  A major motivation for building a quantum computer is that it provides a tool
to efficiently simulate strongly correlated quantum systems. In this work, 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 (FQHE), 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
multi-reference state expansion affects the state overlap. We perform
small-system numerical simulations to study the quality of the two initial
state Ans\"{a}tze in the Lowest Landau Level (LLL) approximation.
