Wolfram Language Paclet Repository
Community-contributed installable additions to the Wolfram Language
QuantumMob`Q3mini`
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Examples
(4)
Basic Examples
(4)
In[1]:=
Let[Qubit,S]
In[2]:=
op=Phase[ϕ,S[3]]
Out[2]=
z
S
This is the matrix representation of the relative phase operator.
In[3]:=
Matrix[op]//MatrixForm
Out[3]//MatrixForm=
1 | 0 |
0 | ϕ |
This expresses the operator explicitly in terms of the Pauli operators.
In[4]:=
Elaborate[op]
Out[4]=
1
2
ϕ
1
2
ϕ
z
S
When it is operated on a state vector or other operators, it is converted automatically to explicit expression.
In[5]:=
op**(Ket[]+Ket[S1])op**S[2]
Out[5]=
z
S
z
S
1
S
Out[5]=
z
S
y
S
In[6]:=
Dagger[op]
Out[6]=
z
S
In[7]:=
Let[Real,ϕ]Dagger[op]
Out[7]=
z
S
In[1]:=
Phase[ϕ,S[1]]//Matrix//MatrixForm
Out[1]//MatrixForm=
1 2 ϕ 2 | 1 2 ϕ 2 |
1 2 ϕ 2 | 1 2 ϕ 2 |
In[2]:=
Phase[ϕ,S[2]]//Matrix//MatrixForm
Out[2]//MatrixForm=
1 2 ϕ 2 | - 2 1 2 ϕ |
2 1 2 ϕ | 1 2 ϕ 2 |
In[3]:=
Phase[ϕ,S[3]]//Matrix//MatrixForm
Out[3]//MatrixForm=
1 | 0 |
0 | ϕ |
In[4]:=
Phase[ϕ,S[1,1]]-Exp[I*ϕ/2]*Rotation[ϕ,S[1,1]]//ElaboratePhase[ϕ,S[1,2]]-Exp[I*ϕ/2]*Rotation[ϕ,S[1,2]]//ElaboratePhase[ϕ,S[1,3]]-Exp[I*ϕ/2]*Rotation[ϕ,S[1,3]]//Elaborate
Out[4]=
0
Out[4]=
0
Out[4]=
0
In[1]:=
QuantumCircuit[Phase[Pi/4,S[1]],Phase[Pi/4,S[2]],Phase[Pi/4,S[3]]]
Out[1]=
In[2]:=
qc=QuantumCircuit[Phase[Pi/4,S[3]]]op=ExpressionFor[qc]
Out[2]=
Out[2]=
1
2
1/4
(-1)
1
2
1/4
(-1)
z
S
In[3]:=
qc**S[1]
Out[3]=
1
2
1/4
(-1)
x
S
1
2
1/4
(-1)
y
S
In[1]:=
qc=QuantumCircuit[ControlledGate[S[1],Phase[Pi/4,S[2,3]]]]
Out[1]=
In[2]:=
op=ExpressionFor[qc]
Out[2]=
1
4
1/4
(-1)
1
4
1/4
(-1)
z
S
1
z
S
2
1
4
1/4
(-1)
z
S
1
1
4
1/4
(-1)
z
S
2
In[3]:=
op**S[2,1]
Out[3]=
1
4
1/4
(-1)
z
S
1
x
S
2
1
4
1/4
(-1)
z
S
1
y
S
2
1
4
1/4
(-1)
x
S
2
1
4
1/4
(-1)
y
S
2
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""