OVERVIEW OF QUANTUM COMPUTATION - Theoretical and Computational Research in the 21st Century - page 108

5.1 INTRODUCTION
Computation and quantum information [1] are an extension of the infor-
mation process concept, and they are used for the effects of quantum me-
chanic [2]. This new scheme provides a work scene that is not restricted to
only two operations; on the contrary, this can gain multiple intermediate
states as a result of these two ways of superposition. By performing this
operation, the system can evaluate all possibilities in only one step by
making a parallel computation; meanwhile, in the classic way, this evalu-
ation is carried out independently of each other, and in different steps. The
quantum parallelism can be defined as a reduction in time and an increase
in the fast of information process. In this chapter, the fundamental ele-
ments that make possible to use the mechanical-quantum phenomena as a
tool in the process information are presented.
5.2 THE QUBIT
As in the classical computational systems in which the lowest amount of
information unit is the bit, in the quantum computation theory this ele-
ment has its counterpart, known as quantum bit or qubit [1, 3]. Even when
this entity is described as a mathematical object that has certain specific
properties, it also has a physical reality, which is represented by a two-
way quantum system, but in which every management is entirely abstract,
giving freedom in order to generate a computation general theory and in-
formation that does not depend on the physical system needed for its per-
formance. By considering these types of systems as minimum information
units is necessary to implement the mathematical formalism of quantum
mechanics in order to gain a description correct. Although many plots to
describe the stages in a quantum system are available, the most adequate
and brief is the “Dirac notation” [4], which has turned into a standard in
modern physics [1, 3, 5-8]. In this model, a quantum stage is represented
by a vector, which is named “ket” ( ), and all the operations are carried
out through operators that are lineal transformations that act on the ket.
The two basic possible stages for a qubit are 0 and 1 and are equal
in analogy to the 0 and 1 in a classical bit. The potential of this scheme
is based on that qubit can take a different value than the other two men-
tioned, due to the lineal combination of the stages, whereby a qubit in its
most general way is represented by