Compressed variational quantum eigensolver for the Fermi-Hubbard model

Understand

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.