Roadmap for quantum simulation of the fractional quantum Hall effect

• URL: http://arxiv.org/abs/2003.02517v1
• Date: Thu, 5 Mar 2020 10:17:21 GMT
• Title: Roadmap for quantum simulation of the fractional quantum Hall effect
• Authors: Michael Kaicher, Simon Balthasar J\"ager, Pierre-Luc Dallaire-Demers, Frank Wilhelm
• Abstract summary: 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 magnetic field---on a quantum computer.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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