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Community-contributed installable additions to the Wolfram Language
QuantumMob`Q3mini`
WickState  |  |
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Details and Options
Examples
(9)
Basic Examples
(5)
We will consider a fixed number of bare fermion modes.
In[1]:=
$n=5;
Consider a quantum state filling every two fermion modes.
In[2]:=
in=WickState[{1,0},$n]
Out[2]=
WickState
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To examine the Wick state in more common forms, let consider a labeled fermion modes.
In[3]:=
Let[Fermion,c]cc=c[Range@$n]
Out[3]=
{,,,,}
c
1
c
2
c
3
c
4
c
5
Convince yourself that the Wick state form is equivalent to the conventional form.
In[4]:=
ExpressionFor[in,cc]
Out[4]=
1
c
1
0
c
2
1
c
3
0
c
4
1
c
5
In[5]:=
Matrix[in,cc]//IntegerChop//Normal
Out[5]=
{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0}
Consider a unitary time-evolution operator.
In[1]:=
SeedRandom[370];
In[2]:=
wu=RandomWickUnitary[$n]
Out[2]=
WickUnitary
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In[3]:=
out=wu**in
Out[3]=
WickState
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In[4]:=
Matrix[out]//ArrayShort
Out[4]=
{0,0.452764,0.264602-0.239179,0,…}
Consider a measurement of the occupation number of the 2nd fermion mode.
In[1]:=
msr=WickMeasurement[2]
Out[1]=
WickMeasurement[2]
Prepare a state.
In[2]:=
ket=wu**in
Out[2]=
WickState
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Perform the measurement on the above state.
In[3]:=
out=msr**ket
Out[3]=
WickState
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In[4]:=
Matrix[out]//ArrayShort
Out[4]=
{0,0.588577,0.343973-0.310924,0,…}
Consider a quantum jump operator.
In[1]:=
jmp=RandomWickJump[3,$n]
Out[1]=
WickJump
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Operate the quantum jump operator.
In[2]:=
out=jmp**in
Out[2]=
WickState
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In this case, the state is normalized since the process causes a "collapse" of the wave function.
In[3]:=
NormSquare[out]
Out[3]=
1
Consider a non-unitary time-evolution operator.
In[1]:=
non=RandomWickNonunitary[$n]
Out[1]=
WickNonunitary
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Operate the non-unitary evolution operator.
In[2]:=
out=non**in
Out[2]=
WickState
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Note that the output state is not normalized since the time-evolution is not unitary.
In[3]:=
Norm[out]
Out[3]=
18.554
It may look like a mixed state due to numerical errors.
In[4]:=
Chop[Matrix[out],1*^-6]//ArrayShort
Out[4]//MatrixForm=
0 | 0 | 0 | 0 | … |
0 | 16.995 | -8.11841+18.639 | 0 | … |
0 | -8.11841-18.639 | 24.3201 | 0 | … |
0 | 0 | 0 | 0 | … |
… | … | … | … | … |
Scope
(4)
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