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Quantum speedup for solving the one-dimensional Hubbard model using quantum annealing

Kunal Vyas1,2,*, Fengping Jin1,†, Hans De Raedt1, and Kristel Michielsen1,3

  • *Contact author: k.vyas@fz-juelich.de
  • †Contact author: f.jin@fz-juelich.de
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Phys. Rev. Research 8, 023109 – Published 1 May, 2026

DOI: https://doi.org/10.1103/bj6c-t252

Abstract

The Hubbard model has occupied the minds of condensed matter physicists for most part of the last century. This model provides insight into a range of phenomena in correlated electron systems. We wish to examine the paradigm of quantum algorithms for solving such many-body problems. The focus of our current work is on the one-dimensional model that is integrable, meaning that there exist analytical results for determining its ground state. In particular, we demonstrate how to perform a gate-based quantum computer simulation of quantum annealing for the Hubbard Hamiltonian. We perform simulations for systems with up to 40 qubits to study the scaling of required annealing time for obtaining the ground state. We find that for the half-filled cases considered, there is a polynomial quantum speedup over algorithms based on the Bethe-ansatz equations.

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Phys. Rev. Research 8, 023109– Published 1 May, 2026
  • Received 14 October 2025
  • Accepted 7 April 2026
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