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Published papers:
Buckyball quantum computer: realization of a quantum gate , M.S. Garelli and F.V. Kusmartsev, European Physical Journal B, Vol. 48, No. 2, p. 199, (2005)
Fast Quantum Computing with Buckyballs, M.S. Garelli and F.V. Kusmartsev, Proceedings of SPIE, Vol. 6264, 62640A (2006)
Theoretical Realization of Quantum Gates Using Interacting Endohedral Fullerene Molecules:
We have studied a physical system composed of two interacting endohedral fullerene molecules for quantum computational purposes. The mutual interaction between these two molecules is determined by their spin dipolar interaction. The action of static magnetic fields on the whole system allow to encode the qubit in the electron spin of the encased atom.
We herein present a theoretical model which enables us to realize singlequbit and twoqubit gates through the system under consideration. Singlequbit operations can be achieved by applying to the system resonant timedependent microwave fields. Since the dipolar spin interaction couples the two qubitencoding spins, twoqubit gates are naturally performed by allowing the system to evolve freely. This theoretical model is applied to two realistic architectures of two interacting endohedrals. In the first realistic system the two molecules are placed at a distance of $1.14 nm$. In the second design the two molecules are separated by a distance of $7 nm$. In the latter case the condition $\Delta\omega_p>>g(r)$ is satisfied, i.e. the difference between the precession frequencies of the two spins is much greater than the dipolar coupling strength. This allows us to adopt a simplified theoretical model for the realization of quantum gates.
The realization of quantum gates for these realistic systems is provided by studying the dynamics of the system. In this extent we have numerically solved a set of Schr{\"o}dinger equations needed for reproducing the respective gate, i.e. phasegate, $\pi$gate and CNOTgate. For each quantum gate reproduced through the realistic system, we have estimated their reliability by calculating their related fidelity.
Finally, we present new ideas regarding architectures of systems composed of endohedral fullerenes, which could allow these systems to become reliable building blocks for the realization of quantum computers.
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