TY  - JOUR
AU  - Kaicher, Michael P.
AU  - Jäger, Simon B.
AU  - Dallaire-Demers, Pierre-Luc
AU  - Wilhelm, Frank K.
TI  - Roadmap for quantum simulation of the fractional quantum Hall effect
JO  - Physical review / A
VL  - 102
IS  - 2
SN  - 2469-9926
CY  - Woodbury, NY
PB  - Inst.
M1  - FZJ-2022-03062
SP  - 022607
PY  - 2020
AB  - 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.
LB  - PUB:(DE-HGF)16
UR  - <Go to ISI:>//WOS:000560651300001
DO  - DOI:10.1103/PhysRevA.102.022607
UR  - https://juser.fz-juelich.de/record/909194
ER  -