Sequences of these transformations are used to define logic gates, and sequences of these gates define circuits. These matrices are sparse and therefore they do not need to be explicitly written down. Representing qubit values with state vectors. The first four vectors represent a single value. The last vector represents all possible values.
Errors limit the effectiveness of any physical realization of a quantum computer.
A quantum computer is subject to two different types of errors, decoherence and inaccuracies. Decoherence occurs when a quantum computer interacts with the environment. This interaction destroys the quantum parallelism by turning a quantum calculation into a classical one. In this model, the internal states of ions represent the zero and one values of a qubit. Lasers directed at the ions change their internal state and can be used to implement logic gates.