UNESCO has designated 2025 as the International Year of Quantum (IQY2025). My friend, William, recently shared an insightful LinkedIn post discussing the IQY2025 logo and its resemblance to a knot. While the logo itself represents a trivial knot, its structure offers an intriguing framework for exploring certain quantum properties. In this essay, I examine the eigensystem characteristics associated with this region and its opened ring, highlighting potential quantum features embedded within its topology.
Special thanks to my colleague Kurt Gimbel at Wolfram Research, for his help with making the logo computational, and also Michael Trott, for his suggestions and helps.
Get IQY2025 logo:
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img=Import[URL["https://quantum2025.org/wp-content/uploads/2024/12/IYQST-horiz-rgb.png"],"PNG"]
Crop it:
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crop=ImagePad[ImageTake[img,{0,418},{0,428}],10,GrayLevel[1,0]]
Some image processing explorations:
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darker=Nest[Darker,crop,3];erosion=ColorNegate@Erosion[Binarize[darker,0.0001],1];dilation=Dilation[EdgeDetect@darker,2];add=ColorNegate@ImageAdd[erosion,dilation];shapes=ImageMesh[add];colorize=Colorize[MorphologicalComponents[add],ColorFunction->ColorData["BrightBands"]];{shapes,colorize}
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,
Some of my colleagues kindly help and manually extract some points from the 2D image and turn it into 3D to be as close as possible to the 2D logo.
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pnts=;
Create a B-spline curve through these points:
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Graphics3D[{BSplineCurve[pnts,SplineDegree30],Red,Point@pnts},ViewPoint->{0,0,Infinity},Boxed->False]
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Make a tube out of it:
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tube=Tube[BSplineCurve[Rescale@pnts,SplineDegree20,SplineClosed->True],.03];
Visualize it:
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Graphics3D[{tube},ViewPoint->{0,0,Infinity},Boxed->False]
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Find arc length of this knot and find the corresponding radius of a circle with the same circumference:
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r=ArcLength@Line@Rescale@pnts/(2π)
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0.94869
Create a ring and show log0’s knot and ring together:
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Graphics3D[{tube,ring=Torus[RegionCentroid[DiscretizeGraphics@tube],{r-.03,r+.03}]},ViewPoint->{0,0,Infinity},Boxed->False]
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Turn the knot into a mesh region and find the first 200 eigensystems:
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dg=DiscretizeGraphics[tube];filledTube=BoundaryMeshRegion[MeshCoordinates[dg],MeshCells[dg,{2}]];{valsLogo,funsLogo}=NDEigensystem[-Laplacian[u[x,y,z],{x,y,z}],u,{x,y,z}∈filledTube,500,Method{"Eigensystem"{"Arnoldi","MaxIterations"∞},"PDEDiscretization"{"FiniteElement",{"MeshOptions"{"MaxCellMeasure"0.0001}}}}];
Find the first 200 eigensystems of the ring:
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{valsRing,funsRing}=NDEigensystem[-Laplacian[u[x,y,z],{x,y,z}],u,{x,y,z}∈ring,500,Method{"Eigensystem"{"Arnoldi","MaxIterations"∞},"PDEDiscretization"{"FiniteElement",{"MeshOptions"{"MaxCellMeasure"0.0001}}}}];
Plot eigen-energy of ring and logo:
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GraphicsRow[{ListLinePlot[Chop@{valsLogo,valsRing}[[All,;;30]],PlotMarkers->Automatic,PlotLegends->Placed[{"Logo","Ring"},{Left,Top}],Frame->True,FrameLabel->{"Energy level","Eigenenergy"},ImageSize->400,AspectRatio->1/2],ListLinePlot[Chop@{valsLogo,valsRing},PlotLegends->Placed[{"Logo","Ring"},{Left,Top}],Frame->True,FrameLabel->{"Energy level","Eigenenergy"},ImageSize->400,AspectRatio->1/2]}]
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A simple energy-level statistic is the probability distribution of the spacings between neighbouring levels:
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Histogram[{Differences@valsLogo,Differences@valsRing},40,"PDF",PlotLabel->"Energy-level spacings distributions",AspectRatio->1/2,ChartLegends->Placed[{"Logo","Ring"},{Right,Center}]]
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Get the points from the mesh created for reach region (to be used as points for visualizations):
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cLogo=funsLogo[[1]]["ElementMesh"]["Coordinates"];cRing=funsRing[[1]]["ElementMesh"]["Coordinates"];
Visualize eigenstates:
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imgsEigenstates=Table[Graphics3D[{{PointSize[.02],Point[cRing,VertexColors->ColorData["SunsetColors"]/@Rescale[Abs@*funsRing[[i]]@@@cRing]]},{Point[cLogo,VertexColors->ColorData["SunsetColors"]/@Rescale[Abs@*funsLogo[[i]]@@@cLogo]]}},Boxed->False,ViewPoint->{0,0,Infinity},Boxed->False],{i,200}];
Turn them into a GIF:
Show a few of them:
Pick the level 160:
Rotate it from different view points:
Make a GIF:
CITE THIS NOTEBOOK
CITE THIS NOTEBOOK
Logo of International Year of Quantum Science and Technology: topological quantum features
by Mohammad Bahrami
Wolfram Community, STAFF PICKS, February 17, 2025
https://community.wolfram.com/groups/-/m/t/3396129
by Mohammad Bahrami
Wolfram Community, STAFF PICKS, February 17, 2025
https://community.wolfram.com/groups/-/m/t/3396129