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WOLFRAM NOTEBOOK
(Modified) Quantum Package
(Modified) Quantum Package
Yoav Presentation
Yoav Presentation
Set variables:
◼
N1: Number to be factored.
◼
a: Initial guess (a<N1).
◼
q: Counting qubits .
(≤<2)
2
N1
q
2
2
N1
◼
n: Ancilla qubits (n ≥ N1).
log
2
In[]:=
N1=6a=7;N1^2
Out[]=
6
Out[]=
36
In[]:=
q=3;2^q
Out[]=
8
In[]:=
n=2;Ceiling[Log[2,N1]]
Out[]=
3
Prepare initial circuit state (counting qubits already in plus state, ancilla qubits in 0 state)
In[]:=
initialstates=QuantumTensorProduct[Catenate[{Table[QuantumDiscreteState["Plus"],{i,1,q}],Table[QuantumDiscreteState[{0,1},2],{j,1,n-1}],{QuantumDiscreteState[{1,0},2]}}]]
Out[]=
QuantumDiscreteState
Naming basis elements
In[]:=
map=AssociationThread[Flatten[Table[Ket[i,j],{i,0,2^q-1},{j,0,2^n-1}]]Range[2^(n+q)]]
Out[]=
|0,0〉1,|0,1〉2,|0,2〉3,|0,3〉4,|1,0〉5,|1,1〉6,|1,2〉7,|1,3〉8,|2,0〉9,|2,1〉10,|2,2〉11,|2,3〉12,|3,0〉13,|3,1〉14,|3,2〉15,|3,3〉16,|4,0〉17,|4,1〉18,|4,2〉19,|4,3〉20,|5,0〉21,|5,1〉22,|5,2〉23,|5,3〉24,|6,0〉25,|6,1〉26,|6,2〉27,|6,3〉28,|7,0〉29,|7,1〉30,|7,2〉31,|7,3〉32
Defining required operator action
In[]:=
action=Association[Table[Ket[i,0]Ket[i,Mod[a^i,N1]],{i,0,2^q-1}]]
Out[]=
|0,0〉|0,1〉,|1,0〉|1,1〉,|2,0〉|2,1〉,|3,0〉|3,1〉,|4,0〉|4,1〉,|5,0〉|5,1〉,|6,0〉|6,1〉,|7,0〉|7,1〉
Constructing matrix form
In[]:=
inputoutput=KeyMap[Replace[map]]@(action/.map);
In[]:=
replacements=Flatten[KeyValueMap[{{#1,#2}1,{#2,#1}1,{#1,#1}0,{#2,#2}0}&,inputoutput]];
In[]:=
matrixForm=ReplacePart[IdentityMatrix[2^(q+n)],replacements];
Constructing and applying CondModExp operator (may take a while)
In[]:=
condModExp=QuantumDiscreteOperator[N[matrixForm],Range[q+n]]
Out[]=
QuantumDiscreteOperator
In[]:=
moddedstates=condModExp[initialstates]
Out[]=
QuantumDiscreteState
Constructing and applying inverse QFT (May take a while)
In[]:=
QFT=QuantumDiscreteOperator[{"Fourier",1,2^q},Range[q]]
Out[]=
QuantumDiscreteOperator
In[]:=
iQFT=QuantumDiscreteOperator[Inverse[N[QFT["MatrixRepresentation"]]],Range[q]]
Out[]=
QuantumDiscreteOperator
In[]:=
finalstates=iQFT[moddedstates]
Out[]=
QuantumDiscreteState
Evaluating final state
In[]:=
KeyValueMap[If[Abs[#2]>0.001,First[First[Position[#1,1]]]#2,##&[]]&,KeyMap[Replace[finalstates["Basis"]["BasisElementAssociation"]]]@finalstates["Amplitudes"]]/.Association[KeyValueMap[#2#1&,map]]
Out[]=
{|7,1〉1.-1.2326×}
-32
10
In[]:=
QMS=ResourceFunction["QuantumToMultiwaySystem"]
Out[]=
Converting superpositions to proportional initial states
In[]:=
toProp[stateV_]:=(probs=Table[If[#[[i]]>0,#[[i]]^2ReplacePart[ConstantArray[0,Length[#]],{i}1],##&[]],{i,1,Length[#]}]&@stateV;out=Catenate[Table[Table[#[[i,2]],{j,1,#[[i,1]]/Min[probs[[All,1]]]}],{i,1,Length[#]}]]&@probs;Return[out];)
In[]:=
QMS[Floor[condModExp["MatrixRepresentation"]],toProp[initialstates["StateVector"]],1,"EvolutionGraph","IncludeStatePathWeights"True,VertexLabels"VertexWeight"]
Out[]=
In[]:=
QMS[Floor[iQFT["MatrixRepresentation"]],toProp[moddedstates["StateVector"]],2]
Out[]=
{{{0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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, 0, 0, 0, 0, 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, 0, 0, 0, 0, 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, 0, 0, 0, 0, 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, 0, 0, 0},{0, 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, 0, 0, 0, 0, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0}},{},{}}