Representation of the quantum Fourier transform on multilevel basic elements by a sequence of selective rotation operators.

Ermilov, A. S.; Zobov, V. E.

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.

FOURIER transform spectroscopy; QUANTUM computers; MAGNETIC fields; LINEAR algebra; FIELD theory (Physics)

Optics & Spectroscopy, 2007, Vol 103, Issue 6, p969

0030-400X

Academic Journal

10.1134/S0030400X07120211