Journal Article

FZJ-2022-03062

http://join2-wiki.gsi.de/foswiki/pub/Main/Artwork/join2_logo100x88.png Roadmap for quantum simulation of the fractional quantum Hall effect

Kaicher, M. P. ; Jäger, S. B. ; Dallaire-Demers, P.-L. ; Wilhelm, F. K. (Corresponding author)FZJ*

2020
Inst. Woodbury, NY

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Please use a persistent id in citations: http://hdl.handle.net/2128/31657  doi:10.1103/PhysRevA.102.022607

Abstract: 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 Ansätze in the lowest Landau level approximation.

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Contributing Institute(s):

1. Quantum Computing Analytics (PGI-12)

Research Program(s):

1. 5215 - Towards Quantum and Neuromorphic Computing Functionalities (POF4-521) (POF4-521)

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Database coverage:
; ; ; Clarivate Analytics Master Journal List ; Current Contents - Electronics and Telecommunications Collection ; Current Contents - Physical, Chemical and Earth Sciences ; Ebsco Academic Search ; Essential Science Indicators ; IF < 5 ; JCR ; SCOPUS ; Science Citation Index Expanded ; Web of Science Core Collection

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