Programming optical-lattice Fermi-Hubbard quantum simulators

TL;DR

This paper develops variational quantum algorithms for preparing ground states of Fermi-Hubbard models on optical lattice simulators, enabling efficient exploration of complex many-body fermionic systems beyond classical capabilities.

Contribution

It introduces variational, pre-compiled quantum circuits for ground-state preparation of native Fermi-Hubbard models, including extended models with non-native terms, and discusses imaginary-time evolution techniques.

Findings

Significant speedups over adiabatic protocols for ground-state preparation.

Ability to target extended Fermi-Hubbard models with non-native terms.

Protocols applicable to 2D setups beyond classical simulation capabilities.

Abstract

Fermionic atoms in optical lattices provide a native implementation of Fermi-Hubbard (FH) models that can be used as analog quantum simulators of many-body fermionic systems. Recent experimental advances include the time-dependent local control of chemical potentials and tunnelings, and thus enable to operate this platform digitally as a programmable quantum simulator. Here, we explore these opportunities and develop ground-state preparation algorithms for different fermionic models, based on the ability to implement both single-particle and many-body, high-fidelity fermionic gates, as provided by the native FH Hamiltonian. In particular, we first design variational, pre-compiled quantum circuits to prepare the ground state of the natively implemented FH model, with significant speedups relative to competing adiabatic protocols. Besides, the versatility of this variational approach enables to target extended FH models, i.e., including terms that are not natively realized on the platform. As an illustration, we include next-nearest-neighbor tunnelings at finite dopings, relevant in the context of $d$-wave superconductivity. Furthermore, we discuss how to approximate the imaginary-time evolution using variational fermionic circuits, both as an alternative state-preparation strategy, and as a subroutine for the Quantum Lanczos algorithm to further improve the energy estimation. We benchmark our protocols for ladder geometries, though they can be readily applied to 2D experimental setups to address regimes beyond the capabilities of current classical methods. These results pave the way for more efficient and comprehensive explorations of relevant many-body phases with existing programmable fermionic quantum simulators.