Theoretical model for the realization of quantum gates using interacting endohedral fullerene molecules

We have studied a physical system composed oftwo 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 allows us to encode the qubit in the electron spin of the encased atom. We present a theoretical model which enables us to realize single-qubit and twoqubit gates through the system under consideration. Single-qubit operations can be achieved by applying to the system time-dependent microwave fields. Since the dipolar spin interaction couples the two qubit-encoding spins, two-qubit 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 1.14nm. In the second design the two molecules are separated by a distance of 7nm. In the latter case the condition b..wP > > 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 solved sets of Schrodinger equations needed for reproducing the respective gates, i.e. phase-gate, 1r-gate and CNOT-gate. For each quantum gate reproduced through the realistic. system, we have estimated their reliability by calculating the related fidelity. The presented two-qubit gates are characterized by very high values of fidelity. The value of minimum fidelity related to the realization of a CNOT-gate is :F = 0.9995, which differs from the ideal value :F = 1 by of the order of w-2%. We also present suggestions regarding the improvements on systems composed of endohedral fullerenes in order to enable the experimental realization of quantum gates. This would allow these systems to become reliable building blocks of a quantum computer.