  We discuss the implementation of quantum algorithms for lattice $\Phi^4$
theory on circuit quantum electrodynamics (cQED) system. The field is
represented on qudits in a discretized field amplitude basis. The main
advantage of qudit systems is that its multi-level characteristic allows the
field interaction to be implemented only with diagonal single-qudit gates.
Considering the set of universal gates formed by the single-qudit phase gate
and the displacement gate, we address initial state preparation and
single-qudit gate synthesis with variational methods.
