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
(10)
Create a 2-dimensional basis:
In[1]:=
 | QuantumBasis |
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QuantumBasis
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Note with no input, the basis is automatically set to 2D by default:
In[2]:=
 | QuantumBasis |
| QuantumBasis |
Out[2]=
True
Create a 3-dimensional basis:
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QuantumBasis
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Create a 2×2×2 dimensional basis (three qubits):
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QuantumBasis
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Create a composite basis of 2- and 3-dimensional qudits (a qubit with a qutrit):
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QuantumBasis
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Create a 2-dimensional basis using an explicit element representation with arbitrary names:
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QuantumBasis
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Construct a Pauli-Y basis:
In[1]:=
basis=
["Y"]
| QuantumBasis |
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QuantumBasis
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Construct a Bell basis for a single 4-dimensional qudit (quqrit):
In[1]:=
basis=
["Bell"]
| QuantumBasis |
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QuantumBasis
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Return its association (basis names with corresponding representations):
In[2]:=
basis["Association"]
Out[2]=
,0,0,-,0,,-,0,0,,,0,,0,0,
-
Φ
1
2
1
2
-
Ψ
1
2
1
2
+
Ψ
1
2
1
2
+
Φ
1
2
1
2
A quantum basis with Pauli-X as the output and computational 2-dimensional basis as the input:
In[1]:=
| QuantumBasis |
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QuantumBasis
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Show its elements:
In[2]:=
| QuantumBasis |
Out[2]=
0SparseArray
,1SparseArray
,0SparseArray
,1SparseArray
+
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+
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−
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−
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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 its 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
Represent the 2-dimensional Schwinger basis of rank-2 (matrix) elements:
In[1]:=
| QuantumBasis |
Out[1]=
QuantumBasis
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In[2]:=
%["Association"]
Out[2]=
|〉{{1,0},{0,1}},|〉{{1,0},{0,-1}},|〉{{0,1},{1,0}},|〉{{0,-1},{1,0}}
S
00
S
01
S
10
S
11
Generalizations & Extensions
(1)
Applications
(4)
Properties & Relations
(5)
Interactive Examples
(1)
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