Install the quantum framework
Install the quantum framework
Install quantum paclet: https://www.wolfram.com/quantum-computation-framework/
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PacletInstall["https://wolfr.am/DevWQCF",ForceVersionInstall->True]<<Wolfram`QuantumFramework`
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PacletObject
Create visualization of qubit in different phase space
Create visualization of qubit in different phase space
Work flow:
pointNames: these are names of some quantum state we will use as reference points, for future geometric transformation
labels: common states along Cartesian axis in Bloch sphere. We will use them to show how there are transformed in the phase space.
refpoints: Bloch vectors of pointNames.
spheres: list of different phase space representation (which are different basis for a qubit).
center: the center of multi-dimensional of geometric object in the phase space of corresponding basis.
points: the phase space points of pointNames in a give basis, relative to the center.
labelPoints: the phase space points of labels in a give basis, relative to the center.
ConvexHullMesh part: a geometric transformation from Bloch to phase space, but manipulating the transformation of refpoints
pointNames: these are names of some quantum state we will use as reference points, for future geometric transformation
labels: common states along Cartesian axis in Bloch sphere. We will use them to show how there are transformed in the phase space.
refpoints: Bloch vectors of pointNames.
spheres: list of different phase space representation (which are different basis for a qubit).
center: the center of multi-dimensional of geometric object in the phase space of corresponding basis.
points: the phase space points of pointNames in a give basis, relative to the center.
labelPoints: the phase space points of labels in a give basis, relative to the center.
ConvexHullMesh part: a geometric transformation from Bloch to phase space, but manipulating the transformation of refpoints
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list=Module{refpoints,pointNames,spheres,labels,labelPoints},pointNames={"1","0","+","R"};labels={"1","0","+","-","R","L"};refpoints=1
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Prepend[#,Norm[#]]&@QuantumState[#]["BlochVector"]&/@pointNames;spheres={"Wigner","WignerMIC","Wootters","Tetrahedron","Pauli","GellMann","GellMannMIC","GellMannBlochMIC","QBismSIC","Feynman","RandomMIC","RandomMIC"[Method->"Bloch"]};AssociationMap[Block[{basis=QuditBasis[#],center,points},center=QuantumPhaseSpaceTransform[QuantumState["UniformMixture"],basis]["StateVector"];points=Chop[QuantumState[QuantumState[#]["Double"],basis]["StateVector"]-center]&/@pointNames//Normal;labelPoints=Chop[QuantumState[QuantumState[#]["Double"],basis]["StateVector"]-center]&/@labels//Normal;Graphics3D[{PointSize[0.03],Transpose[{{Blue,Green,Red},Through[{Point,Line}[#]]&/@{{{0,0,1},{0,0,-1}},{{1,0,0},{-1,0,0}},{{0,1,0},{0,-1,0}}}}],Transpose[{{Blue,Green,Red},Through[{Point,Line}[#]]&/@Partition[Re@Chop@N@Rest[#]&/@Normal[labelPoints+Threaded[center]],2]}],Opacity[.5],(*Sphere[],*)ColorData[97][1],ConvexHullMesh[Chop@*Rest/@(Threaded[center]+AffineTransform[Transpose[points].Inverse[Transpose[refpoints]]]@RandomPoint[Sphere[{0,0,0,0}],6000]),MeshCellStyle->{1->None}]},Boxed->False]]&,spheres];To see the visualization better, we create a list of of them from different angles.
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img=Table[GraphicsGrid[Partition[KeyValueMap[Show[#2,QuantumState["UniformMixture"]["BlochPlot","ShowAxes"->False,ImageSize->Small],ViewVector->{5{Cos[θ]Sin[θ],Cos[θ]^2,Sin[θ]},{0,0,0}},ViewAngle->Pi/4,PlotLabel->#1]&]@list,UpTo[3]],ImageSize->Large,FrameAll],{θ,0,4π,.1}];
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ParametricPlot3D[{5{Cos[θ]Sin[θ],Cos[θ]^2,Sin[θ]},{0,0,0}},{θ,0,4π}]
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Export them as GIF
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Export[NotebookDirectory[]<>"qubit_basis.gif",img,AnimationRepetitions->Infinity]
Visualize it
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AnimatedImage[Import[NotebookDirectory[]<>"qubit_basis.gif"]]
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CITE THIS NOTEBOOK
CITE THIS NOTEBOOK
Qubit in the phase space: quasi-probability, simplex and different look into quantum states
by Wolfram quantum team: quantum AT wolfram.com
Wolfram Community, STAFF PICKS, May 3, 2024
https://community.wolfram.com/groups/-/m/t/3169726
by Wolfram quantum team: quantum AT wolfram.com
Wolfram Community, STAFF PICKS, May 3, 2024
https://community.wolfram.com/groups/-/m/t/3169726