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000909194 1001_ $$00000-0001-7986-5127$$aKaicher, Michael P.$$b0
000909194 245__ $$aRoadmap for quantum simulation of the fractional quantum Hall effect
000909194 260__ $$aWoodbury, NY$$bInst.$$c2020
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000909194 520__ $$aA 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.
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000909194 7001_ $$0P:(DE-Juel1)188115$$aJäger, Simon B.$$b1
000909194 7001_ $$00000-0002-9316-5597$$aDallaire-Demers, Pierre-Luc$$b2
000909194 7001_ $$0P:(DE-HGF)0$$aWilhelm, Frank K.$$b3$$eCorresponding author
000909194 773__ $$0PERI:(DE-600)2844156-4$$a10.1103/PhysRevA.102.022607$$gVol. 102, no. 2, p. 022607$$n2$$p022607$$tPhysical review / A$$v102$$x2469-9926$$y2020
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