Roadmap for quantum simulation of the fractional quantum Hall effect

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 Ansatze in the lowest Landau level approximation.