Wolfram Language Paclet Repository
Community-contributed installable additions to the Wolfram Language
QuantumMob`Q3mini`
Pauli |
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Details and Options
Examples
(9)
Basic Examples
(6)
This is the identity operator on a single qubit.
In[1]:=
Pauli[0]
Out[1]=
I
These are the Pauli X, Y, and Z operators on a single qubit.
In[2]:=
{Pauli[1],Pauli[2],Pauli[3]}
Out[2]=
{X,Y,Z}
In[3]:=
Pauli[All]
Out[3]=
{X,Y,Z}
In[4]:=
Pauli[Full]
Out[4]=
{I,X,Y,Z}
Note that the expression is displayed as above, but is still interpreted as . To see this, copy and paste the output above to use the displayed form in later calculations.
In[5]:=
{"I","X","Y","Z"}//InputForm
Out[5]//InputForm=
{Pauli[{0}], Pauli[{1}], Pauli[{2}], Pauli[{3}]}
Pauli[4]
Pauli[]
Raising
Pauli[5]
Pauli[]
Lowering
Pauli[]
Raising
Pauli[5]
Pauli[1]
Pauli[2]
Pauli[4]
Pauli[5]
In[6]:=
Pauli[4]Pauli[5]
Out[6]=
+
X
Out[6]=
-
X
In[7]:=
Pauli[Raising]Pauli[Lowering]
Out[7]=
1
2
Out[7]=
1
2
Pauli[6]
In[8]:=
Pauli[6]
Out[8]=
H
In[9]:=
Pauli[Hadamard]
Out[9]=
X+Z
2
Pauli[7]
Pauli[8]
In[10]:=
Pauli[7]Pauli[8]Pauli[9]
Out[10]=
S
Out[10]=
T
Out[10]=
F
In[11]:=
Matrix[Pauli[7]]//MatrixFormMatrix[Pauli[8]]//MatrixForm
Out[11]//MatrixForm=
1 | 0 |
0 | |
Out[11]//MatrixForm=
1 | 0 |
0 | π 4 |
In[12]:=
Pauli[Quadrant]Pauli[Octant]
Out[12]=
1
2
2
1
2
2
Out[12]=
1
2
π
4
1
2
π
4
Pauli[10]
Pauli[11]
In[13]:=
Pauli[10]Pauli[11]
Out[13]=
|0〉〈0|
Out[13]=
|1〉〈1|
In[14]:=
Matrix[Pauli[10]]//MatrixFormMatrix[Pauli[11]]//MatrixForm
Out[14]//MatrixForm=
1 | 0 |
0 | 0 |
Out[14]//MatrixForm=
0 | 0 |
0 | 1 |
In[1]:=
Pauli[-1](*phasegate*)
Out[1]=
X
In[2]:=
Pauli[-2](*quadrantphasegate*)Pauli[-2]//Matrix//MatrixForm
Out[2]=
Y
Out[2]//MatrixForm=
0 | - |
| 0 |
The (non-commutative) multiplication of single-qubit Pauli operators.
Tensor products of Pauli matrices
Out[5]//TeXForm=
rac{1}{2} ext{X}\otimes ext{Y}\otimes ext{X}\otimes ( ext{X}+i ext{Y})
rac{1}{2} ext{X}\otimes ext{Y}\otimes ext{X}\otimes ( ext{X}+i ext{Y})
The (non-commutative) multiplication of multi-qubit Pauli operators.