  The Fermi-Hubbard model is a plausible target to be solved by a quantum
computer using the variational quantum eigensolver algorithm. However, problem
sizes beyond the reach of classical exact diagonalisation are also beyond the
reach of current quantum computing hardware. Here we use a simple method which
compresses the first nontrivial subcase of the Hubbard model -- with one
spin-up and one spin-down fermion -- enabling larger instances to be addressed
using current quantum computing hardware. We implement this method on a
superconducting quantum hardware platform for the case of the $2 \times 1$
Hubbard model, including error-mitigation techniques, and show that the ground
state is found with relatively high accuracy.
