Wolfram Language Paclet Repository
Community-contributed installable additions to the Wolfram Language
QuantumMob`Q3mini`
ControlledGate  |
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Details and Options
Examples
(10)
Basic Examples
(4)
In[1]:=
Let[Qubit,S]
This is a controlled-U operator. Usually it remains unevaluated.
In[2]:=
op=ControlledGate[S[1],S[2,1]]
Out[2]=
ControlledGate{1},
S
1
X
S
2
In[3]:=
Elaborate[op]
Out[3]=
1
2
1
2
Z
S
1
X
S
2
1
2
Z
S
1
1
2
X
S
2
In[4]:=
Matrix[op]//MatrixForm
Out[4]//MatrixForm=
1 | 0 | 0 | 0 |
0 | 1 | 0 | 0 |
0 | 0 | 0 | 1 |
0 | 0 | 1 | 0 |
In[5]:=
Elaborate[op]
Out[5]=
1
2
1
2
Z
S
1
X
S
2
1
2
Z
S
1
1
2
X
S
2
In[6]:=
op**S[2,3]//Elaborate
Out[6]=
1
2
Z
S
1
Y
S
2
1
2
Z
S
1
Z
S
2
1
2
Y
S
2
1
2
Z
S
2
In the quantum circuit model, a controlled-U gate is depicted by the following quantum circuit element.
In[1]:=
QuantumCircuit[op]
Out[1]=
is a special case of controlled-U gate.
In[2]:=
x1=Elaborate@ControlledGate[S[1],S[2,1]]//Simplifyx2=Elaborate@CNOT[S[1],S[2]]//Simplifyx1-x2//Simplify
Out[2]=
1
2
Z
S
1
X
S
2
Z
S
1
X
S
2
Out[2]=
1
2
Z
S
1
X
S
2
Z
S
1
X
S
2
Out[2]=
0
In[3]:=
x1=Elaborate@ControlledGate[{S[1],S[2]},S[3,1]]//Simplifyx2=Elaborate[Toffoli[S[1],S[2],S[3]]]//Simplifyx1-x2//Simplify
Out[3]=
1
4
Z
S
1
Z
S
2
Z
S
1
X
S
3
Z
S
2
X
S
3
Z
S
1
Z
S
2
X
S
3
Z
S
1
Z
S
2
X
S
3
Out[3]=
1
4
Z
S
1
Z
S
2
Z
S
1
X
S
3
Z
S
2
X
S
3
Z
S
1
Z
S
2
X
S
3
Z
S
1
Z
S
2
X
S
3
Out[3]=
0
Here, the controlled-unitary gate has the unitary operator acting on multiple qubits.
In[1]:=
U=Rotation[ϕ,S[2,1]]**Rotation[θ,S[3,2]]
Out[1]=
Exp-ϕExp-θ
1
2
X
S
2
1
2
Y
S
3
In[2]:=
qc=QuantumCircuit[ControlledGate[S[1],U,"Label""U"]]
Out[2]=
In[3]:=
Elaborate[qc]
Out[3]=
1
2
θ
2
ϕ
2
1
2
θ
2
ϕ
2
Z
S
1
1
2
ϕ
2
Z
S
1
Y
S
3
θ
2
1
2
ϕ
2
Y
S
3
θ
2
1
2
θ
2
Z
S
1
X
S
2
ϕ
2
1
2
θ
2
X
S
2
ϕ
2
1
2
X
S
2
Y
S
3
θ
2
ϕ
2
1
2
Z
S
1
X
S
2
Y
S
3
θ
2
ϕ
2
It is more common to have multiple controlled qubits.
In[4]:=
qc=QuantumCircuit[ControlledGate[S@{1,2},Rotation[ϕ,S[3,2]]]]
Out[4]=
In[5]:=
Elaborate@qc
Out[5]=
1
4
ϕ
2
1
2
Z
S
1
Z
S
2
2
Sin
ϕ
4
1
2
Z
S
1
2
Sin
ϕ
4
1
2
Z
S
2
2
Sin
ϕ
4
1
4
Z
S
1
Y
S
3
ϕ
2
1
4
Z
S
2
Y
S
3
ϕ
2
1
4
Z
S
1
Z
S
2
Y
S
3
ϕ
2
1
4
Y
S
3
ϕ
2
In[1]:=
qc=QuantumCircuit[ControlledGate[S@{1,2}{1,0},Rotation[ϕ,S[3,2]]]]
Out[1]=
In[2]:=
new=QuantumCircuit[S[2,1],ControlledGate[S@{1,2},Rotation[ϕ,S[3,2]]],S[2,1]]
Out[2]=
In[3]:=
new-qc//Elaborate//Simplify
Out[3]=
0
Scope
(4)
Generalizations & Extensions
(2)
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