Effect of the nuclear hyperfine field, and the Dzyaloshinskii–Moriya term on the (swap) α quantum gate

International Conference on Quantum Physics and Nuclear Engineering

March 14-16, 2016 London, UK

Roberto J Guerrero and F Rojas

Universidad Aut�³noma de Baja California, Mexico
Universidad Nacional Aut�³noma de M�©xico, Mexico

Posters & Accepted Abstracts: J Laser Opt Photonics

Abstract :

We consider a system of two coupled electronic spins where the Dzyloshinskiâ��Moriya (DM) term is present, imbedded in the magnetic field caused by the surrounding nuclei. In order to describe the statistical effect of the nuclei (Hiperfine field, HF), we consider the system to be under the quasi-static approximation (QSA). The HF will have important consequences on the operation of the (SWAP)1/2 gate, utilized in the construction of the CNOT gate. Recently, it has been proposed that a more general two qubit quantum gate, (SWAP)�±, could be used in place of the CNOT for two qubit gates. It was demonstrated also that (SWAP)�± is universal, and equally efficient, in the number of gates used, as the CNOT gate. In this work, we study the effect of the hiperfine field and spinorbit interactions in the (SWAP)�± gate operation. By selecting the area of the exchange J over a period of time, we try to produce the required gate operation; we have calculated dynamical properties of the probability of the two spin states, one spin polarization, entanglement (concurrence) and gate fidelity. We demonstrate that the gate fidelity will never reach a maximum value of 1 due to the DM term. It was found that this error is proportional to the square value of the DM term by the net value of the concurrence. Results are presented for the (SWAP)�± gates, with �± = �½, �¼ and 1, where we have calculated for each �± the adequate area width of J for which the correct quantum gate is performed, and the pulse correction need it to perform a correct operation with a non-cero DM element. For each gate the hyperfine field strength has been modified an evaluated.

Biography :

Email: rjgm76@uabc.edu.mx