Wolfram Language Paclet Repository
Community-contributed installable additions to the Wolfram Language
QuantumMob`Q3mini`
WickMeasurement  |  |
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Details and Options
Examples
(13)
Basic Examples
(3)
Consider a certain number of fermion modes.
In[1]:=
$n=4;
Take an initial state.
In[2]:=
SeedRandom[370];
In[3]:=
in=RandomWickState[$n]
Out[3]=
WickState
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Make sure it is normalized.
In[4]:=
Norm[in]
Out[4]=
1
Pick a fermion mode to perform the measurement on.
In[5]:=
msr=WickMeasurement[1]
Out[5]=
WickMeasurement[1]
Operate the measurement on the input state.
In[6]:=
out=msr[in]Readout[msr]
Out[6]=
WickState
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Out[6]=
0
Repeatedly perform measurements.
In[7]:=
{states,data}=Transpose@Table[{out=msr@in,Readout[msr]},10];
In[8]:=
states//ArrayShort
Out[8]=
WickState
,WickState
,WickState
,WickState
,…
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In[9]:=
data
Out[9]=
{0,0,1,1,1,0,1,1,0,1}
Let us verify the above results by conventional methods. To analyse the results, consider a specific set of fermion modes.
In[1]:=
Let[Fermion,c]cc=c[Range@$n]cd=Join[cc,Dagger@cc]
Out[1]=
{,,,}
c
1
c
2
c
3
c
4
Out[1]=
,,,,,,,
c
1
c
2
c
3
c
4
†
c
1
†
c
2
†
c
3
†
c
4
In[2]:=
EchoTiming[alt=ExpressionFor[Matrix[in],cc]//Chop]
⌚
0.008723
Out[2]=
0.437105-(0.391019+0.307682)+(0.0836836+0.220554)+(0.116218+0.100849)+(0.194988+0.105684)-(0.382598-0.279783)+(0.0774607+0.262235)+(0.357178-0.0765382)
0
c
1
0
c
2
0
c
3
0
c
4
0
c
1
0
c
2
1
c
3
1
c
4
0
c
1
1
c
2
0
c
3
1
c
4
0
c
1
1
c
2
1
c
3
0
c
4
1
c
1
0
c
2
0
c
3
1
c
4
1
c
1
0
c
2
1
c
3
0
c
4
1
c
1
1
c
2
0
c
3
0
c
4
1
c
1
1
c
2
1
c
3
1
c
4
Define the projection operator for each outcome.
In[3]:=
Clear[prj]prj[0]:=AbsSquareLeft[c@First@msr]prj[1]:=AbsSquareRight[c@First@msr]
Get the post-measurement states by applying the projection operators corresponding to the outcomes.
In[4]:=
mint=Chop@KetNormalize[(prj/@data)**alt];
Compare the post-measurement states from the two methods.
In[5]:=
vv=Matrix[states,cc];ww=CanonicalizeVector/@Matrix[mint,cc];vv-ww//ArrayZeroQ
Out[5]=
True
Let us examine the distribution of measurement outcomes. To do that, first calculate the probability to get 0.
In[1]:=
prb=Dagger[alt]**prj[0]**alt//Chop
Out[1]=
0.517949
Perform the measurement repeatedly many times.
In[2]:=
data=Table[msr@in;Readout[msr],samples=1000];
In[3]:=
Histogram[data,PlotRange{0,samples},FrameLabel{"outcome","counts"}]
Out[3]=
Scope
(3)
Applications
(3)
Properties & Relations
(4)
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