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Programming Optical-Lattice Fermi-Hubbard Quantum Simulators

Cristian Tabares1,*, Christian Kokail2,3, Peter Zoller4,5, Daniel González-Cuadra1,3,4,5,†, and Alejandro González-Tudela1,‡

  • *Contact author: cristian.tabares@csic.es
  • †Contact author: dgonzalezcuadra@fas.harvard.edu
  • ‡Contact author: a.gonzalez.tudela@csic.es
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PRX Quantum 6, 030356 – Published 19 September, 2025

DOI: https://doi.org/10.1103/3nx4-bnyy

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 us 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 precompiled 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 us 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 two-dimensional 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.

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Popular Summary

Quantum simulators made with fermionic atoms trapped in optical lattices enable the study of many-body electron problems in regimes inaccessible to current classical computers. This approach may help address open questions in condensed-matter and materials science, such as high-temperature superconductivity. Nevertheless, preparing the atoms to mimic these complex regimes is challenging. In this study, we propose a new method to do so.

Previous state-preparation methods imply either cooling a gas of atoms or adiabatically deforming an initial product state. The latter, although advantageous, requires long execution times, reducing the quantum properties of the system in the process. With the help of classical optimization algorithms, we show that it is possible to significantly decrease the time needed to prepare the same states. We also present a way to implement nonunitary operations in the system, which in principle would be prohibited by quantum mechanics but can be used as building blocks of more complicated algorithms.

Given experimental advances in the field, this study demonstrates that programming cold atoms in optical lattices is a way to bring near-term devices closer to practical utility in understanding complex condensed-matter and materials-science systems.

Article Text

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PRX Quantum 6, 030356– Published 19 September, 2025
  • Received 19 February 2025
  • Revised 29 May 2025
  • Accepted 21 July 2025
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