Ground state preparation of the Fermi–Hubbard model on a quantum computer

The electronic band-structure of a material is responsible for many of its properties, such as its emission and absorption spectra and electrical conductivity. For materials with strongly interacting electrons, the Fermi–Hubbard model—where electrons can only interact with their on-site neighbors—is commonly used, as it captures much of the essential physics behind interacting electrons without long range interactions. Despite the Fermi–Hubbard model’s apparent simplicity, it is impossible to generally and analytically solve outside of a single dimension. Here, we present a method for finding the ground state of the two-site Fermi–Hubbard model on an IBM quantum computer by calculating phase angles analytically from an ansatz of the model’s ground state given the hopping and interaction energies, then building the circuit in Qiskit using those phase angles. Our method is relatively easy to implement, does not require the use of either Jordan–Wigner Z strings or Bravyi–Kitaev transformations, and obtains the Fermi–Hubbard model’s ground state with reasonable accuracy and minimal error corrections; the method’s general simplicity also makes it quite useful as a way to introduce undergraduate students to both many-body physics and quantum computing. Further work—such as building numerical solvers for the phase angles—and improvements in quantum hardware are needed to implement our method for a greater amount of sites.