2 research outputs found
Summation formulas associated with the Lauricella function FA(r)
AbstractThe authors make use of some rather elementary techniques in order to derive several summation formulas associated with Lauricella's hypergeometric function FA(r) in r variables (and also with its familiar generalizations). A number of (known or new) consequences of these summation formulas are also considered
Roadmap for quantum simulation of the fractional quantum Hall effect
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 Landau levels at a cutoff 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 table