  The Fermi-Hubbard model, a fundamental framework for studying strongly
correlated phenomena could significantly benefit from quantum simulations when
exploring non-trivial settings. However, simulating this problem requires twice
as many qubits as the physical sites, in addition to complicated on-chip
connectivities and swap gates required to simulate the physical interactions.
In this work, we introduce a novel quantum simulation approach utilizing qudits
to overcome such complexities. Leveraging on the symmetries of the
Fermi-Hubbard model and their intrinsic relation to Clifford algebras, we first
demonstrate a Qudit Fermionic Mapping (QFM) that reduces the encoding cost
associated with the qubit-based approach. We then describe the unitary
evolution of the mapped Hamiltonian by interpreting the resulting Majorana
operators in terms of physical single- and two-qudit gates. While the QFM can
be used for any quantum hardware with four accessible energy levels, we
demonstrate the specific reduction in overhead resulting from utilizing the
native Controlled-SUM gate (equivalent to qubit CNOT) for a fixed-frequency
ququart transmon. We further transpile the resulting two transmon-qudit gates
by demonstrating a qudit operator Schmidt decomposition using the
Controlled-SUM gate. Finally, we demonstrate the efficacy of our proposal by
numerical simulation of local observables such as the filling factor and
Green's function for various Trotter steps. The compatibility of our approach
with different qudit platforms paves the path for achieving quantum advantage
in simulating non-trivial quantum many-body systems.
