ 2469-9926
%C Woodbury, NY
%I Inst.
%M FZJ-2022-03062
%P 022607
%D 2020
%X A major motivation for building a quantum computer is that it provides a tool to efficiently simulate strongly correlated quantum systems. In this paper, we present a detailed roadmap on how to simulate a two-dimensional electron gas—cooled to absolute zero and pierced by a strong transversal magnetic field—on a quantum computer. This system describes the setting of the fractional quantum Hall effect, one of the pillars of modern condensed-matter theory. We give analytical expressions for the two-body integrals that allow for mixing between N Landau levels at a cutoff M in angular momentum and give gate-count estimates for the efficient simulation of the energy spectrum of the Hamiltonian on an error-corrected quantum computer. We then focus on studying efficiently preparable initial states and their overlap with the exact ground state for noisy as well as error-corrected quantum computers. By performing an imaginary time evolution of the covariance matrix, we find the generalized Hartree-Fock solution to the many-body problem and study how a multireference state expansion affects the state overlap. We perform small-system numerical simulations to study the quality of the two initial state Ansätze in the lowest Landau level approximation.
%F PUB:(DE-HGF)16
%9 Journal Article
%U <Go to ISI:>//WOS:000560651300001
%R 10.1103/PhysRevA.102.022607
%U https://juser.fz-juelich.de/record/909194