To understand the ways in which a quantum computer is different from a
classical computer you must first understand the rudiments of the
classical computer. The most fundamental building block of a
classical computer is the bit. A bit is capable of storing one piece
of information, it can have a value of either 0 or 1. Any amount of
information can be encoded into a list of bits. In a classical
computer a bit is typically stored in a silicone chip, or on a metal
hard drive platter, or on a magnetic tape. As this paper is written
about 
atoms are typically used to store one bit of
information. The smallest conceivable storage for a bit involves a
single elementary particle of some sort. For example, any particle
with a spin-1/2 characteristic can be characterized by its spin value,
which when measured is either 
or 
. We can thus encode 1
to be and 0 to be , and if we assume we can measure and
manipulate the spin of such a particle then we could theoretically use
this particle to store one bit of information. If we were to try to
use this spin-1/2 particle as a classical bit, one that is always in
the 0 or 1 state, we would fail. We would be trying to apply
classical physics on a scale where it simply is not applicable. This
single spin-1/2 particle will instead act in a quantum
manner. (Williams, Clearwater)
This spin-1/2 particle which behaves in a quantum manner could be the fundamental building block of a Quantum computer. We could call it a qubit, to denote that it is analogous in some ways to a bit in a classical computer. Just as a memory register in a classical computer is an array of bits, a quantum memory register is composed of several qubits. There is no particular need for the spin-1/2 particle, equally well we could use a Hydrogen atom, and designate its electron being measured in the ground state to be the 0 state, and it being in the first excited state to be the 1 state. For simplicity I will discus only qubits from here on, ignoring their particular implementation.