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Programmable digital quantum simulation of 2D Fermi-Hubbard dynamics using 72 superconducting qubits
Authors:
Faisal Alam,
Jan Lukas Bosse,
Ieva Čepaitė,
Adrian Chapman,
Laura Clinton,
Marcos Crichigno,
Elizabeth Crosson,
Toby Cubitt,
Charles Derby,
Oliver Dowinton,
Paul K. Faehrmann,
Steve Flammia,
Brian Flynn,
Filippo Maria Gambetta,
Raúl García-Patrón,
Max Hunter-Gordon,
Glenn Jones,
Abhishek Khedkar,
Joel Klassen,
Michael Kreshchuk,
Edward Harry McMullan,
Lana Mineh,
Ashley Montanaro,
Caterina Mora,
John J. L. Morton
, et al. (10 additional authors not shown)
Abstract:
Simulating the time-dynamics of quantum many-body systems was the original use of quantum computers proposed by Feynman, motivated by the critical role of quantum interactions between electrons in the properties of materials and molecules. Accurately simulating such systems remains one of the most promising applications of general-purpose digital quantum computers, in which all the parameters of t…
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Simulating the time-dynamics of quantum many-body systems was the original use of quantum computers proposed by Feynman, motivated by the critical role of quantum interactions between electrons in the properties of materials and molecules. Accurately simulating such systems remains one of the most promising applications of general-purpose digital quantum computers, in which all the parameters of the model can be programmed and any desired physical quantity output. However, performing such simulations on today's quantum computers at a scale beyond the reach of classical methods requires advances in the efficiency of simulation algorithms and error mitigation techniques. Here we demonstrate programmable digital quantum simulation of the dynamics of the 2D Fermi-Hubbard model -- one of the best-known simplified models of electrons in crystalline solids -- at a scale beyond exact classical state-vector simulation. We implement simulations of this model on lattice sizes up to ${6\times 6}$ using 72 qubits on Google's Willow quantum processor, across a range of physical parameters, including different on-site electron-electron interaction strengths and magnetic flux values, and study phenomena including formation of magnetic polarons (charge carriers surrounded by local magnetic polarisation), dynamical symmetry-breaking in stripe-ordered states, attraction of charge carriers on an entangled background state known as a valence bond solid, and the approach to equilibrium through thermalisation. We validate our results against exact calculations in parameter regimes where these are feasible, and compare them to approximate classical simulations performed using tensor network and operator propagation methods. Our results demonstrate that meaningful programmable digital quantum simulation of many-body interacting electron models is now feasible on state-of-the-art quantum hardware.
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Submitted 19 December, 2025; v1 submitted 30 October, 2025;
originally announced October 2025.
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Fermionic dynamics on a trapped-ion quantum computer beyond exact classical simulation
Authors:
Faisal Alam,
Jan Lukas Bosse,
Ieva Čepaitė,
Adrian Chapman,
Laura Clinton,
Marcos Crichigno,
Elizabeth Crosson,
Toby Cubitt,
Charles Derby,
Oliver Dowinton,
Norhan Eassa,
Paul K. Faehrmann,
Steve Flammia,
Brian Flynn,
Filippo Maria Gambetta,
Raúl García-Patrón,
Max Hunter-Gordon,
Glenn Jones,
Abhishek Khedkar,
Joel Klassen,
Michael Kreshchuk,
Edward Harry McMullan,
Lana Mineh,
Ashley Montanaro,
Caterina Mora
, et al. (15 additional authors not shown)
Abstract:
Simulation of the time-dynamics of fermionic many-body systems has long been predicted to be one of the key applications of quantum computers. Such simulations -- for which classical methods are often inaccurate -- are critical to advancing our knowledge and understanding of quantum chemistry and materials, underpinning a wide range of fields, from biochemistry to clean-energy technologies and che…
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Simulation of the time-dynamics of fermionic many-body systems has long been predicted to be one of the key applications of quantum computers. Such simulations -- for which classical methods are often inaccurate -- are critical to advancing our knowledge and understanding of quantum chemistry and materials, underpinning a wide range of fields, from biochemistry to clean-energy technologies and chemical synthesis. However, the performance of all previous digital quantum simulations of fermions has been matched by classical methods, and it has thus far remained unclear whether near-term, intermediate-scale quantum hardware could offer any computational advantage in this area. Here, we implement an efficient quantum simulation algorithm on Quantinuum's System Model H2 trapped-ion quantum computer for the time dynamics of a 56-qubit system that is too complex for exact classical simulation. We focus on the periodic spinful 2D Fermi-Hubbard model and present evidence of spin-charge separation, where the elementary electron's charge and spin decouple. In the limited cases where ground truth is available through exact classical simulation, we find that it agrees with the results we obtain from the quantum device. Employing long-range Wilson operators to study deconfinement of the effective gauge field between spinons and the effective potential between charge carriers, we find behaviour that differs from predictions made by classical tensor network methods. Our results herald the use of quantum computing for simulating strongly correlated electronic systems beyond the capacity of classical computing.
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Submitted 19 December, 2025; v1 submitted 30 October, 2025;
originally announced October 2025.
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Enhancing density functional theory using the variational quantum eigensolver
Authors:
Evan Sheridan,
Lana Mineh,
Raul A. Santos,
Toby Cubitt
Abstract:
Quantum computers open up new avenues for modelling the physical properties of materials and molecules. Density Functional Theory (DFT) is the gold standard classical algorithm for predicting these properties, but relies on approximations of the unknown universal functional, limiting its general applicability for many fundamental and technologically relevant systems. In this work we develop a hybr…
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Quantum computers open up new avenues for modelling the physical properties of materials and molecules. Density Functional Theory (DFT) is the gold standard classical algorithm for predicting these properties, but relies on approximations of the unknown universal functional, limiting its general applicability for many fundamental and technologically relevant systems. In this work we develop a hybrid quantum/classical algorithm called quantum enhanced DFT (QEDFT) that systematically constructs quantum approximations of the universal functional using data obtained from a quantum computer.
We benchmark the QEDFT algorithm on the Fermi-Hubbard model, both numerically and on data from experiments on real quantum hardware. We find that QEDFT surpasses the quality of groundstate results obtained from Hartree-Fock DFT, as well as from direct application of conventional quantum algorithms such as VQE. Furthermore, we demonstrate that QEDFT works even when only noisy, low-depth quantum computation is available, by benchmarking the algorithm on data obtained from Google's quantum computer.
We further show how QEDFT also captures quintessential properties of strongly correlated Mott physics for large Fermi-Hubbard systems using functionals generated on much smaller system sizes. Our results indicate that QEDFT can be applied to realistic materials and molecular systems, and has the potential to outperform the direct application of either DFT or VQE alone, without the requirement of large scale or fully fault-tolerant quantum computers.
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Submitted 28 February, 2024;
originally announced February 2024.