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=5d=5 single qudit state. Manipulation with an ancillary level in the systems allows effective implementation of operators from U(4) group via operators from 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 (Kessel et al., 2002 [9]).