Wolfram Language Paclet Repository
Community-contributed installable additions to the Wolfram Language
QuantumMob`Q3mini`
RandomWickCircuitSimulate  |  |
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Details and Options
Examples
(11)
Basic Examples
(3)
Set the number of fermion modes to consider.
In[1]:=
$n=4;
The probability to perform a measurement on each fermion mode.
In[2]:=
$p=.3;
The depth of quantum circuit.
In[3]:=
$T=10;
In[4]:=
in=WickState[{1,0},$n]
Out[4]=
WickState
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In[5]:=
SeedRandom[370];
In[6]:=
wu=RandomWickUnitary[$n,"Label""U"]
Out[6]=
WickUnitary
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Construct 8 random circuits and simulate each circuit 5 times.
In[7]:=
EchoTiming[data=RandomWickCircuitSimulate[in,{wu,$p},$T,"Samples"{50,10}]];
⌚
0.901998
Examine the data structure of the result.
In[8]:=
Dimensions[data]
Out[8]=
{50,10,11}
Examine the output states from the second "Wick circuit".
In[9]:=
data〚2,1,5〛
Out[9]=
WickState
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Further convert it into the list of trajectories of Wick states.
{…,{,,…,,…},…}
ws
k1
ws
k2
ws
kt
In[10]:=
EchoTiming[trj=Flatten[data,1];]
⌚
0.000179
In[11]:=
Dimensions[trj]
Out[11]=
{500,11}
In[12]:=
trj〚1〛
Out[12]=
WickState
,WickState
,WickState
,WickState
,WickState
,WickState
,WickState
,WickState
,WickState
,WickState
,WickState
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In[13]:=
EchoTiming[nrm=Map[NormSquare,trj,{2}];]nrm//ArrayShort
⌚
0.005857
Out[13]//MatrixForm=
1 | 1 | 1 | 1 | … |
1 | 1 | 1 | 1 | … |
1 | 1 | 1 | 1 | … |
1 | 1 | 1 | 1 | … |
… | … | … | … | … |
In[14]:=
nrm-1//ArrayZeroQ
Out[14]=
True
Take a part of the system, and examine the entanglement between the subsystem and the rest.
In[1]:=
kk=Range[$n/2]
Out[1]=
{1,2}
Calculate the entanglement entropy (EE) between the subsystem and the rest..
In[2]:=
EchoTiming[ee=WickEntanglementEntropy[trj,kk]];Dimensions[ee]
⌚
0.820182
Out[2]=
{500,11}
In[3]:=
ListLinePlot[Mean[ee],DataRange{0,$T},PlotMarkersAutomatic,FrameLabel{"time","〈EE (L, L/2)〉"}]
Out[3]=
Calculate the mutual information (MI) between the subsystem and the rest.
In[4]:=
EchoTiming[mi=WickMutualInformation[trj,kk]];Dimensions[mi]
⌚
2.53692
Out[4]=
{500,11}
In[5]:=
ListLinePlot[Mean[mi],DataRange{0,$T},PlotMarkersAutomatic,FrameLabel{"time","〈MI (L, L/2)〉"}]
Out[5]=
Calculate the logarithmic negativity (LN) between the subsystem and the rest. (Note that here, Re is necessary to ignore small imaginary parts due to numerical errors.)
Finally, construct an approximate density matrices by averaging states in different trajectories, and calculate the the logarithmic negativity (LN) between the subsystem and the rest.