Quantum computation is usually realized via qubits, i.e. two-level quantum systems. From a mathematical viewpoint, a composite system of several qubits is identical to a single multi-level system. We will analyze 4-, 5-, 7-, and 8-level systems for realization of 2- and 3-qubit gates, including Deutsch-Josza algorithm and the parity check.
Based on Ph.D. thesis and the following publications:
E.O. Kiktenko, A.K. Fedorov, A.A. Strakhov, and V.I. Man'ko Phys. Lett. A 379, 1409 (2015)
E.O. Kiktenko, A.K. Fedorov, O.V. Man'ko, and V.I. Man'ko Phys. Rev. A 91, 042312 (2015)
E.O. Kiktenko, A.K. Fedorov and V.I. Man'ko Quantum Meas. Quantum Metrol. 3, 15 (2016)
A.A. Popov, E.O. Kiktenko, A.K. Fedorov, V.I. Man'ko arXiv:1610.05576 (2016)