Wolfram Language Paclet Repository
Community-contributed installable additions to the Wolfram Language
Wolfram`QuantumFramework`
QuantumBasis  |
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Details and Options
Examples
(21)
Basic Examples
(14)
Create 2-dimensional basis:
In[1]:=
 | QuantumBasis |
Out[1]=
QuantumBasis
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Note with no input, the basis is automatically set as 2D, bu default
In[2]:=
 | QuantumBasis |
| QuantumBasis |
Out[2]=
True
Create 3-dimensional basis:
In[1]:=
| QuantumBasis |
Out[1]=
QuantumBasis
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Create a 2×2×2 dimensional basis (three qubits):
In[1]:=
| QuantumBasis |
Out[1]=
QuantumBasis
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Create composite basis of two 2 and 3-dimensional qudits:
In[1]:=
| QuantumBasis |
Out[1]=
QuantumBasis
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Create a 2-dimensional basis using explicit element representations:
In[1]:=
| QuantumBasis |
Out[1]=
QuantumBasis
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Construct a Pauli-Y basis for 2 qubits:
In[1]:=
basis=
["Y"]
| QuantumBasis |
Out[1]=
QuantumBasis
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Represent the Bell basis for a single qubit (default):
In[1]:=
basis=
["Bell"]
| QuantumBasis |
Out[1]=
QuantumBasis
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Return its element names:
In[2]:=
basis["Names"]
Out[2]=
{|〉,|〉,|〉,|〉}
+
Φ
-
Φ
+
Ψ
-
Ψ
A quantum basis with Pauli-X as the input and computational basis as the output
In[1]:=
| QuantumBasis |
Out[1]=
QuantumBasis
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Show elements:
In[2]:=
Normal/@
[{"X"},{2}]["ElementAssociation"]
 | QuantumBasis |
Out[2]=
0,0,,0,10,,0,,0,0,-,0,10,,0,-
+
1
2
1
2
+
1
2
1
2
−
1
2
1
2
−
1
2
1
2
Construct 5-dimensional computational basis,
In[1]:=
basis=
[5];Normal/@basis["Association"]
| QuantumBasis |
Out[1]=
|0〉{1,0,0,0,0},|1〉{0,1,0,0,0},|2〉{0,0,1,0,0},|3〉{0,0,0,1,0},|4〉{0,0,0,0,1}
Construct a Bell (entangled) basis,
In[1]:=
bell=
["Bell"]
| QuantumBasis |
Out[1]=
QuantumBasis
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In[2]:=
Normal/@bell["Association"]
Out[2]=
,0,0,,,0,0,-,0,,,0,0,,-,0
+
Φ
1
2
1
2
-
Φ
1
2
1
2
+
Ψ
1
2
1
2
-
Ψ
1
2
1
2
The elements of a 3-dimensional can be arbitrary (potentially non-orthonormal) vectors:
In[1]:=
| QuantumBasis |
Out[1]=
QuantumBasis
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Return the list of orthogonalized basis elements:
In[2]:=
%["OrthogonalElements"]
Out[2]=
,-,0,,,,-,-,
1
10
3
10
3
14
1
14
2
7
3
35
1
35
5
7
Create a 3-qubit version of the same basis by taking a tensor product of the basis with itself 3 times:
In[1]:=
| QuantumBasis |
Out[1]=
QuantumBasis
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View the element names of the 3-qubit system:
In[2]:=
%["Names"]
Out[2]=
{|〉,|〉,|〉,|〉,|〉,|〉,|〉,|〉}
+
+
+
+
+
−
+
−
+
+
−
−
−
+
+
−
+
−
−
−
+
−
−
−
View the dual element names:
Represent the 2-dimensional Schwinger basis of rank-2 (matrix) elements:
Represent the 3-dimensional Schwinger basis:
Represent a collection of 2 qudits: