Wolfram Language Paclet Repository
Community-contributed installable additions to the Wolfram Language
Variational Quantum Classifier: Iris
This demonstration is a translation of the tutorial “” in PennyLane by Maria Schuld. It demonstrates variational quantum classifiers; that is, quantum circuits that can be trained from labelled data to classify new data samples.
In particular, we will see how to encode real vectors as amplitude vectors (amplitude encoding) and train the model to recognize the first two classes of flowers in the Iris dataset.
Encodes data into amplitudes of a quantum state | |
AmplitudeEmbeddingGate | Quantum circuit model to implement amplitude embedding |
Find the minimum of a function |
Frequently used function in variational classification.
Make sure to load the Q3 package.
In[487]:=
Needs["QuantumMob`Q3`"]
Amplitude Embedding: Method
In[488]:=
Let[Qubit,S]
In[489]:=
$n=2;$N=Power[2,$n];kk=Range[$n];SS=S[kk,$]
Out[492]=
{,}
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Get the data.
In[493]:=
aa=Normalize@RandomReal[{0,1},$N]
Out[493]=
{0.18426,0.535389,0.670164,0.479883}
Embed the data into a quantum state.
In[494]:=
in=AmplitudeEmbedding[aa,SS]
Out[494]=
0.18426+0.535389+0.670164+0.479883
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Quantum circuit implementation
Quantum circuit implementation
Embedding the data into a quantum state as above on actual quantum computer is not trivial. One implementation based on quantum circuit model may be achieved by the following function.
In[508]:=
op=AmplitudeEmbeddingGate[aa,SS]
Out[508]=
AmplitudeEmbeddingGate[{0.18426,0.535389,0.670164,0.479883},{,}]
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In[509]:=
QuantumCircuit[op]
Out[509]=
More explicitly, the above quantum circuit is equivalent to the following.
In[510]:=
QuantumCircuit[ExpandAll@op]
Out[510]=
The above quantum circuit may be further simplified.
In[511]:=
qc=QuantumCircuit[GateFactor/@Expand@op]
Out[511]=
In[502]:=
new=qc**Ket[SS]//Chop
Out[502]=
0.18426+0.535389+0.670164+0.479883
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In[503]:=
Fidelity[new,in]
Out[503]=
1.
Data
Data loading and embedding
Data loading and embedding
Import the iris date and check the first three entries.
In[33]:=
raw=Import[PacletObject["QuantumPlaybook"]["AssetLocation","Iris"],"Table"];raw=Map[Most[#]Round[Last@#]&,raw];raw〚;;3〛
Out[35]=
{{0.399999999999999911,0.750000000000000000,0.199999999999999956,0.05000000000000000278}-1,{0.300000000000000267,0.5000000000000000000,0.199999999999999956,0.05000000000000000278}-1,{0.2000000000000001776,0.600000000000000089,0.150000000000000022,0.05000000000000000278}-1}
Renormalize the data.
In[81]:=
data=Thread[Map[Normalize@Join[Take[#,2],0.3{1,0}]&,Keys@raw]Values[raw]];data〚1〛
Out[82]=
{0.44376,0.83205,0.33282,0.}-1
Here, vector representation is nothing but the input data itself since we just simulate the amplitude embedding.
In[83]:=
(*in=AmplitudeEmbedding[#,SS]&/@Keys[data]//Chop;in=Matrix[in,SS];*)$in=Keys[data];
Features
Features
In[40]:=
gg=Map[Take[#,2]&,GroupBy[raw,Last,Map[First]],{2}];Graphics[{PointSize[0.02],Red,Point/@gg[1],Blue,Point/@gg[-1]},PlotLabel"Original",ImageSizeMedium,FrameTrue]
Out[41]=
In[42]:=
gg=Map[Take[#,2]&,GroupBy[data,Last,Map[First]],{2}];Graphics[{PointSize[0.02],Red,Point/@gg[1],Blue,Point/@gg[-1]},PlotLabel"Renormalized",ImageSizeMedium,FrameTrue]
Out[43]=
Quantum Circuit Layer
Construct the basic quantum circuit layer to use.
Check it by show two layers.
Optimization
Using three layers
Using three layers
Find the optimal values of the parameters iteratively.
From the optimized parameters, make predictions.
Using five layers
Using five layers
Find the optimal values of the parameters iteratively.
From the optimized parameters, make predictions.