Representation of the quantum Fourier transform on multilevel basic elements by a sequence of selective rotation operators |
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Authors: | A S Ermilov V E Zobov |
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Institution: | (1) Kirenskiĭ Institute of Physics, Siberian Branch, Russian Academy of Sciences, Krasnoyarsk, 660036, Russia |
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Abstract: | To experimentally realize quantum computations on d-level basic elements (qudits) at d > 2, it is necessary to develop schemes for the technical realization of elementary logical operators. We have found sequences of selective rotation operators that represent the operators of the quantum Fourier transform (Walsh-Hadamard matrices) for d = 3–10. For the prime numbers 3, 5, and 7, the well-known method of linear algebra is applied, whereas, for the factorable numbers 6, 9, and 10, the representation of virtual spins is used (which we previously applied for d = 4, 8). Selective rotations can be realized, for example, by means of pulses of an RF magnetic field for systems of quadrupole nuclei or laser pulses for atoms and ions in traps. |
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