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

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