  Qubits, which are quantum counterparts of classical bits, are used as basic
information units for quantum information processing, whereas underlying
physical information carriers, e.g. (artificial) atoms or ions, admit encoding
of more complex multilevel states -- qudits. Recently, significant attention is
paid to the idea of using qudit encoding as a way for further scaling quantum
processors. In this work, we present an efficient decomposition of the
generalized Toffoli gate on the five-level quantum systems, so-called ququints,
that uses ququints' space as the space of two qubits with a joint ancillary
state. The basic two-qubit operation that we use is a version of
controlled-phase gate. The proposed $N$-qubit Toffoli gate decomposition has
$O(N)$ asymptotic depth using no ancillary qubits. We then apply our results
for Grover's algorithm, where we indicate on the sizable advantage of the using
qudit-based approach with the proposed decomposition. We expect that our
results are applicable for quantum processors based on various physical
platforms.
