Hubbard physics with Rydberg atoms: using a quantum spin simulator to simulate strong fermionic correlations

TL;DR

This paper introduces a hybrid quantum-classical approach using Rydberg atoms to simulate strongly correlated fermionic systems, effectively capturing equilibrium and dynamic properties despite experimental imperfections.

Contribution

It presents a novel slave-spin method combined with Rydberg-based quantum processors to simulate fermionic models without traditional fermion-to-spin mappings.

Findings

Method yields accurate results despite imperfections

Enables study of out-of-equilibrium Hubbard physics

Applicable to complex regimes like doping and multiorbital systems

Abstract

We propose a hybrid quantum-classical method to investigate the equilibrium physics and the dynamics of strongly correlated fermionic models with spin-based quantum processors. Our proposal avoids the usual pitfalls of fermion-to-spin mappings thanks to a slave-spin method which allows to approximate the original Hamiltonian into a sum of self-correlated free-fermions and spin Hamiltonians. Taking as an example a Rydberg-based analog quantum processor to solve the interacting spin model, we avoid the challenges of variational algorithms or Trotterization methods. We explore the robustness of the method to experimental imperfections by applying it to the half-filled, single-orbital Hubbard model on the square lattice in and out of equilibrium. We show, through realistic numerical simulations of current Rydberg processors, that the method yields quantitatively viable results even in the presence of imperfections: it allows to gain insights into equilibrium Mott physics as well as the dynamics under interaction quenches. This method thus paves the way to the investigation of physical regimes -- whether out-of-equilibrium, doped, or multiorbital -- that are difficult to explore with classical processors.