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Design of a large-scale quantum computer has paramount importance for scienceand technologies. We investigate a scheme for realization of quantum algorithmsusing noncomposite quantum systems, i.e., systems without subsystems. In thisframework, $n$ artificially allocated "subsystems" play a role of qubits in$n$-qubits quantum algorithms. With focus on two-qubit quantum algorithms, wedemonstrate a realization of the universal set of gates using a $d=5$ singlequdit state. Manipulation for an ancillary level in the systems allowseffective implementation of operators from ${\rm U}(4)$ group via operatorsfrom ${\rm SU}(5)$ group. Using a possible experimental realization of suchsystems through anharmonic superconducting many-level quantum circuits, wepresent a blueprint for a single qudit realization of the Deutsch algorithm,which generalizes previously studied realization based on the virtual spinrepresentation [A.R. Kessel et al., Phys. Rev. A 66, 062322 (2002)].

Single qudit realization of the Deutsch algorithm using superconducting many-level quantum circuits