The Fermi-Hubbard Model for Universal Quantum Computation

Quantum circuits based only on matchgates are able to perform non-trivial (but not universal) quantum algorithms. Because matchgates can be mapped to non-interacting fermions, these circuits can be efficiently simulated on a classical computer. One can perform universal quantum computation by adding any non-matchgate parity-preserving gate, implying that interacting fermions are natural candidates for universal quantum computation within the circuit model. Most work to date has focused on Majorana fermions, which are difficult to realize in the laboratory. We instead explore both spinless (spin-polarized) and spin-1/2 fermions within the context of matchgate circuits, investigating interactions within a family of Fermi-Hubbard Hamiltonians, to obtain experimentally realizable conditions under which interacting fermions are able to perform universal quantum computation.