• Arovas, D. P., Berg, E., Kivelson, S. A. & Raghu, S. The Hubbard model. Annu. Rev. Condens. Matter Phys. 13, 239 (2022).

    Article 
    ADS 

    Google Scholar
     

  • 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).

    Article 
    ADS 

    Google Scholar
     

  • Wilson, J. A., Di Salvo, F. J. & Mahajan, S. Charge-density waves in metallic, layered, transition-metal dichalcogenides. Phys. Rev. Lett. 32, 882 (1974).

    Article 
    ADS 

    Google Scholar
     

  • Bednorz, J. G. & Müller, K. A. Possible highTc superconductivity in the BaLaCuO system. Zeitschrift für Physik B 64, 189–193 (1986).

    Article 
    ADS 

    Google Scholar
     

  • Takada, K. et al. Superconductivity in two-dimensional CoO2 layers. Nature 422, 53–55 (2003).

    Article 
    ADS 

    Google Scholar
     

  • Catalano, S. et al. Rare-earth nickelates RNiO3: thin films and heterostructures. Rep. Prog. Phys. 81, 046501 (2018).

    Article 
    ADS 
    MathSciNet 

    Google Scholar
     

  • Wu, F., Lovorn, T., Tutuc, E. & MacDonald, A. Hubbard model physics in transition metal dichalcogenide Moire bands. Phys. Rev. Lett. 121, 026402 (2018).

    Article 
    ADS 

    Google Scholar
     

  • Ponsioen, B., Chung, S. S. & Corboz, P. Period 4 stripe in the extended two-dimensional Hubbard model. Phys. Rev. B 100, 195141 (2019).

    Article 
    ADS 

    Google Scholar
     

  • 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).

    Article 

    Google Scholar
     

  • Zhang, Y., Mondaini, R. & Scalettar, R. T. Photoinduced enhancement of superconductivity in the plaquette Hubbard model. Phys. Rev. B 107, 064309 (2023).

    Article 
    ADS 

    Google Scholar
     

  • Kaneko, T., Shirakawa, T., Sorella, S. & Yunoki, S. Photoinduced eta-pairing in the Hubbard model. Phys. Rev. Lett. 122, 077002 (2019).

    Article 
    ADS 

    Google Scholar
     

  • 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).

    Article 
    ADS 

    Google Scholar
     

  • 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).

    Article 

    Google Scholar
     

  • Mitra, D. et al. Quantum gas microscopy of an attractive Fermi–Hubbard system. Nat. Phys. 14, 173–177 (2018).

    Article 

    Google Scholar
     

  • 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).

    Article 
    ADS 

    Google Scholar
     

  • 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).

    Article 
    ADS 

    Google Scholar
     

  • Hilker, T. A. et al. Revealing hidden antiferromagnetic correlations in doped Hubbard chains via string correlators. Science 357, 484–487 (2017).

    Article 
    ADS 
    MathSciNet 
    MATH 

    Google Scholar
     

  • Mazurenko, A. et al. A cold-atom Fermi–Hubbard antiferromagnet. Nature 545, 462–466 (2017).

    Article 
    ADS 

    Google Scholar
     

  • 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).

    Article 
    ADS 

    Google Scholar
     

  • 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).

    Article 

    Google Scholar
     

  • 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).

    Article 
    ADS 
    MATH 

    Google Scholar
     

  • Kivlichan, I. D. et al. Quantum simulation of electronic structure with linear depth and connectivity. Phys. Rev. Lett. 120, 110501 (2018).

    Article 
    ADS 
    MathSciNet 

    Google Scholar
     

  • Granet, E. & Dreyer, H. Dilution of error in digital Hamiltonian simulation. PRX Quantum 6, 010333 (2025).

    Article 

    Google Scholar
     

  • 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).

    Article 
    ADS 

    Google Scholar
     

  • 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).

    Article 
    ADS 

    Google Scholar
     

  • 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).

    MathSciNet 

    Google Scholar
     

  • Moses, S. et al. A race-track trapped-ion quantum processor. Phys. Rev. X 13, 041052 (2023).


    Google Scholar
     

  • DeCross, M. et al. The computational power of random quantum circuits in arbitrary geometries. Phys. Rev. X 15, 021052 (2025).


    Google Scholar
     

  • 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).


    Google Scholar
     

  • 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).

    Article 
    ADS 

    Google Scholar
     

  • Kovalsky, L. K. et al. Self-healing of Trotter error in digital adiabatic state preparation. Phys. Rev. Lett. 131, 060602 (2023).

    Article 
    ADS 

    Google Scholar
     

  • Tang, J. et al. Exploring ground states of Fermi–Hubbard model on honeycomb lattices with counterdiabaticity. npj Quantum Mater. 9, 87 (2024).

    Article 

    Google Scholar
     

  • Schiffer, B. F., Tura, J. & Cirac, J. I. Adiabatic spectroscopy and a variational quantum adiabatic algorithm. PRX Quantum 3, 020347 (2022).

    Article 
    ADS 

    Google Scholar
     

  • 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).

    Article 
    ADS 

    Google Scholar
     

  • Setia, K., Bravyi, S., Mezzacapo, A. & Whitfield, J. D. Superfast encodings for fermionic quantum simulation. Phys. Rev. Res. 1, 033033 (2019).

    Article 

    Google Scholar
     

  • 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).