Arovas, D. P., Berg, E., Kivelson, S. A. & Raghu, S. The Hubbard model. Annu. Rev. Condens. Matter Phys. 13, 239 (2022).
Qin, M., Schäfer, T., Andergassen, S., Corboz, P. & Gull, E. The Hubbard model: a computational perspective. Annu. Rev. Condens. Matter Phys. 13, 275–302 (2022).
Wilson, J. A., Di Salvo, F. J. & Mahajan, S. Charge-density waves in metallic, layered, transition-metal dichalcogenides. Phys. Rev. Lett. 32, 882 (1974).
Bednorz, J. G. & Müller, K. A. Possible highTc superconductivity in the BaLaCuO system. Zeitschrift für Physik B 64, 189–193 (1986).
Takada, K. et al. Superconductivity in two-dimensional CoO2 layers. Nature 422, 53–55 (2003).
Catalano, S. et al. Rare-earth nickelates RNiO3: thin films and heterostructures. Rep. Prog. Phys. 81, 046501 (2018).
Wu, F., Lovorn, T., Tutuc, E. & MacDonald, A. Hubbard model physics in transition metal dichalcogenide Moire bands. Phys. Rev. Lett. 121, 026402 (2018).
Ponsioen, B., Chung, S. S. & Corboz, P. Period 4 stripe in the extended two-dimensional Hubbard model. Phys. Rev. B 100, 195141 (2019).
Xu, H. et al. Coexistence of superconductivity with partially filled stripes in the Hubbard model. Science https://doi.org/10.1126/science.adh7691 (2024).
Ray, S. & Werner, P. Photoinduced ferromagnetic and superconducting orders in multiorbital Hubbard models. Phys. Rev. B 110, L041109 (2024).
Zhang, Y., Mondaini, R. & Scalettar, R. T. Photoinduced enhancement of superconductivity in the plaquette Hubbard model. Phys. Rev. B 107, 064309 (2023).
Kaneko, T., Shirakawa, T., Sorella, S. & Yunoki, S. Photoinduced eta-pairing in the Hubbard model. Phys. Rev. Lett. 122, 077002 (2019).
White, I. G., Hulet, R. G. & Hazzard, K. R. A. Correlations generated from high-temperature states: nonequilibrium dynamics in the Fermi–Hubbard model. Phys. Rev. A 100, 033612 (2019).
Mehio, O. et al. A Hubbard exciton fluid in a photo-doped antiferromagnetic Mott insulator. Nat. Phys. https://doi.org/10.1038/s41567-023-02204-2 (2023).
Fava, S. et al. Magnetic field expulsion in optically driven YBa2Cu3O6.48. Nature 632, 75–80 (2024).
Mitra, D. et al. Quantum gas microscopy of an attractive Fermi–Hubbard system. Nat. Phys. 14, 173–177 (2018).
Bakr, W. S., Gillen, J. I., Peng, A., Fölling, S. & Greiner, M. A quantum gas microscope for detecting single atoms in a Hubbard-regime optical lattice. Nature 462, 74–77 (2009).
Greif, D., Uehlinger, T., Jotzu, G., Tarruell, L. & Esslinger, T. Short-range quantum magnetism of ultracold fermions in an optical lattice. Science 340, 1307–1310 (2013).
Hilker, T. A. et al. Revealing hidden antiferromagnetic correlations in doped Hubbard chains via string correlators. Science 357, 484–487 (2017).
Mazurenko, A. et al. A cold-atom Fermi–Hubbard antiferromagnet. Nature 545, 462–466 (2017).
Stanisic, S. et al. Observing ground-state properties of the Fermi–Hubbard model using a scalable algorithm on a quantum computer. Nat. Commun. 13, 5743 (2022).
Hémery, K. et al. Measuring the Loschmidt amplitude for finite-energy properties of the Fermi–Hubbard model on an ion-trap quantum computer. PRX Quantum 5, 030323 (2024).
Arute, F. et al. Observation of separated dynamics of charge and spin in the Fermi–Hubbard model. Preprint at https://arxiv.org/abs/2010.07965 (2020).
Jordan, P. & Wigner, E. Über das Paulische Äquivalenzverbot. Zeitschrift für Physik 47, 631–651 (1928).
Kivlichan, I. D. et al. Quantum simulation of electronic structure with linear depth and connectivity. Phys. Rev. Lett. 120, 110501 (2018).
Granet, E. & Dreyer, H. Dilution of error in digital Hamiltonian simulation. PRX Quantum 6, 010333 (2025).
Chertkov, E., Chen, Y.-H., Lubasch, M., Hayes, D. & Foss-Feig, M. Robustness of near-thermal dynamics on digital quantum computers. Preprint at https://arxiv.org/abs/2410.10794
Schiffer, B. F., Rubio, A. F., Trivedi, R. & Cirac, J. I. The quantum adiabatic algorithm suppresses the proliferation of errors. Preprint at https://arxiv.org/abs/2404.15397
Derby, C., Klassen, J., Bausch, J. & Cubitt, T. Compact fermion to qubit mappings. Phys. Rev. B 104, 035118 (2021).
Jafarizadeh, A., Pollmann, F. & Gammon-Smith, A. A recipe for local simulation of strongly-correlated fermionic matter on quantum computers: the 2D Fermi–Hubbard model. Preprint at https://arxiv.org/abs/2408.14543 (2024).
Cade, C., Mineh, L., Montanaro, A. & Stanisic, S. Strategies for solving the Fermi–Hubbard model on near-term quantum computers. Phys. Rev. B 102, 235122 (2020).
Nielsen, M. A. & Chuang, I. L. Quantum Computation and Quantum Information 10th Anniversary edn (Cambridge Univ. Press, 2010).
Hastings, M. B., Wecker, D., Bauer, B. & Troyer, M. Improving quantum algorithms for quantum chemistry. Quantum Info. Comput. 15, 1–21 (2015).
Moses, S. et al. A race-track trapped-ion quantum processor. Phys. Rev. X 13, 041052 (2023).
DeCross, M. et al. The computational power of random quantum circuits in arbitrary geometries. Phys. Rev. X 15, 021052 (2025).
Bausch, J., Cubitt, T., Derby, C. & Klassen, J. Mitigating errors in local fermionic encodings. Preprint at https://arxiv.org/abs/2003.07125 (2020).
Iqbal, M. et al. Topological order from measurements and feed-forward on a trapped ion quantum computer. Nat. Commun. Phys. 7, 205 (2024).
Foss-Feig, M. et al. Experimental demonstration of the advantage of adaptive quantum circuits. Preprint at https://arxiv.org/abs/2302.03029 (2023).
Xie, Q., Seki, K. & Yunoki, S. Variational counterdiabatic driving of the Hubbard model for ground-state preparation. Phys. Rev. B 106, 155153 (2022).
Kovalsky, L. K. et al. Self-healing of Trotter error in digital adiabatic state preparation. Phys. Rev. Lett. 131, 060602 (2023).
Tang, J. et al. Exploring ground states of Fermi–Hubbard model on honeycomb lattices with counterdiabaticity. npj Quantum Mater. 9, 87 (2024).
Schiffer, B. F., Tura, J. & Cirac, J. I. Adiabatic spectroscopy and a variational quantum adiabatic algorithm. PRX Quantum 3, 020347 (2022).
Derby, C. Compact Fermion to Qubit Mappings for Quantum Simulation. PhD thesis, Univ. College London (2023); https://discovery.ucl.ac.uk/id/eprint/10165683/
Clinton, L. et al. Towards near-term quantum simulation of materials. Nat. Commun. 15, 211 (2024).
Setia, K., Bravyi, S., Mezzacapo, A. & Whitfield, J. D. Superfast encodings for fermionic quantum simulation. Phys. Rev. Res. 1, 033033 (2019).
Chien, R. W., Setia, K., Bonet-Monroig, X., Steudtner, M. & Whitfield, J. D. Simulating quantum error mitigation in fermionic encodings. Preprint at https://arxiv.org/abs/2303.02270 (2023).
Nigmatullin, R. et al. Supporting data for ‘Experimental demonstration of break-even for the compact fermionic encoding’. Zenodo https://doi.org/10.5281/zenodo.13624900 (2024).