Two-level quantum dynamics, integrability and unitary NOT gates

Details Two-level quantum dynamics, integrability and unitary NOT gates Two-level quantum dynamics, integrability and unitary NOT gates

2005-09-21

arxiv.org/abs/quant-ph/0509148v1

Physical Review A 72, 034105 (2005)

Physics

Quantum Physics

4 pages and 2 figures

Scientific paper

10.1103/PhysRevA.72.034105

We study the dynamics of a two-level quantum system interacting with an external electromagnetic field periodic and quasiperiodic in time. The quantum evolution is described exactly by the classical equations of motion of a gyromagnet in a time-dependent magnetic field. We prove that this classical system is integrable as a consequence of the underlying unitary quantum dynamics. As a consequence, for the periodic case: i) rigorous assessment of the validity of the rotating-wave approximation (RWA) becomes possible even beyond the assumptions of resonance and weak coupling (the latter conditions are also shown to follow from the method of averaging); ii) we determine conditions for the realization of the quantum NOT operation beyond the RWA, by means of classical stroboscopic maps. The results bear upon areas as diverse as quantum optics, nuclear magnetic resonance, and quantum computation.

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