Implementing single-qubit operations

We have seen that qubits can be accomplished by different quantum properties of a system. The basic requirement is that they must be well characterized and susceptible to manipulation by an external perturbation, so that the input states can be adequately prepared and controlled to produce the desired calculation. Besides, the physical representation of the qubit in quantum information processing must be unequivocal. This is certainly a requirement that NMR systems fulflll. In fact, a natural implementation of a qubit is an isolated spin 1/2 in a magnetic field [1]. In the operator basis, the general state of this spin can be represented by IV ) = a -l-l/2) - - j8 —1/2) (Figure 4.1). Labeling the states -l-l/2) as 0) and I-1/2) as 1), each state of the system can be represented by a single label, 0) or 11), which means one-qubit of information. 

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