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Abstract: With the help of the spin-orbit interaction, we propose a scheme to performholonomic single qubit gates on the electron spin confined to a quantum dot.The manipulation is done in the absence or presence of an applied magneticfield. By adiabatic changing the position of the confinement potential, one canrotate the spin state of the electron around the Bloch sphere in semiconductorheterostructures. The dynamics of the system is equivalent to employing aneffective non-Abelian gauge potential whose structure depends on the type ofthe spin-orbit interaction. As an example, we find an analytic expression forthe electron spin dynamics when the dot is moved around a circular path withradius R on the two dimensional electron gas 2DEG, and show that all singlequbit gates can be realized by tuning the radius and orientation of thecircular paths. Moreover, using the Heisenberg exchange interaction, wedemonstrate how one can generate two-qubit gates by bringing two quantum dotsnear each other, yielding a scalable scheme to perform quantum computing onarbitrary N qubits.This proposal shows a way of realizing holonomic quantum computers insolid-state systems.



Autor: Vitaly N. Golovach, Massoud Borhani, Daniel Loss

Fuente: https://arxiv.org/



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