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Quantum Simulation of the Fermi-Hubbard Model

Geoffrey Ji, Christie Chiu, Annabelle Bohrdt +7 more

Bulletin of the American Physical SocietyMar 5, 20190 citations

Quantum simulations of a Fermi-Hubbard model using a semiconductor quantum dot array

Toivo Hensgens, T. Fujita, Laurens Janssen +5 more

Bulletin of the American Physical SocietyMar 15, 20170 citations

Quantum simulation of a Fermi–Hubbard model using a semiconductor quantum dot array

Toivo Hensgens, T. Fujita, Laurens Janssen +6 more

arXiv:1702.07511NatureAug 1, 2017352 citations

Quantum simulation of Fermi-Hubbard models in semiconductor quantum-dot arrays

Na Young Kim, Tim Byrnes, Kenichiro Kusudo +1 more

Bulletin of the American Physical SocietyMar 18, 20090 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.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:2312.09292Physical Review AJun 14, 20244 citations

An application benchmark for fermionic quantum simulations

Pierre-Luc Dallaire-Demers, Michał Stęchły, Jérôme F. Gonthier +3 more

It is expected that the simulation of correlated fermions in chemistry and material science will be one of the first practical applications of quantum processors. Given the rapid evolution of quantum hardware, it is increasingly important to develop robust benchmarking techniques to gauge the capacity of quantum hardware specifically for the purpose of fermionic simulation. Here we propose using the one-dimensional Fermi-Hubbard model as an application benchmark for variational quantum simulations on near-term quantum devices. Since the one-dimensional Hubbard model is both strongly correlated and exactly solvable with the Bethe ansatz, it provides a reference ground state energy that a given device with limited coherence will be able to approximate up to a maximal size. The length of the largest chain that can be simulated provides an effective fermionic length. We use variational quantum eigensolver to approximate the ground state energy values of Fermi-Hubbard instances and show how the fermionic length benchmark can be used in practice to assess the performance of bounded-depth devices in a scalable fashion.It is expected that the simulation of correlated fermions in chemistry and material science will be one of the first practical applications of quantum processors. Given the rapid evolution of quantum hardware, it is increasingly important to develop robust benchmarking techniques to gauge the capacity of quantum hardware specifically for the purpose of fermionic simulation. Here we propose using the one-dimensional Fermi-Hubbard model as an application benchmark for variational quantum simulations on near-term quantum devices. Since the one-dimensional Hubbard model is both strongly correlated and exactly solvable with the Bethe ansatz, it provides a reference ground state energy that a given device with limited coherence will be able to approximate up to a maximal size. The length of the largest chain that can be simulated provides an effective fermionic length. We use variational quantum eigensolver to approximate the ground state energy values of Fermi-Hubbard instances and show how the fermionic length benchmark can be used in practice to assess the performance of bounded-depth devices in a scalable fashion.

arXiv:2003.01862Bulletin of the American Physical SocietyMar 4, 202025 citations

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