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Single qudit realization of the Deutsch algorithm using superconducting many-level quantum circuits. (English) Zbl 1349.81071
Summary: 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 with an ancillary level in the systems allows effective implementation of operators from \(\mathrm{U}(4)\) group via operators from \(\mathrm{SU}(5)\) 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 and N. M. Yakovleva, “Implementation schemes in NMR of quantum processors and the Deutsch-Jozsa algorithm by using virtual spin representation”, Phys. Rev. A (3) 66, No. 6, p. 062322 (2002; doi:10.1103/PhysRevA.66.062322)].

MSC:
81P68 Quantum computation
68Q12 Quantum algorithms and complexity in the theory of computing
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