Wolfram Language Paclet Repository
Community-contributed installable additions to the Wolfram Language
Wolfram`QuantumFramework`
QuantumWignerTransform  |
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Details and Options
Examples
(22)
Basic Examples
(5)
Generate the Wigner transformation a quantum state in the phase space:
In[1]:=
ρ=
["RandomMixed",3];
[ρ]
 | QuantumState |
 | QuantumWignerTransform |
Out[1]=
QuantumState
 |  |
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It is the same as the basis transformation of the doubled state into the corresponding Wigner basis:
In[2]:=
 | QuantumState |
 | QuantumBasis |
Out[2]=
True
The state vector in the Wigner basis corresponds to PhaseSpace representation of the state
In[1]:=
ρ=
["RandomMixed",3];
[ρ]["StateVector"]Flatten@ρ["PhaseSpace"]
| QuantumState |
| QuantumWignerTransform |
Out[1]=
True
Note for odd dimensions, PhaseSpace has the dimension
d×d
In[2]:=
MatrixForm[ρ["PhaseSpace"]]
Out[2]//MatrixForm=
0.130718 | 0.118202 | 0.163459 |
0.0412652 | -0.0685234 | 0.178726 |
0.240855 | 0.158132 | 0.0371668 |
For even dimensions, PhaseSpace has the dimension
2d×2d
In[1]:=
d=4;ρ=
["RandomMixed",d];ρ["PhaseSpace"]
| QuantumState |
Out[1]=
SparseArray
|  |
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If we partition the PhaseSpace into four blocks of the dimension , the upper left one corresponds to the StateVector of the Wigner transformation:
d×d
In[2]:=
| QuantumWignerTransform |
Out[2]=
True
Winger transformation of an operator:
In[1]:=
op=
["X"]
| QuantumWignerTransform |
| QuantumOperator |
Out[1]=
QuantumOperator
|  |
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Show its representation in the phase space:
In[2]:=
TraditionalForm[op]
Out[2]//TraditionalForm=
+--
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Wigner transformation of a quantum circuit (pay attention to wire dimensions)
In[1]:=
qc=
["Bell"];qc["Diagram","ShowWireDimensions"True]
| QuantumWignerTransform |
| QuantumCircuitOperator |
Out[1]=
Return the result of circuit on a register state:
In[2]:=
qc[]["Amplitudes"]
Out[2]=
,0,0,0,0,,0,0,0,0,,0,0,0,0,-
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Check that the Weyl transformation of the outcome is the same as the Bell state:
In[3]:=
QuantumWeylTransform[qc[]]["Formula"]
Out[3]=
1
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1
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Scope
(8)
Generalizations & Extensions
(4)
Applications
(4)
Interactive Examples
(1)
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