The last years a variety of quantum systems have been proposed as a possible quantum bits for quantum computers. In the search for new solid state materials zinc oxide can be an interesting alternative to silicon. In this case it is easy to eliminate the superhyperfine interactions in ZnO since nuclear spin-free isotopes of Zn are highly abundant (~96%). ZnO is thus one of the rare semiconductors that can be isotopically purified and that offers the possibility to combine electrical and optical methods to control the quantum state of spin qubits. The spin state of a single Fe3+ spin qubit could be readout by optical methods and it could by coherently manipulated using pulsed electron spin resonanse methods.
In present work, we assume an Ising-type interactions between nearest and second-nearest neighbors. This system must be subjected to a magnetic field, constant in time with a sufficiently strong variation along the spin chain. Additional radio-frequency(rf) pulses allow the coherent control of the state of the system such that a quantum protocol can be realized. These rf-perturbations are used to implement universal quantum gates from which any unitary quantum algorithm can be constructed. We implemented Fredkin universal quantum gate on an Ising chain of length 4, taking into account first and second neighbor couplings. The coupling strength of second neighbors is much weaker than that of first neighbors which means that the dominant source for errors are near resonant transitions. The accumulated errors in the course of the quantum algorithm are quantified by the fidelity. We investigate its temporal behavior as well as its final value, as a function of the Rabi frequency and the coupling parameter. We performed also some preliminary studies using fluctuating Larmor frequencies, simulating tiny variations of the external magnetic field. This is a simple way to introduce decoherence into our model.