Dynamics of a quantum control-not gate for an ensemble of four-spin molecules at room temperature

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Abstract
We investigate numerically a single-electromagnetic-pulse implementation of a quantum control-not (CN) gate for an ensemble of Ising spin systems at room temperature. For an ensemble of four-spin “molecules” we simulate the time evolution of the density matrix for both digital and superpositional initial conditions. Our numerical calculations confirm the feasibility of implementation of a quantum CN gate in this system at finite temperature, using a single electromagnetic π pulse. We also study the quantum dynamics of creating entangled states in a macroscopic paramagnetic spin system at low temperatures, and compare the related quantum and corresponding classical dynamics. In the quantum case, one can create entangled states using a resonant interaction between the spin system and the electromagnetic π pulse. In the classical limit, the interaction of the spin system with the same pulse becomes nonresonant and the corresponding classical dynamics differs significantly from the quantum dynamics. This difference in the behavior of the macroscopic magnetization can be used in experiments as an indication of the existence of entangled states.
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