Luca Innocenti lucainnocenti
lucainnocenti
/ scramblingDynamics.m
Last active
July 28, 2022 09:40
Examples of scrambling (cit) dynamics
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| (* this one gives maximally negative tripartite *) | |
| superScrambling2qutritsUnitary := Table[ | |
| Normal @ Flatten @ KroneckerProduct[ | |
| SparseArray[{Mod[i + j, 3] + 1 -> 1}, 3], | |
| SparseArray[{Mod[i - j, 3] + 1 -> 1}, 3] | |
| ], | |
| {i, {0, 1, 2}}, {j, {0, 1, 2}} | |
| ] // ArrayReshape[#, {9, 9}] & // Transpose; | |
| (* unitary changing local bases to Fourier bases *) |
lucainnocenti
/ weirdPauliMatricesDecomposition.m
Created
June 7, 2022 16:22
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| generatePair[pauliIndices_List, tuple_List] := { | |
| BitXor[ | |
| ReplaceAll[ | |
| pauliIndices, {3 -> 0, 2 -> 1} | |
| ], | |
| tuple | |
| ], | |
| (-1)^Total@tuple[[Flatten@Position[pauliIndices, 2 | 3]]] | |
| }; |
lucainnocenti
/ shannonEntropy.m
Created
November 15, 2021 02:44
Two-dimensional visualisation of Shannon entropy
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| ShannonEntropy[probs_] := -Total[# * Log @ #] & @ DeleteCases[probs, _?PossibleZeroQ]; | |
| par[t_, s_] = {1, 0, 0} + t / Sqrt@2 {-1, 1, 0} + s/Sqrt[3/2] {-1/2, -1/2, 1} // Simplify; | |
| par[pars_List] := par @@ pars; | |
| ContourPlot[ | |
| ShannonEntropy@par[t, s], {t, 0, Sqrt@2}, {s, 0, Sqrt[3/2]}, | |
| PlotRange -> All, | |
| ColorFunction -> "TemperatureMap", PlotRangePadding -> None, | |
| Contours -> 10, | |
| FrameStyle -> Directive[Large, Black, FontFamily -> "Latin Modern Math"], | |
| FrameLabel -> (MaTeX[#, Magnification -> 2] & /@ {"t", "s"}), |
lucainnocenti
/ visualiseDualFrames.m
Last active
November 11, 2021 16:53
Dynamically visualise dual and parseval frames
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| getDualBasis[vecs_List] := With[{ | |
| sMatrix = Total[KroneckerProduct[#, Conjugate@#] & /@ vecs] | |
| }, | |
| Dot[Inverse@sMatrix, #] & /@ vecs | |
| ]; | |
| getParsevalFrame[vecs_List] := With[{ | |
| sMatrix = Total[KroneckerProduct[#, Conjugate@#] & /@ vecs] | |
| }, | |
| Dot[MatrixFunction[Sqrt, Inverse@sMatrix], #] & /@ vecs | |
| ]; |
lucainnocenti
/ dynamicStereographicProjectionIn3D.m
Created
August 8, 2021 23:29
Dynamic visualisation of stereographic projection of the sphere
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| stereoTo3D[x_, y_] := 1/(1 + x^2 + y^2) {2 x, 2 y, 1 - x^2 - y^2}; | |
| DynamicModule[ | |
| {pt = {0, 0}}, | |
| Row @ { | |
| LocatorPane[Dynamic @ pt, | |
| Graphics[{Gray, Disk[]}, Frame -> True, ImageSize -> 200] | |
| ], | |
| Graphics3D[ | |
| { |
lucainnocenti
/ euclideanAlgorithm.m
Created
April 29, 2021 17:38
Perform and visualise Euclidean algorithm on a pair of integers
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| euclideanAlgorithmList[a_Integer, b_Integer] := NestWhileList[ | |
| With[{newSortedPair = {Max@# - Floor[Max@#/Min@#] Min@#, Min@#}}, | |
| If[#[[1]] > #[[2]], newSortedPair, Reverse@newSortedPair] | |
| ] &, | |
| {a, b}, | |
| Min @ # > 1 & | |
| ]; | |
| DynamicModule[{a = 17, b = 10}, | |
| EventHandler[ |
lucainnocenti
/ pointPlanesDualityInR2.m
Last active
August 29, 2020 22:03
Dynamic visualisation of point-plane duality in convex geometry
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| DynamicModule[{pts={{1,1}}, activePoint=None}, | |
| EventHandler[ | |
| Dynamic @ Show[ | |
| Graphics[{ | |
| PointSize@0.04,Dynamic@Point@pts, | |
| Circle[], | |
| If[activePoint =!= None, | |
| {Blue, Point @ pts[[activePoint]]}, {} | |
| ], | |
| InfiniteLine[# / Norm[#]^2, Cross @ #] & /@ pts // Dynamic |
lucainnocenti
/ interpolationLinearApprox.m
Created
July 31, 2020 12:34
linear approximation of function in MMA
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| xMax = 1.4; | |
| numPartitions = 10; dx = xMax/numPartitions; | |
| pointsAndLines[pts_] := {Point@pts, Line@pts}; | |
| fun[x_] := x^2; | |
| Plot[fun@x, {x, 0, xMax}, | |
| PlotRange -> All, PlotStyle -> Directive[Thick], Frame -> True, | |
| GridLines -> Automatic, | |
| FrameStyle -> Directive[Black, Thick, Large], | |
| PlotLegends -> "Expressions", | |
| ImageSize -> 500 |
lucainnocenti
/ distribute.m
Last active
May 17, 2020 20:18
Replacement rules implementing a noncommutative algebra, and functions to show how expressions are written in terms of nested commutators
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| << MaTeX` | |
| distribute[args_] := (args //. { | |
| HoldPattern[nc[l___, Plus[m__], r___]] :> Total[nc[l, #, r] & /@ {m}], | |
| nc[l___, c_*nc[m__], r___] :> c nc[l, m, r], | |
| nc[l___, nc[m__], r___] :> nc[l, m, r], | |
| nc[-a_, b_] :> -nc[a, b], | |
| nc[a_, -b_] :> -nc[a, b], | |
| nc[nc[l : __], r_] :> nc[l, r], nc[l_, nc[r : __]] :> nc[l, r], | |
| nc[a_] :> a |
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| zeros[0] = 0; | |
| zeros[dim_] := ConstantArray[0, {dim, dim}]; | |
| MF[expr_] := MatrixForm@expr; | |
| (* take small matrix and embed it into a larger matrix, padding with zeros *) | |
| injectIntoLargerMatrix[mat_, largerMatDim_, position_Integer: 1] := Module[{outMat}, | |
| (* put zeros on bottom right *) | |
| If[largerMatDim - Length@mat - position + 1 > 0, | |
| outMat = ArrayFlatten[{ |
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