*1-qbit
gates*

*The
Pauli gates*

The *X *gate swaps
The Y gate also swaps

the canonical basis
the canonical basis

vectors |0> and |1>
vectors |0> and |1>

on the 1-qbit space
but with a change of

phase

The Z gate changes

the phase of the

canonical vector

basis

*The
Hadamard gate General
gate*

The *Hadamard *gate,
A general

denoted by *H*, acts
gate acts

on the 1-qbit space
as a unitary

as a 2x2 unitary matrix.
matrix

It also coincides with

the Fourier transform

on the group with two

elements (binary bits).

*The
S- and T- gates*

The *S-*gate changes
The T-gate changes

the phase of the second
the phase of the second

qubit by 90 degrees.
qubit by 45 degrees.

*2-qbit
gates and circuits*

*The
CNOT gate*

The *controlled NOT* gate
It can be used to "*copy*"

(or CNOT)
an unknown bit or qubit

acts on the 2-qbits space.

It transforms the state |xy>

into the state |x(x+y)>,

where the addition of binary

bits *x* and *y* is taken *mod.2*