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Update transformation docs
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@jofrevalles
jofrevalles committed Sep 13, 2023
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Expand Up @@ -14,11 +14,11 @@ transform!
```

# Example
Here we show how can we reduce the complexity of the tensor network by applying a tranformation to it:
Here we show how can we reduce the complexity of the tensor network by applying a tranformation to it. We take as an example the Sycamore circuit from the [Google's quantum supremacy paper](https://www.nature.com/articles/s41586-019-1666-5)

```@setup plot
using Makie
Makie.inline!(true)
set_theme!(resolution=(800,200))
using CairoMakie
using Tenet
Expand Down Expand Up @@ -50,152 +50,264 @@ function smooth_annotation!(f; color=Makie.RGBAf(110 // 256, 170 // 256, 250 //
poly!(ax, circle_points, color=color, closed=true)
end
bg_blue = Makie.RGBAf(110 // 256, 170 // 256, 250 // 256, 50 // 256) #hide
orange = Makie.RGBf(240 // 256, 180 // 256, 100 // 256) #hide
red = Makie.RGBf(240 // 256, 90 // 256, 70 // 256) #hide
```
```@example plot
using QuacIO
set_theme!(resolution=(800,400)) # hide
sites = [5, 6, 14, 15, 16, 17, 24, 25, 26, 27, 28, 32, 33, 34, 35, 36, 37, 38, 39, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 61, 62, 63, 64, 65, 66, 67, 72, 73, 74, 75, 76, 83, 84, 85, 94]
circuit = QuacIO.parse(joinpath(@__DIR__, "sycamore_53_10_0.qasm"), format=QuacIO.Qflex(), sites=sites)
tn = TensorNetwork(circuit)
transformed_tn = transform(tn, Tenet.RankSimplification)
fig = Figure() # hide
ax1 = Axis(fig[1, 1]; title="Original TensorNetwork") # hide
p1 = plot!(ax1, tn; node_size=5.) # hide
ax2 = Axis(fig[1, 2], title="Transformed TensorNetwork") # hide
p2 = plot!(ax2, transformed_tn; node_size=5.) # hide
ax1.titlesize=20 # hide
ax2.titlesize=20 # hide
ax1 = Axis(fig[1, 1]) # hide
p1 = plot!(ax1, tn; edge_width=0.75, node_size=8., node_attr=(strokecolor=:black, strokewidth=0.5)) # hide
ax2 = Axis(fig[1, 2]) # hide
p2 = plot!(ax2, transformed_tn; edge_width=0.75, node_size=8., node_attr=(strokecolor=:black, strokewidth=0.5)) # hide
ax1.titlesize, ax2.titlesize = 20, 20 # hide
hidedecorations!(ax1) # hide
hidespines!(ax1) # hide
hidedecorations!(ax2) # hide
hidespines!(ax2) # hide
Label(fig[1, 1, Bottom()], "Original Tensor Network") # hide
Label(fig[1, 2, Bottom()], "Transformed Tensor Network") # hide
fig # hide
```

# Transformations

## Rank simplification
!!! warn ""
## Hyperindex converter
!!! warn "Note"
This transformation is always used by default when visualizing a `TensorNetwork` with `plot`.
```@docs
Tenet.HyperindConverter
```

## Diagonal reduction
```@example plot
fig = Figure() #hide
data = zeros(Float64, 2, 2, 2, 2) #hide
for i in 1:2 #hide
for j in 1:2 #hide
for k in 1:2 #hide
data[i, i, j, k] = k #hide
end #hide
set_theme!(resolution=(800,200)) # hide
fig = Figure() #hide
data = zeros(Float64, 2, 2, 2, 2) #hide
for i in 1:2 #hide
for j in 1:2 #hide
for k in 1:2 #hide
data[i, i, j, k] = k #hide
end #hide
end #hide
A = Tensor(data, (:i, :j, :k, :l)) #hide
B = Tensor(rand(2, 2), (:i, :m)) #hide
C = Tensor(rand(2, 2), (:j, :n)) #hide
bg_blue = Makie.RGBAf(110 // 256, 170 // 256, 250 // 256, 50 // 256) #hide
orange = Makie.RGBf(240 // 256, 180 // 256, 100 // 256) #hide
red = Makie.RGBf(240 // 256, 90 // 256, 70 // 256) #hide
tn = TensorNetwork([A, B, C]) #hide
reduced = transform(tn, Tenet.DiagonalReduction) #hide
smooth_annotation!( #hide
fig[1, 1]; #hide
color = bg_blue, #hide
xlims = [-2, 2], #hide
ylims = [-2, 2], #hide
offset_x = -0.21, #hide
offset_y = -0.42, #hide
radius_x = 0.38, #hide
radius_y = 0.8, #hide
num_waves = 6, #hide
fluctuation_amplitude = 0.02, #hide
phase_shift = 0.0) #hide
plot!(fig[1, 1], tn, layout=Spring(iterations=1000, C=0.5, seed=100); node_color=[red, orange, orange, :black, :black,:black, :black]) #hide
smooth_annotation!( #hide
fig[1, 2]; #hide
color = bg_blue, #hide
xlims = [-2, 2], #hide
ylims = [-2, 2], #hide
offset_x = 0.1, #hide
offset_y = -0.35, #hide
radius_x = 0.38, #hide
radius_y = 1.1, #hide
num_waves = 5, #hide
fluctuation_amplitude = 0.02, #hide
phase_shift = 1.9) #hide
plot!(fig[1, 2], reduced, layout=Spring(iterations=1000, C=0.5, seed=100), node_color=[orange, orange, red, :black, :black, :black, :black, :black]) #hide
Label(fig[1, 1, Bottom()], "Original Tensor Network") #hide
Label(fig[1, 2, Bottom()], "Transformed Tensor Network") #hide
fig #hide
end #hide
A = Tensor(data, (:i, :j, :k, :l)) #hide
B = Tensor(rand(2, 2), (:i, :m)) #hide
C = Tensor(rand(2, 2), (:j, :n)) #hide
tn = TensorNetwork([A, B, C]) #hide
reduced = transform(tn, Tenet.DiagonalReduction) #hide
smooth_annotation!( #hide
fig[1, 1]; #hide
color = bg_blue, #hide
xlims = [-2, 2], #hide
ylims = [-2, 2], #hide
offset_x = -0.21, #hide
offset_y = -0.42, #hide
radius_x = 0.38, #hide
radius_y = 0.8, #hide
num_waves = 6, #hide
fluctuation_amplitude = 0.02, #hide
phase_shift = 0.0) #hide
plot!(fig[1, 1], tn, layout=Spring(iterations=1000, C=0.5, seed=100); node_color=[red, orange, orange, :black, :black,:black, :black]) #hide
smooth_annotation!( #hide
fig[1, 2]; #hide
color = bg_blue, #hide
xlims = [-2, 2], #hide
ylims = [-2, 2], #hide
offset_x = 0.1, #hide
offset_y = -0.35, #hide
radius_x = 0.38, #hide
radius_y = 1.1, #hide
num_waves = 5, #hide
fluctuation_amplitude = 0.02, #hide
phase_shift = 1.9) #hide
plot!(fig[1, 2], reduced, layout=Spring(iterations=1000, C=0.5, seed=100), node_color=[orange, orange, red, :black, :black, :black, :black, :black]) #hide
Label(fig[1, 1, Bottom()], "Original Tensor Network") #hide
Label(fig[1, 2, Bottom()], "Transformed Tensor Network") #hide
fig #hide
```

```@docs
Tenet.DiagonalReduction
```

## Rank reduction
## Anti-diagonal reduction
```@docs
Tenet.RankReduction
Tenet.AntiDiagonalGauging
```

## Rank simplification
```@docs
Tenet.RankSimplification
```

```@example plot
fig = Figure() #hide
A = Tensor(rand(2, 2, 2, 2), (:i, :j, :k, :l)) #hide
B = Tensor(rand(2, 2), (:i, :m)) #hide
C = Tensor(rand(2, 2, 2), (:m, :n, :o)) #hide
E = Tensor(rand(2, 2, 2, 2), (:o, :p, :q, :j)) #hide
bg_blue = Makie.RGBAf(110 // 256, 170 // 256, 250 // 256, 50 // 256) #hide
orange = Makie.RGBf(240 // 256, 180 // 256, 100 // 256) #hide
red = Makie.RGBf(240 // 256, 90 // 256, 70 // 256) #hide
tn = TensorNetwork([A, B, C, E]) #hide
reduced = transform(tn, Tenet.RankSimplification) #hide
smooth_annotation!( #hide
fig[1, 1]; #hide
color = bg_blue, #hide
xlims = [-2, 2], #hide
ylims = [-2, 2], #hide
offset_x = -0.32, #hide
offset_y = -0.5, #hide
radius_x = 0.25, #hide
radius_y = 0.94, #hide
num_waves = 6, #hide
fluctuation_amplitude = 0.01, #hide
phase_shift = 0.0) #hide
plot!(fig[1, 1], tn, layout=Spring(iterations=1000, C=0.5, seed=20); node_color=[orange, red, orange, orange, :black, :black, :black, :black, :black]) #hide
smooth_annotation!( #hide
fig[1, 2]; #hide
color = bg_blue, #hide
xlims = [-2, 2], #hide
ylims = [-2, 2], #hide
offset_x = 0.12, #hide
offset_y = -0.62, #hide
radius_x = 0.18, #hide
radius_y = 0.46, #hide
num_waves = 5, #hide
fluctuation_amplitude = 0.01, #hide
phase_shift = 0) #hide
plot!(fig[1, 2], reduced, layout=Spring(iterations=1000, C=0.5, seed=1); node_color=[red, orange, orange, :black, :black, :black, :black, :black]) #hide
Label(fig[1, 1, Bottom()], "Original Tensor Network") #hide
Label(fig[1, 2, Bottom()], "Transformed Tensor Network") #hide
fig #hide
set_theme!(resolution=(800,200)) # hide
fig = Figure() #hide
A = Tensor(rand(2, 2, 2, 2), (:i, :j, :k, :l)) #hide
B = Tensor(rand(2, 2), (:i, :m)) #hide
C = Tensor(rand(2, 2, 2), (:m, :n, :o)) #hide
E = Tensor(rand(2, 2, 2, 2), (:o, :p, :q, :j)) #hide
tn = TensorNetwork([A, B, C, E]) #hide
reduced = transform(tn, Tenet.RankSimplification) #hide
smooth_annotation!( #hide
fig[1, 1]; #hide
color = bg_blue, #hide
xlims = [-2, 2], #hide
ylims = [-2, 2], #hide
offset_x = -0.32, #hide
offset_y = -0.5, #hide
radius_x = 0.25, #hide
radius_y = 0.94, #hide
num_waves = 6, #hide
fluctuation_amplitude = 0.01, #hide
phase_shift = 0.0) #hide
plot!(fig[1, 1], tn, layout=Spring(iterations=1000, C=0.5, seed=20); node_color=[orange, red, orange, orange, :black, :black, :black, :black, :black]) #hide
smooth_annotation!( #hide
fig[1, 2]; #hide
color = bg_blue, #hide
xlims = [-2, 2], #hide
ylims = [-2, 2], #hide
offset_x = 0.12, #hide
offset_y = -0.62, #hide
radius_x = 0.18, #hide
radius_y = 0.46, #hide
num_waves = 5, #hide
fluctuation_amplitude = 0.01, #hide
phase_shift = 0) #hide
plot!(fig[1, 2], reduced, layout=Spring(iterations=1000, C=0.5, seed=1); node_color=[red, orange, orange, :black, :black, :black, :black, :black]) #hide
Label(fig[1, 1, Bottom()], "Original Tensor Network") #hide
Label(fig[1, 2, Bottom()], "Transformed Tensor Network") #hide
fig #hide
```

## Column reduction

```@docs
Tenet.AntiDiagonalGauging
Tenet.ColumnReduction
```

```@example plot
set_theme!(resolution=(800,200)) # hide
fig = Figure() #hide
data = rand(3, 3, 3) #hide
data[:, 1:2, :] .= 0 #hide
A = Tensor(data, (:i, :j, :k)) #hide
B = Tensor(rand(3, 3), (:j, :l)) #hide
C = Tensor(rand(3, 3), (:l, :m)) #hide
tn = TensorNetwork([A, B, C]) #hide
reduced = transform(tn, Tenet.ColumnReduction) #hide
smooth_annotation!( #hide
fig[1, 1]; #hide
color = bg_blue, #hide
xlims = [-2, 2], #hide
ylims = [-2, 2], #hide
offset_x = -1.12, #hide
offset_y = -0.22, #hide
radius_x = 0.35, #hide
radius_y = 0.84, #hide
num_waves = 4, #hide
fluctuation_amplitude = 0.02, #hide
phase_shift = 0.0) #hide
plot!(fig[1, 1], tn, layout=Spring(iterations=1000, C=0.5, seed=6); node_color=[red, orange, orange, :black, :black, :black]) #hide
smooth_annotation!( #hide
fig[1, 2]; #hide
color = bg_blue, #hide
xlims = [-2, 2], #hide
ylims = [-2, 2], #hide
offset_x = -0.64, #hide
offset_y = 1.2, #hide
radius_x = 0.32, #hide
radius_y = 0.78, #hide
num_waves = 5, #hide
fluctuation_amplitude = 0.02, #hide
phase_shift = 0) #hide
Label(fig[1, 1, Bottom()], "Original Tensor Network") #hide
Label(fig[1, 2, Bottom()], "Transformed Tensor Network") #hide
plot!(fig[1, 2], reduced, layout=Spring(iterations=2000, C=40, seed=8); node_color=[red, orange, orange, :black, :black, :black]) #hide
fig #hide
```

## Split simplification
```@docs
Tenet.SplitSimplification
```

```@example plot
set_theme!(resolution=(800,200)) # hide
fig = Figure() #hide
v1 = Tensor([1, 2, 3], (:i,)) #hide
v2 = Tensor([4, 5, 6], (:j,)) #hide
m1 = Tensor(rand(3, 3), (:k, :l)) #hide
t1 = contract(v1, v2) #hide
tensor = contract(t1, m1) #hide
tn = TensorNetwork([tensor, Tensor(rand(3, 3, 3), (:k, :m, :n)), Tensor(rand(3, 3, 3), (:l, :n, :o))]) #hide
reduced = transform(tn, Tenet.SplitSimplification) #hide
smooth_annotation!( #hide
fig[1, 1]; #hide
color = bg_blue, #hide
xlims = [-2, 2], #hide
ylims = [-2, 2], #hide
offset_x = 0.24, #hide
offset_y = 0.6, #hide
radius_x = 0.32, #hide
radius_y = 0.78, #hide
num_waves = 5, #hide
fluctuation_amplitude = 0.015, #hide
phase_shift = 0.0) #hide
plot!(fig[1, 1], tn, layout=Spring(iterations=10000, C=0.5, seed=12); node_color=[red, orange, orange, :black, :black, :black, :black]) #hide
smooth_annotation!( #hide
fig[1, 2]; #hide
color = bg_blue, #hide
xlims = [-2, 2], #hide
ylims = [-2, 2], #hide
offset_x = -0.2, #hide
offset_y = -0.4, #hide
radius_x = 1.1, #hide
radius_y = 0.75, #hide
num_waves = 3, #hide
fluctuation_amplitude = 0.18, #hide
phase_shift = 0.8) #hide
Label(fig[1, 1, Bottom()], "Original Tensor Network") #hide
Label(fig[1, 2, Bottom()], "Transformed Tensor Network") #hide
plot!(fig[1, 2], reduced, layout=Spring(iterations=10000, C=13, seed=151); node_color=[orange, orange, red, red, red, :black, :black, :black, :black]) #hide
fig #hide
```

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