Introduction to quantum gate.

We found the combination of quantum gates: I, Pauli-X, Y and Z, 
form a finite group under usual matrix multiplication, namely, 
operating the combination of Pauli-X, Y 
and Z on a certain vector is equivalent to operating one of Pauli-X, Y and Z 
on the same vector.

The reference is
http://en.m.wikipedia.org/wiki/Quantum_gate