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

thesis

posted on 2013-08-29, 13:46 authored by M.S. GarelliWe 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.

## History

## School

- Science

## Department

- Physics

## Publisher

© M.S. Garelli## Publication date

2006## Notes

A Doctoral Thesis. Submitted in partial fulfilment of the requirements for the award of Doctor of Philosophy of Loughborough University## EThOS Persistent ID

uk.bl.ethos.479008## Language

- en