  The structure and dynamics of quantum many-body systems are the result of a
delicate interplay between underlying interactions, which leads to intricate
entanglement structures. Despite this apparent complexity, symmetries emerge
and have long been used to determine the relevant degrees of freedom and
simplify classical descriptions of these systems. In this work, we explore the
potential utility of quantum computers with arrays of qudits in simulating
interacting fermionic systems, when the qudits can naturally map these relevant
degrees of freedom. The Agassi model of fermions is based on an underlying
$so(5)$ algebra, and the systems it describes can be partitioned into pairs of
modes with five basis states, which naturally embed in arrays of $d=5$ qudits
(qu5its). Classical noiseless simulations of the time evolution of systems of
fermions embedded in up to twelve qu5its are performed using Google's cirq
software. The resource requirements of the qu5it circuits are analyzed and
compared with two different mappings to qubit systems, a physics-aware
Jordan-Wigner mapping and a state-to-state mapping. We find advantages in using
qudits, specifically in lowering the required quantum resources and reducing
anticipated errors that take the simulation out of the physical space. A
previously unrecognized sign problem has been identified from Trotterization
errors in time evolving high-energy excitations. This has implications for
quantum simulations in high-energy and nuclear physics, specifically of
fragmentation and highly inelastic, multi-channel processes.
