Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Bulletin of the American Physical Society

A method to efficiently simulate the thermodynamic properties of the Fermi-Hubbard model on a quantum computer

Pierre-Luc Dallaire-Demers, Frank K. Wilhelm

Published Mar 15, 2016• 0 citations
OpenAlex

Related papers

Method to efficiently simulate the thermodynamic properties of the Fermi-Hubbard model on a quantum computer

Pierre-Luc Dallaire-Demers, Frank K. Wilhelm

Many phenomena of strongly correlated materials are encapsulated in the Fermi-Hubbard model whose thermodynamic properties can be computed from its grand-canonical potential. In general, there is no closed-form expression of the grand-canonical potential for lattices of more than one spatial dimension, but solutions can be numerically approximated using cluster methods. To model long-range effects such as order parameters, a powerful method to compute the cluster's Green's function consists of finding its self-energy through a variational principle. This allows the possibility of studying various phase transitions at finite temperature in the Fermi-Hubbard model. However, a classical cluster solver quickly hits an exponential wall in the memory (or computation time) required to store the computation variables. Here it is shown theoretically that the cluster solver can be mapped to a subroutine on a quantum computer whose quantum memory usage scales linearly with the number of orbitals in the simulated cluster and the number of measurements scales quadratically. A quantum computer with a few tens of qubits could therefore simulate the thermodynamic properties of complex fermionic lattices inaccessible to classical supercomputers.

arXiv:1508.04328•Physical Review A•Mar 2, 2016•31 citations

Quantum Simulation of the Fermi-Hubbard Model

Geoffrey Ji, Christie Chiu, Annabelle Bohrdt +7 more

Bulletin of the American Physical Society•Mar 5, 2019•0 citations

Exploring thermal equilibria of the Fermi-Hubbard model with variational quantum algorithms

Jack Y. Araz, Michael Spannowsky, Matthew Wingate A

This study investigates the thermal properties of the repulsive Fermi-Hubbard model with chemical potential using variational quantum algorithms, crucial in comprehending particle behavior within lattices at high temperatures in condensed matter systems. Conventional computational methods encounter challenges, especially in managing chemical potential, prompting exploration into Hamiltonian approaches. Despite the promise of quantum algorithms, their efficacy is hampered by coherence limitations when simulating extended imaginary time evolution sequences. To overcome such constraints, this research focuses on optimizing variational quantum algorithms to probe the thermal properties of the Fermi-Hubbard model. Physics-inspired circuit designs are tailored to alleviate coherence constraints, facilitating a more comprehensive exploration of materials at elevated temperatures. Our study demonstrates the potential of variational algorithms in simulating the thermal properties of the Fermi-Hubbard model while acknowledging limitations stemming from error sources in quantum devices and encountering barren plateaus.

arXiv:2312.09292•Physical Review A•Jun 14, 2024•4 citations

Variational quantum simulation of the Fermi-Hubbard model

Alexandre Choquette, Agustín Di Paolo, Panagiotis Kl. Barkoutsos +3 more

Bulletin of the American Physical Society•Mar 3, 2020•0 citations

Feedback-based Quantum Algorithms for Ground State Preparation of the Fermi-Hubbard Model

James Larsen, Matthew Grace, Andrew Baczewski +1 more

APS March Meeting Abstracts•Mar 1, 2023•3 citations

Phase-Sensitive Measurements on a Fermi–Hubbard Quantum Processor

Alberto R. Cavallar, Luis Escalera‐Moreno, Titus Franz +4 more

Fermionic quantum processors are a promising platform for quantum simulation of correlated fermionic matter. In this work, we study a hardware-efficient protocol for measuring complex expectation values of the time-evolution operator, commonly referred to as Loschmidt echoes, with fermions in an optical superlattice. We analyze the algorithm for the Fermi–Hubbard model at half-filling as well as at finite doping. The method relies on global quench dynamics and short imaginary time evolution, the latter being realized by architecture-tailored pulse sequences starting from a product state of plaquettes. Our numerical results show that complex Loschmidt echoes can be efficiently obtained for large many-body states over a broad spectral range. This allows one to measure spectral properties of the Fermi–Hubbard model, such as the local density of states, and paves the way for the study of finite-temperature properties in current fermionic quantum simulators.

arXiv:2509.01637•Quantum•May 12, 2026•1 citation
Many phenomena of strongly correlated materials are encapsulated in the Fermi-Hubbard model whose thermodynamic properties can be computed from its grand-canonical potential. In general, there is no closed-form expression of the grand-canonical potential for lattices of more than one spatial dimension, but solutions can be numerically approximated using cluster methods. To model long-range effects such as order parameters, a powerful method to compute the cluster's Green's function consists of finding its self-energy through a variational principle. This allows the possibility of studying various phase transitions at finite temperature in the Fermi-Hubbard model. However, a classical cluster solver quickly hits an exponential wall in the memory (or computation time) required to store the computation variables. Here it is shown theoretically that the cluster solver can be mapped to a subroutine on a quantum computer whose quantum memory usage scales linearly with the number of orbitals in the simulated cluster and the number of measurements scales quadratically. A quantum computer with a few tens of qubits could therefore simulate the thermodynamic properties of complex fermionic lattices inaccessible to classical supercomputers.
This study investigates the thermal properties of the repulsive Fermi-Hubbard model with chemical potential using variational quantum algorithms, crucial in comprehending particle behavior within lattices at high temperatures in condensed matter systems. Conventional computational methods encounter challenges, especially in managing chemical potential, prompting exploration into Hamiltonian approaches. Despite the promise of quantum algorithms, their efficacy is hampered by coherence limitations when simulating extended imaginary time evolution sequences. To overcome such constraints, this research focuses on optimizing variational quantum algorithms to probe the thermal properties of the Fermi-Hubbard model. Physics-inspired circuit designs are tailored to alleviate coherence constraints, facilitating a more comprehensive exploration of materials at elevated temperatures. Our study demonstrates the potential of variational algorithms in simulating the thermal properties of the Fermi-Hubbard model while acknowledging limitations stemming from error sources in quantum devices and encountering barren plateaus.
Fermionic quantum processors are a promising platform for quantum simulation of correlated fermionic matter. In this work, we study a hardware-efficient protocol for measuring complex expectation values of the time-evolution operator, commonly referred to as Loschmidt echoes, with fermions in an optical superlattice. We analyze the algorithm for the Fermi–Hubbard model at half-filling as well as at finite doping. The method relies on global quench dynamics and short imaginary time evolution, the latter being realized by architecture-tailored pulse sequences starting from a product state of plaquettes. Our numerical results show that complex Loschmidt echoes can be efficiently obtained for large many-body states over a broad spectral range. This allows one to measure spectral properties of the Fermi–Hubbard model, such as the local density of states, and paves the way for the study of finite-temperature properties in current fermionic quantum simulators.