Benchmarking a novel efficient numerical method for localized 1D
Fermi-Hubbard systems on a quantum simulator
- URL: http://arxiv.org/abs/2105.06372v2
- Date: Mon, 8 Nov 2021 19:07:36 GMT
- Title: Benchmarking a novel efficient numerical method for localized 1D
Fermi-Hubbard systems on a quantum simulator
- Authors: Bharath Hebbe Madhusudhana, Sebastian Scherg, Thomas Kohlert, Immanuel
Bloch, Monika Aidelsburger
- Abstract summary: We show that a quantum simulator can be used to in-effect solve for the dynamics of a many-body system.
We use a neutral-atom Fermi-Hubbard quantum simulator with $L_textexpsimeq290$ lattice sites to benchmark its performance.
We derive a simple prediction of the behaviour of interacting Bloch oscillations for spin-imbalanced Fermi-Hubbard systems.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: Quantum simulators have made a remarkable progress towards exploring the
dynamics of many-body systems, many of which offer a formidable challenge to
both theoretical and numerical methods. While state-of-the-art quantum
simulators are in principle able to simulate quantum dynamics well outside the
domain of classical computers, they are noisy and limited in the variability of
the initial state of the dynamics and the observables that can be measured.
Despite these limitations, here we show that such a quantum simulator can be
used to in-effect solve for the dynamics of a many-body system. We develop an
efficient numerical technique that facilitates classical simulations in regimes
not accessible to exact calculations or other established numerical techniques.
The method is based on approximations that are well suited to describe
localized one-dimensional Fermi-Hubbard systems. Since this new method does not
have an error estimate and the approximations do not hold in general, we use a
neutral-atom Fermi-Hubbard quantum simulator with $L_{\text{exp}}\simeq290$
lattice sites to benchmark its performance in terms of accuracy and convergence
for evolution times up to $700$ tunnelling times. We then use these
approximations in order to derive a simple prediction of the behaviour of
interacting Bloch oscillations for spin-imbalanced Fermi-Hubbard systems, which
we show to be in quantitative agreement with experimental results. Finally, we
demonstrate that the convergence of our method is the slowest when the
entanglement depth developed in the many-body system we consider is neither too
small nor too large. This represents a promising regime for near-term
applications of quantum simulators.
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