Roadmap for quantum simulation of the fractional quantum Hall effect

Autor: Kaicher, Michael, Jäger, Simon Balthasar, Dallaire-Demers, Pierre-Luc, Wilhelm, Frank
Rok vydání: 2020
Předmět:
Zdroj: Phys. Rev. A 102, 022607 (2020)
Druh dokumentu: Working Paper
DOI: 10.1103/PhysRevA.102.022607
Popis: 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.
Comment: 30 pages, 8 figures, 4 tables
Databáze: arXiv