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Fault-Tolerant Quantum Simulation of Generalized Hubbard Models

Andreas Juul Bay-Smidt1,2,*, Frederik Ravn Klausen1,3, Christoph Sünderhauf4, Róbert Izsák4, Gemma C. Solomon1,2,†, and Nick S. Blunt4,‡

  • *Contact author: andreas.bay-smidt@nbi.ku.dk
  • †Contact author: gsolomon@chem.ku.dk
  • ‡Contact author: nick.blunt@riverlane.com
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PRX Quantum 6, 030348 – Published 12 September, 2025

DOI: https://doi.org/10.1103/gr4t-b1w5

Abstract

Quantum simulations of strongly interacting fermionic systems, such as those described by the Hubbard model, are promising candidates for useful early fault-tolerant quantum computing applications. This paper presents tile Trotterization, a generalization of plaquette Trotterization, which uses a set of tiles to construct Trotter decompositions of arbitrary lattice Hubbard models. The tile Trotterization scheme also enables the simulation of more complex models, including the extended Hubbard model. We improve previous Hubbard-model commutator bounds, further provide tight commutator bounds for periodic extended Hubbard models, and demonstrate the use of tensor network methods for this task. We consider applications of tile Trotterization to simulate hexagonal lattice Hubbard models and compare the resource requirements of tile Trotterization for performing quantum phase estimation to a qubitization-based approach, demonstrating that tile Trotterization scales more efficiently with system size. These advancements significantly broaden the potential applications of early fault-tolerant quantum computers to models of practical interest in materials research and organic chemistry.

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Popular Summary

Our work provides a path toward practical quantum computing applications for materials with strongly interacting electrons. Even with current state-of-the-art experimental and computational methods, it remains challenging to uncover the mechanism behind phenomena such as unconventional forms of superconductivity and magnetism. This paper presents an efficient and low-cost quantum simulation method for implementing time evolution, or Hamiltonian simulation, for models of strongly interacting electrons. Our method is especially suitable for early fault-tolerant quantum computers, which are considered the next big milestone in the quantum computing community.

Efficient implementation of Hamiltonian simulation will be essential in many early fault-tolerant quantum algorithms. Previous quantum simulation methods for addressing this challenge were only applicable to a limited set of models, which omit important aspects of many real-life materials. To improve on this, we constructed a much more general method that allows simulation of a broader range of strongly interacting electron models. We compare our approach to an existing state-of-the-art simulation method and show that our approach obtains better scaling with the size of the model, while also being applicable to models of many important phenomena in chemistry and condensed-matter physics.

A possible next step for this research is to perform compilation for the architectures and algorithms that will be used by the first generation of error-corrected quantum computers. This will provide a better understanding of the requirements of these early devices to perform useful quantum computation.

Article Text

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PRX Quantum 6, 030348– Published 12 September, 2025
  • Received 24 January 2025
  • Accepted 30 July 2025
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