TLS_State_to_State.jl

### A Pluto.jl notebook ###
# v0.20.13

using Markdown
using InteractiveUtils

# This Pluto notebook uses @bind for interactivity. When running this notebook outside of Pluto, the following 'mock version' of @bind gives bound variables a default value (instead of an error).
macro bind(def, element)
    #! format: off
    return quote
        local iv = try Base.loaded_modules[Base.PkgId(Base.UUID("6e696c72-6542-2067-7265-42206c756150"), "AbstractPlutoDingetjes")].Bonds.initial_value catch; b -> missing; end
        local el = $(esc(element))
        global $(esc(def)) = Core.applicable(Base.get, el) ? Base.get(el) : iv(el)
        el
    end
    #! format: on
end

# ╔═╡ 55f8b637-5938-4a3d-8d82-62e03507296b
begin
	using LinearAlgebra
	import QuantumControl
	using PlutoUI
	using Plots
	import Pkg
	Plots.default(
	    linewidth               = 3,
	    size                    = (550, 300),
	    legend                  = :right,
	    foreground_color_legend = nothing,
	    background_color_legend = RGBA(1, 1, 1, 0.8)
	)
	TableOfContents()
end

# ╔═╡ 017e2537-5315-4431-a4fd-9d514efb8d7c
using QuantumControl: hamiltonian

# ╔═╡ ffeedd55-31f9-49c2-9ef4-de7e3d4db19e
using QuantumControl: Trajectory

# ╔═╡ 982d89b2-f541-40a7-9048-1a3107e2ea19
using QuantumControl: propagate_trajectory

# ╔═╡ 447018f0-b509-42e3-91cd-6bdad4d4f83f
using QuantumPropagators: ExpProp

# ╔═╡ 187c295d-c3c6-45da-89d6-c8bc520a7dab
using QuantumControl: ControlProblem

# ╔═╡ 11edb079-c331-4ae4-9c94-c18e0384e6f0
using QuantumControl.Functionals: J_T_sm

# ╔═╡ f8a135c1-d9a0-4377-a080-65790d9d48e2
using QuantumControl: @optimize_or_load

# ╔═╡ 74e4da66-8cb3-4f3a-bc52-bd99ddae170c
using GRAPE

# ╔═╡ d0facb2c-c898-4298-912e-b61a3f8be6a1
using Krotov

# ╔═╡ 4407caad-a77d-4b14-b924-24ea2273d36b
using QuantumControl.Controls: substitute

# ╔═╡ fe2480b6-153a-11f0-0c2d-35f102edea84
md"""
# State-To-State Transfer in a Two-Level-System

``
\newcommand{tr}[0]{\operatorname{tr}}
\newcommand{diag}[0]{\operatorname{diag}}
\newcommand{abs}[0]{\operatorname{abs}}
\newcommand{pop}[0]{\operatorname{pop}}
\newcommand{aux}[0]{\text{aux}}
\newcommand{opt}[0]{\text{opt}}
\newcommand{tgt}[0]{\text{tgt}}
\newcommand{init}[0]{\text{init}}
\newcommand{lab}[0]{\text{lab}}
\newcommand{rwa}[0]{\text{rwa}}
\newcommand{bra}[1]{\langle#1\vert}
\newcommand{ket}[1]{\vert#1\rangle}
\newcommand{Bra}[1]{\left\langle#1\right\vert}
\newcommand{Ket}[1]{\left\vert#1\right\rangle}
\newcommand{Braket}[2]{\left\langle #1\vphantom{#2}\mid{#2}\vphantom{#1}\right\rangle}
\newcommand{op}[1]{\hat{#1}}
\newcommand{Op}[1]{\hat{#1}}
\newcommand{dd}[0]{\,\text{d}}
\newcommand{Liouville}[0]{\mathcal{L}}
\newcommand{DynMap}[0]{\mathcal{E}}
\newcommand{identity}[0]{\mathbf{1}}
\newcommand{Norm}[1]{\lVert#1\rVert}
\newcommand{Abs}[1]{\left\vert#1\right\vert}
\newcommand{avg}[1]{\langle#1\rangle}
\newcommand{Avg}[1]{\left\langle#1\right\rangle}
\newcommand{AbsSq}[1]{\left\vert#1\right\vert^2}
\newcommand{Re}[0]{\operatorname{Re}}
\newcommand{Im}[0]{\operatorname{Im}}
``
"""

# ╔═╡ 03284e97-5807-4b2e-b732-5c3c25d0e300
Markdown.parse(
	"""
	This tutorial teaches the fundamental concepts of quantum control with `QuantumControl.jl` for the example of population transfer in a two-level system.
		
	It uses the following package versions:

	""" *
	join(
		[
			"* `$(p[1])`: `$(p[2])`"
			for p in sort(
				map(
					r -> (r.name, r.version),
					filter(
						r -> (r.is_direct_dep && !(r.name in ["Pkg"])),
						collect(values(Pkg.dependencies()))
					)
				), by=r->r[1]
			)
		],
		"\n"
	)
)


# ╔═╡ 138c98d1-dbd5-4c81-ad86-7528eeb930d4
md"""
## Two-level Hamiltonian

We consider the Hamiltonian ``\op{H} = \op{H}_0 + \epsilon(t) \op{H}_1`` with

```math
\op{H}_{0}
= - \frac{\omega}{2} \op{\sigma}_{z}
= \begin{pmatrix} - \frac{\omega}{2} & 0 \\ 0 & \frac{\omega}{2} \end{pmatrix}\,,
```

representing a simple qubit with energy level splitting ``\omega`` in the canonical basis

```math
\ket{0} = \begin{pmatrix}1\\0\end{pmatrix},\qquad
\ket{1} = = \begin{pmatrix}0\\1\end{pmatrix}\,.
```
"""


# ╔═╡ f71c9a93-7aee-4098-acd0-1c0bdbbfe22e
function ket(label)
    result = Dict(
		"0" => Vector{ComplexF64}([1, 0]),
		"1" => Vector{ComplexF64}([0, 1])
	)
    return result[string(label)]
end;

# ╔═╡ 51605cfe-80c5-40a7-be34-adb56d222791
md"""
The control field ``\epsilon(t)`` is assumed to couple via the Hamiltonian

```math
\op{H}_1
= \op{\sigma}_{x}
= \begin{pmatrix} 0 & 1 \\ 1 & 0 \end{pmatrix}
```

to the qubit, i.e., the control field effectively drives transitions between both qubit states.

We construct the full time-dependent Hamiltonian via the
"""

# ╔═╡ 3c917ae5-ae57-4ef5-8805-0d84a13aefb4
md"""
function:
"""

# ╔═╡ 553c4f5a-2fc1-432d-981e-4c4d88b7a6db
md"""
 The control field here switches on from zero at ``t=0`` to it's maximum amplitude 0.2 within the time period 0.3 (the switch-on shape is half a [Blackman pulse](https://en.wikipedia.org/wiki/Window_function#Blackman_window)). It switches off again in the time period 0.3 before the final time ``T=5``). We use a time grid with 500 time steps between 0 and ``T``
"""

# ╔═╡ dea94e06-fce3-4f82-b856-17dd0e67c011
ϵ(t) = 0.2 * QuantumControl.Shapes.flattop(t, T=5, t_rise=0.3, func=:blackman);

# ╔═╡ b26a4363-411e-4de4-8585-4ec8106e0da9
function tls_hamiltonian(; ω=1.0, ϵ=ϵ)
    σ̂_z = ComplexF64[
        1  0
        0 -1
    ]
    σ̂_x = ComplexF64[
        0  1
        1  0
    ]
    Ĥ₀ = (-ω/2) * σ̂_z
    Ĥ₁ = σ̂_x
    return hamiltonian(Ĥ₀, (Ĥ₁, ϵ))
end;

# ╔═╡ 9dea1166-c4a5-4ebd-95bc-bf45f3157a2d
H = tls_hamiltonian();

# ╔═╡ 93937d9e-6742-49f2-9b29-e6200db8a27d
tlist = collect(range(0, 5, length=500));

# ╔═╡ 3365b95a-6c9e-4103-8d79-d5f5f4bb317c
plot(tlist, ϵ; xlabel="time", ylabel="amplitude", label="ϵ(t)", legend=:bottom)

# ╔═╡ 0638b982-4082-4696-b7f5-27e14154e68d
md"""
## Optimization target
"""

# ╔═╡ 73ce588c-0884-45d8-88b1-4138588e6d29
md"""
The control problem is defined in terms of the "trajectory",
"""

# ╔═╡ a9b2e927-cbf0-43da-bba4-5bba9e34ae72
md"""
of the initial state ``\ket{0}`` evolving under ``\op{H}(t)``. Ideally, this evolution should reach the target state ``\ket{1}``:
"""

# ╔═╡ 32111d96-9521-4074-ac47-7a66a628b410
traj = Trajectory(initial_state=ket(0), generator=H, target_state=ket(1));

# ╔═╡ 0a72565f-351c-4617-b070-6dd4e93b2cd1
md"""
## Dynamics under the guess pulse

We can simulate the dynamics
"""

# ╔═╡ b8721ee0-d38f-4fb9-ba02-34d735626bdb
md"""
as a convenience wrapper around `QuantumPropagators.propagate`.

For a two-level system, the most efficient way to actually evaluate the propagator
``\op{U} = \exp{-i \op{H}(t) dt}`` (assumed piecewise-constant for a small timestep ``dt``) to to matrix-exponentiate the operator ``(-i \op{H}(t) dt)``, which can be done with
"""

# ╔═╡ d2968662-c4a2-4e0f-956b-554a6b0c69c4
md"""
This allows to obtain the state of the system at every point in time:
"""

# ╔═╡ 070cf752-a81c-4467-8c95-56b856631d06
states = propagate_trajectory(traj, tlist; method=ExpProp, storage=true)

# ╔═╡ 72ac090c-f2c2-43f6-a1cc-da3f229d04d0
md"""
You can see how this varies when changing the amplitude of the field ϵ(t) in the range

0  $(@bind _guess_amplitude_slider Slider(0:0.1:5, default=0.2))  5

or by setting the value directly:
"""

# ╔═╡ 947230c5-cf7f-4d96-8ef5-ec9e153d361b
md"""
|ϵ(t)| = $(@bind _guess_amplitude_str TextField(default=string(_guess_amplitude_slider)))
"""

# ╔═╡ ea46d577-c80c-4af2-84a4-03495b231181
md"""
The dynamics of a two-level system are also analytically solvable. What we are seeing above is ["Rabi cycling"](https://en.wikipedia.org/wiki/Rabi_cycle), where the population cycles between the ``\ket{0}`` and ``\ket{1}`` state depending only on the area under the ``\epsilon(t)`` field. Since the transition is "off-resonant" with $\omega = 1 \ne 0$, the population transfer is not complete (but gets closer and closer as ``|\epsilon(t)| > \omega``).

Try to find an amplitude that gets good population transfer in the off-resonant case as well as the resonant case for ``\omega = 0``:
"""

# ╔═╡ afe49361-2cb2-4c7b-923b-251c5e90c918
md"""
ω = $(@bind _ω_str TextField(default="1.0"))
"""

# ╔═╡ beaa8b71-a44e-4196-9361-c588563cac68
begin
	local _ϵ_0 = 0.2
	try
		_ϵ_0 = parse(Float64, _guess_amplitude_str)
	catch
	end
	_ϵ(t) = _ϵ_0 * QuantumControl.Shapes.flattop(t, T=5, t_rise=0.3, func=:blackman);
	local _ω = 1.0
	try
		_ω = parse(Float64, _ω_str)
	catch
	end
	local _H = tls_hamiltonian(; ω=_ω, ϵ=_ϵ);
	local _traj = Trajectory(initial_state=ket(0), generator=_H, target_state=ket(1));
	local _states = propagate_trajectory(_traj, tlist; method=ExpProp, storage=true)
	local _Ψ_T = _states[:,end]
	local _error = 1 - abs2(_Ψ_T ⋅ ket(1))
	plot(tlist, abs2.(_states)'; label=["|⟨0|Ψ(t)⟩|²" "|⟨1|Ψ(t)⟩|²"], xlabel="time", ylabel="population", title="|ϵ(t)| = $_ϵ_0; error = $(round(_error; digits=3))")
end

# ╔═╡ 18e5972c-a439-470e-bf3c-18636a2d09df
details("Solution", md"""
With the default ω = 1.0, for an amplitude of 3.0, the error is below 5%.

For a resonant field (ω = 0.0), setting |ϵ(t)| = 1/3 produces an error of zero.
""")

# ╔═╡ 4c3bc003-bcb2-43f1-b9dc-2170d5f6e9a4
md"""
## Optimization 

The full control problem,
"""

# ╔═╡ d6de6da7-462f-49c2-92a9-6647aad3b4fa
md"""
includes this trajectory, information about the time grid for the dynamics, and the functional to be used:
"""

# ╔═╡ fc8e3298-4681-4202-ba57-2deab0bc3023
md"""
These are combined in
"""

# ╔═╡ b0327380-2205-49af-aeec-7529591204ef
md"""
In this case, we look at the square-modulus of the overlap with the target state.
"""

# ╔═╡ a94e69cc-ecec-427b-8791-80991e452b36
problem = ControlProblem(
    trajectories=[traj],
    tlist=tlist,
    iter_stop=500,
    prop_method=ExpProp,
    J_T=J_T_sm,
    check_convergence=res -> begin
        ((res.J_T < 1e-3) && (res.converged = true) && (res.message = "J_T < 10⁻³"))
    end,
);

# ╔═╡ f8fc0c53-cc54-404f-8f29-2216cdf4427e
md"""
We solve the control problem
"""

# ╔═╡ bb48bb43-616b-4710-88e7-d667ab77fe15
md"""
which is a wrapper around `QuantumControl.optimize` that caches to the optimization result to a file. For this "trivial" example, the optimization has negligible runtime, but for other examples, an optimization might run for hours or days. Using `@optimize_or_load` ensures we don't have to re-run it, and also, that we keep an intermedite results if the optimization is interruppted.

We can use either one of the two standard gradient-based optimization methods:
"""

# ╔═╡ ce1f718d-dc55-44b2-bca4-e1b7d62f0a40
md"""
Feel free to switch between them to see what changes:
"""

# ╔═╡ 80af33a9-9637-4aae-8382-0adf551d6206
@bind method Select([GRAPE, Krotov])

# ╔═╡ b9040df9-b8c2-4008-97e8-56098d435510
opt_result = @optimize_or_load(
    "opt_result_$method.jld2",
    problem;
	force = false, # set to `true` to overwrite existing jld2 file
    method=method,
);


# ╔═╡ 379b4590-5bb9-4ee4-86e0-51e3c58831d5
opt_result

# ╔═╡ cc387f50-a707-4150-84b5-31b31141a3a2
md"""
We can extract the optimize field (an array of values) from the `opt_result`:
"""

# ╔═╡ ff9d8cb7-bbd5-446d-83bc-c56b5e6b39aa
ϵ_opt = opt_result.optimized_controls[1];

# ╔═╡ 13e23dd0-70bd-4926-b115-7fee2e349004
plot(tlist, ϵ_opt; xlabel="time", ylabel="amplitude", label="ϵ_opt(t)", legend=:bottom)

# ╔═╡ 9ffd341c-4a94-4866-b432-30a3d4662d54
md"""
If we want to see the dynamics under the optimized field,
"""

# ╔═╡ e2bfb504-c2bc-4bb6-8f8e-a40a04655163
md"""
allows to replace the original `ϵ(t)` with `ϵ_opt` inside `traj`:
"""

# ╔═╡ bd111a37-4406-4229-9000-d23dbb03b742
states_opt = propagate_trajectory(
	substitute(traj, IdDict(ϵ => ϵ_opt)),
	tlist;
	method=ExpProp, storage=true
);

# ╔═╡ 55fee8de-854c-436c-8f35-5c8bc6e41e05
begin
	local _Ψ_T = states_opt[:,end]
	local _error = 1 - abs2(_Ψ_T ⋅ ket(1))
	plot(tlist, abs2.(states_opt)'; label=["|⟨0|Ψ(t)⟩|²" "|⟨1|Ψ(t)⟩|²"], xlabel="time", ylabel="population", title="optimized dynamics; error = $(round(_error; digits=3))")
end

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[[deps.Vulkan_Loader_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Wayland_jll", "Xorg_libX11_jll", "Xorg_libXrandr_jll", "xkbcommon_jll"]
git-tree-sha1 = "2f0486047a07670caad3a81a075d2e518acc5c59"
uuid = "a44049a8-05dd-5a78-86c9-5fde0876e88c"
version = "1.3.243+0"

[[deps.Wayland_jll]]
deps = ["Artifacts", "EpollShim_jll", "Expat_jll", "JLLWrappers", "Libdl", "Libffi_jll"]
git-tree-sha1 = "96478df35bbc2f3e1e791bc7a3d0eeee559e60e9"
uuid = "a2964d1f-97da-50d4-b82a-358c7fce9d89"
version = "1.24.0+0"

[[deps.XZ_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "fee71455b0aaa3440dfdd54a9a36ccef829be7d4"
uuid = "ffd25f8a-64ca-5728-b0f7-c24cf3aae800"
version = "5.8.1+0"

[[deps.Xorg_libICE_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "a3ea76ee3f4facd7a64684f9af25310825ee3668"
uuid = "f67eecfb-183a-506d-b269-f58e52b52d7c"
version = "1.1.2+0"

[[deps.Xorg_libSM_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_libICE_jll"]
git-tree-sha1 = "9c7ad99c629a44f81e7799eb05ec2746abb5d588"
uuid = "c834827a-8449-5923-a945-d239c165b7dd"
version = "1.2.6+0"

[[deps.Xorg_libX11_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_libxcb_jll", "Xorg_xtrans_jll"]
git-tree-sha1 = "b5899b25d17bf1889d25906fb9deed5da0c15b3b"
uuid = "4f6342f7-b3d2-589e-9d20-edeb45f2b2bc"
version = "1.8.12+0"

[[deps.Xorg_libXau_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "aa1261ebbac3ccc8d16558ae6799524c450ed16b"
uuid = "0c0b7dd1-d40b-584c-a123-a41640f87eec"
version = "1.0.13+0"

[[deps.Xorg_libXcursor_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_libXfixes_jll", "Xorg_libXrender_jll"]
git-tree-sha1 = "6c74ca84bbabc18c4547014765d194ff0b4dc9da"
uuid = "935fb764-8cf2-53bf-bb30-45bb1f8bf724"
version = "1.2.4+0"

[[deps.Xorg_libXdmcp_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "52858d64353db33a56e13c341d7bf44cd0d7b309"
uuid = "a3789734-cfe1-5b06-b2d0-1dd0d9d62d05"
version = "1.1.6+0"

[[deps.Xorg_libXext_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_libX11_jll"]
git-tree-sha1 = "a4c0ee07ad36bf8bbce1c3bb52d21fb1e0b987fb"
uuid = "1082639a-0dae-5f34-9b06-72781eeb8cb3"
version = "1.3.7+0"

[[deps.Xorg_libXfixes_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_libX11_jll"]
git-tree-sha1 = "9caba99d38404b285db8801d5c45ef4f4f425a6d"
uuid = "d091e8ba-531a-589c-9de9-94069b037ed8"
version = "6.0.1+0"

[[deps.Xorg_libXi_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_libXext_jll", "Xorg_libXfixes_jll"]
git-tree-sha1 = "a376af5c7ae60d29825164db40787f15c80c7c54"
uuid = "a51aa0fd-4e3c-5386-b890-e753decda492"
version = "1.8.3+0"

[[deps.Xorg_libXinerama_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_libXext_jll"]
git-tree-sha1 = "a5bc75478d323358a90dc36766f3c99ba7feb024"
uuid = "d1454406-59df-5ea1-beac-c340f2130bc3"
version = "1.1.6+0"

[[deps.Xorg_libXrandr_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_libXext_jll", "Xorg_libXrender_jll"]
git-tree-sha1 = "aff463c82a773cb86061bce8d53a0d976854923e"
uuid = "ec84b674-ba8e-5d96-8ba1-2a689ba10484"
version = "1.5.5+0"

[[deps.Xorg_libXrender_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_libX11_jll"]
git-tree-sha1 = "7ed9347888fac59a618302ee38216dd0379c480d"
uuid = "ea2f1a96-1ddc-540d-b46f-429655e07cfa"
version = "0.9.12+0"

[[deps.Xorg_libxcb_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_libXau_jll", "Xorg_libXdmcp_jll"]
git-tree-sha1 = "bfcaf7ec088eaba362093393fe11aa141fa15422"
uuid = "c7cfdc94-dc32-55de-ac96-5a1b8d977c5b"
version = "1.17.1+0"

[[deps.Xorg_libxkbfile_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_libX11_jll"]
git-tree-sha1 = "e3150c7400c41e207012b41659591f083f3ef795"
uuid = "cc61e674-0454-545c-8b26-ed2c68acab7a"
version = "1.1.3+0"

[[deps.Xorg_xcb_util_cursor_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_xcb_util_image_jll", "Xorg_xcb_util_jll", "Xorg_xcb_util_renderutil_jll"]
git-tree-sha1 = "c5bf2dad6a03dfef57ea0a170a1fe493601603f2"
uuid = "e920d4aa-a673-5f3a-b3d7-f755a4d47c43"
version = "0.1.5+0"

[[deps.Xorg_xcb_util_image_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_xcb_util_jll"]
git-tree-sha1 = "f4fc02e384b74418679983a97385644b67e1263b"
uuid = "12413925-8142-5f55-bb0e-6d7ca50bb09b"
version = "0.4.1+0"

[[deps.Xorg_xcb_util_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_libxcb_jll"]
git-tree-sha1 = "68da27247e7d8d8dafd1fcf0c3654ad6506f5f97"
uuid = "2def613f-5ad1-5310-b15b-b15d46f528f5"
version = "0.4.1+0"

[[deps.Xorg_xcb_util_keysyms_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_xcb_util_jll"]
git-tree-sha1 = "44ec54b0e2acd408b0fb361e1e9244c60c9c3dd4"
uuid = "975044d2-76e6-5fbe-bf08-97ce7c6574c7"
version = "0.4.1+0"

[[deps.Xorg_xcb_util_renderutil_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_xcb_util_jll"]
git-tree-sha1 = "5b0263b6d080716a02544c55fdff2c8d7f9a16a0"
uuid = "0d47668e-0667-5a69-a72c-f761630bfb7e"
version = "0.3.10+0"

[[deps.Xorg_xcb_util_wm_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_xcb_util_jll"]
git-tree-sha1 = "f233c83cad1fa0e70b7771e0e21b061a116f2763"
uuid = "c22f9ab0-d5fe-5066-847c-f4bb1cd4e361"
version = "0.4.2+0"

[[deps.Xorg_xkbcomp_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_libxkbfile_jll"]
git-tree-sha1 = "801a858fc9fb90c11ffddee1801bb06a738bda9b"
uuid = "35661453-b289-5fab-8a00-3d9160c6a3a4"
version = "1.4.7+0"

[[deps.Xorg_xkeyboard_config_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_xkbcomp_jll"]
git-tree-sha1 = "00af7ebdc563c9217ecc67776d1bbf037dbcebf4"
uuid = "33bec58e-1273-512f-9401-5d533626f822"
version = "2.44.0+0"

[[deps.Xorg_xtrans_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "a63799ff68005991f9d9491b6e95bd3478d783cb"
uuid = "c5fb5394-a638-5e4d-96e5-b29de1b5cf10"
version = "1.6.0+0"

[[deps.Zlib_jll]]
deps = ["Libdl"]
uuid = "83775a58-1f1d-513f-b197-d71354ab007a"
version = "1.2.13+1"

[[deps.Zstd_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "446b23e73536f84e8037f5dce465e92275f6a308"
uuid = "3161d3a3-bdf6-5164-811a-617609db77b4"
version = "1.5.7+1"

[[deps.eudev_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "c3b0e6196d50eab0c5ed34021aaa0bb463489510"
uuid = "35ca27e7-8b34-5b7f-bca9-bdc33f59eb06"
version = "3.2.14+0"

[[deps.fzf_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "b6a34e0e0960190ac2a4363a1bd003504772d631"
uuid = "214eeab7-80f7-51ab-84ad-2988db7cef09"
version = "0.61.1+0"

[[deps.libaom_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "522c1df09d05a71785765d19c9524661234738e9"
uuid = "a4ae2306-e953-59d6-aa16-d00cac43593b"
version = "3.11.0+0"

[[deps.libass_jll]]
deps = ["Artifacts", "Bzip2_jll", "FreeType2_jll", "FriBidi_jll", "HarfBuzz_jll", "JLLWrappers", "Libdl", "Zlib_jll"]
git-tree-sha1 = "e17c115d55c5fbb7e52ebedb427a0dca79d4484e"
uuid = "0ac62f75-1d6f-5e53-bd7c-93b484bb37c0"
version = "0.15.2+0"

[[deps.libblastrampoline_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "8e850b90-86db-534c-a0d3-1478176c7d93"
version = "5.11.0+0"

[[deps.libdecor_jll]]
deps = ["Artifacts", "Dbus_jll", "JLLWrappers", "Libdl", "Libglvnd_jll", "Pango_jll", "Wayland_jll", "xkbcommon_jll"]
git-tree-sha1 = "9bf7903af251d2050b467f76bdbe57ce541f7f4f"
uuid = "1183f4f0-6f2a-5f1a-908b-139f9cdfea6f"
version = "0.2.2+0"

[[deps.libevdev_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "56d643b57b188d30cccc25e331d416d3d358e557"
uuid = "2db6ffa8-e38f-5e21-84af-90c45d0032cc"
version = "1.13.4+0"

[[deps.libfdk_aac_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "646634dd19587a56ee2f1199563ec056c5f228df"
uuid = "f638f0a6-7fb0-5443-88ba-1cc74229b280"
version = "2.0.4+0"

[[deps.libinput_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "eudev_jll", "libevdev_jll", "mtdev_jll"]
git-tree-sha1 = "91d05d7f4a9f67205bd6cf395e488009fe85b499"
uuid = "36db933b-70db-51c0-b978-0f229ee0e533"
version = "1.28.1+0"

[[deps.libpng_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Zlib_jll"]
git-tree-sha1 = "07b6a107d926093898e82b3b1db657ebe33134ec"
uuid = "b53b4c65-9356-5827-b1ea-8c7a1a84506f"
version = "1.6.50+0"

[[deps.libvorbis_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Ogg_jll"]
git-tree-sha1 = "11e1772e7f3cc987e9d3de991dd4f6b2602663a5"
uuid = "f27f6e37-5d2b-51aa-960f-b287f2bc3b7a"
version = "1.3.8+0"

[[deps.mtdev_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "b4d631fd51f2e9cdd93724ae25b2efc198b059b1"
uuid = "009596ad-96f7-51b1-9f1b-5ce2d5e8a71e"
version = "1.1.7+0"

[[deps.nghttp2_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "8e850ede-7688-5339-a07c-302acd2aaf8d"
version = "1.59.0+0"

[[deps.p7zip_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "3f19e933-33d8-53b3-aaab-bd5110c3b7a0"
version = "17.4.0+2"

[[deps.x264_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "4fea590b89e6ec504593146bf8b988b2c00922b2"
uuid = "1270edf5-f2f9-52d2-97e9-ab00b5d0237a"
version = "2021.5.5+0"

[[deps.x265_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "ee567a171cce03570d77ad3a43e90218e38937a9"
uuid = "dfaa095f-4041-5dcd-9319-2fabd8486b76"
version = "3.5.0+0"

[[deps.xkbcommon_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_libxcb_jll", "Xorg_xkeyboard_config_jll"]
git-tree-sha1 = "fbf139bce07a534df0e699dbb5f5cc9346f95cc1"
uuid = "d8fb68d0-12a3-5cfd-a85a-d49703b185fd"
version = "1.9.2+0"
"""

# ╔═╡ Cell order:
# ╟─fe2480b6-153a-11f0-0c2d-35f102edea84
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# ╠═93937d9e-6742-49f2-9b29-e6200db8a27d
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# ╠═11edb079-c331-4ae4-9c94-c18e0384e6f0
# ╟─fc8e3298-4681-4202-ba57-2deab0bc3023
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# ╠═74e4da66-8cb3-4f3a-bc52-bd99ddae170c
# ╠═d0facb2c-c898-4298-912e-b61a3f8be6a1
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# ╠═ff9d8cb7-bbd5-446d-83bc-c56b5e6b39aa
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# ╟─9ffd341c-4a94-4866-b432-30a3d4662d54
# ╠═4407caad-a77d-4b14-b924-24ea2273d36b
# ╟─e2bfb504-c2bc-4bb6-8f8e-a40a04655163
# ╠═bd111a37-4406-4229-9000-d23dbb03b742
# ╟─55fee8de-854c-436c-8f35-5c8bc6e41e05
# ╟─00000000-0000-0000-0000-000000000001
# ╟─00000000-0000-0000-0000-000000000002