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Three-Wave Mixing AutoDiff Example
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jl_exercise_3a.ipynb
{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Parameter Optimization of Three-Wave Mixing in a Three-Level System\n",
"\n",
"This notebook contains the code for running an optimization of three-wave mixing in a three-level system.\n",
"You will learn how to use the `NLopt` package (via `Optimization.jl`) in order to optimize a set of pulses by varying parameters such as the pulse durations and intensities with the goal of driving two three-level systems, describing the quantum states of the enantiomers of a chiral molecule, such that they end up in distinct final states.\n",
"\n",
"To this end, the notebook consists of the following sections\n",
"* [Model](#Model)\n",
"* [Setup](#Setup)\n",
"* [Hamiltonian](#Hamiltonian)\n",
"* [Problem 0: Pulse parameterisation](#Problem-0---Pulse-parameterisation)\n",
"* [Initialise optimization](#Initialise-optimization)\n",
"* [Problem 1: Run optimization](#Problem-1---Run-optimization)\n",
"* [Analyse optimization results](#Analyse-optimization-results)\n",
"\n",
"and should be executed from top to bottom, whilst solving the problems as and when they appear."
]
},
{
"attachments": {},
"cell_type": "markdown",
"metadata": {},
"source": [
"## Model\n",
"\n",
"<img src=\"3-level_mod.svg\" alt=\"Drawing\" style=\"width: 800px;\"/>\n",
"The model above shows two three level systems corresponding to the $+$(left), respectively $-$(right), enantiomer of a chiral molecule.\n",
"Each of the three levels is connected by an electric dipol transition, with the sign of the $\\mu_{c}$ component of the dipole being the only distiguishing factor between the two enantiomers. Obtaining 'enantio selectivity' in this context means that the same sequence of pulses applied to both enantiomers sharing the same initial state will lead to two distinct final states."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Setup\n",
"\n",
"We start with importing the necessary packages, among which are\n",
"* `QuantumPropagators`: Set up time dependent Hamiltonians and propagate them\n",
"* `OrdinaryDiffEq`: The backend to use for `QuantumPropagators.propagate`\n",
"* `Optimization` for optimization, with `OptimizationNLopt` providing the connection to the `NLOpt` backend package.\n",
"* `ComponentArrays`: provides `ComponentVector` to elegantly define vectors of control parameters that can be accessed both by index and by name. The `@unpack` macro from `UnPack.jl` can be used unpack the parameters from the vector into variables"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"execution": {
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"shell.execute_reply": "2024-03-24T15:52:49.271"
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},
"outputs": [],
"source": [
"using QuantumPropagators: hamiltonian, propagate\n",
"using OrdinaryDiffEq\n",
"using Optimization, OptimizationNLopt\n",
"using ComponentArrays: ComponentVector\n",
"using UnPack: @unpack"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"execution": {
"iopub.execute_input": "2024-03-24T15:52:49.392",
"iopub.status.busy": "2024-03-24T15:52:49.297",
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"shell.execute_reply": "2024-03-24T15:52:50.460"
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"outputs": [],
"source": [
"using Plots\n",
"\n",
"# Set up thicker default lines in plots\n",
"Plots.default(\n",
" linewidth = 2.0,\n",
" foreground_color_legend = nothing,\n",
" background_color_legend = RGBA(1, 1, 1, 0.8)\n",
")"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"execution": {
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"shell.execute_reply": "2024-03-24T15:52:50.580"
}
},
"outputs": [],
"source": [
"# Some utilities for showing hints and solutions\n",
"include(\"exercise_3a_utils.jl\");"
]
},
{
"cell_type": "markdown",
"metadata": {
"execution": {
"iopub.execute_input": "2024-03-14T12:45:08.501",
"iopub.status.busy": "2024-03-14T12:45:08.501",
"iopub.status.idle": "2024-03-14T12:45:08.507",
"shell.execute_reply": "2024-03-14T12:45:08.507"
}
},
"source": [
"To make our code slightly easier to read, we define a constant 𝕚 for the imaginary unit:"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"execution": {
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"shell.execute_reply": "2024-03-24T15:52:50.581"
}
},
"outputs": [],
"source": [
"const 𝕚 = 1im; # \"𝕚\" can be typed by \\bbi<tab>"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Hamiltonian\n",
"Next, we define the function `total_enantiomer_ham` that returns the Hamiltonian (in the rotating frame) for either of the two enantiomers, i.e.,\n",
"\n",
"$$\n",
"H_{I}^{(\\pm)}(t) = \\sum_{i=1}^{3} H_{i}^{(\\pm)}(t)\n",
"$$\n",
"\n",
"with\n",
"\n",
"$$\n",
"H_{1}^{(\\pm)}(t)\n",
"=\n",
"- E_{1}(t) \\mu_{b}^{(\\pm)}\n",
"\\begin{pmatrix}\n",
" 0 & e^{i \\phi_{1}} & 0 \\\\\n",
" e^{- i \\phi_{1}} & 0 & 0 \\\\\n",
" 0 & 0 & 0 \\\\\n",
"\\end{pmatrix},\n",
"\\\\\n",
"H_{2}^{(\\pm)}(t)\n",
"=\n",
"- E_{2}(t) \\mu_{a}^{(\\pm)}\n",
"\\begin{pmatrix}\n",
" 0 & 0 & 0 \\\\\n",
" 0 & 0 & e^{i \\phi_{2}} \\\\\n",
" 0 & e^{- i \\phi_{2}} & 0 \\\\\n",
"\\end{pmatrix},\n",
"\\\\\n",
"H_{3}^{(\\pm)}(t)\n",
"=\n",
"- E_{3}(t) \\mu_{c}^{(\\pm)}\n",
"\\begin{pmatrix}\n",
" 0 & 0 & e^{i \\phi_{3}} \\\\\n",
" 0 & 0 & 0 \\\\\n",
" e^{- i \\phi_{3}} & 0 & 0 \\\\\n",
"\\end{pmatrix}\n",
"$$\n",
"\n",
"and where\n",
"\n",
"$$\n",
"E_{i}(t)\n",
"=\n",
"\\frac{E_{i,0}}{2}\n",
"\\left[\\tanh(a (t - t_{i,1})) - \\tanh(a (t - t_{i,2}))\\right]\n",
"$$\n",
"\n",
"for $i \\in \\left\\{1,2,3\\right\\}$ are the envelopes of (microwave) pulses with frequencies $\\omega, \\delta \\omega$ and $\\omega + \\delta \\omega$."
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"execution": {
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"shell.execute_reply": "2024-03-24T15:52:50.583"
}
},
"outputs": [],
"source": [
"E(t; E₀, t₁, t₂, a) = (E₀/2) * (tanh(a*(t-t₁)) - tanh(a*(t-t₂)));"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The `total_enantiomer_ham` function gets a set of control `parameters`, which together specify the Hamiltonian and its control fields entirely. We use here a \"structured\" [`ComponentVector`](https://jonniedie.github.io/ComponentArrays.jl/stable/api/#ComponentArrays.ComponentVector) with three named sub-vectors:\n",
"\n",
"* `ΔT`: A vector of the three durations $\\Delta t_{i} = t_{i,2} - t_{i,1}$ of each of the three fields $E_{i0}(t)$. Field $i$ is assumed to start when field $i-1$ ends. The first field starts at $t_{1,1}=0$.\n",
"* `ϕ`: A vector of the three real phases $\\phi_{i}$ for each field.\n",
"* `E₀`: A vector of the three real amplitudes $E_{i0}$ for each field.\n",
"\n",
"This gets put together as"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"execution": {
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"shell.execute_reply": "2024-03-24T15:52:50.729"
}
},
"outputs": [],
"source": [
"parameters = ComponentVector(ΔT=[0.2, 0.4, 0.3], ϕ=[π, π, π], E₀=[0.45, 0.4, 0.5]);"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The `parameters` array acts as an array with 9 elements that we can index individually:"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {
"execution": {
"iopub.execute_input": "2024-03-24T15:52:50.729",
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}
},
"outputs": [
{
"data": {
"text/plain": [
"9-element Vector{Float64}:\n",
" 0.2\n",
" 0.4\n",
" 0.3\n",
" 3.141592653589793\n",
" 3.141592653589793\n",
" 3.141592653589793\n",
" 0.45\n",
" 0.4\n",
" 0.5"
]
},
"execution_count": 7,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"parameters[1:9]"
]
},
{
"cell_type": "markdown",
"metadata": {
"execution": {
"iopub.execute_input": "2024-03-24T11:40:46.443",
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"shell.execute_reply": "2024-03-24T11:40:46.447"
}
},
"source": [
"But we can also access the sub-vectors by name:"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {
"execution": {
"iopub.execute_input": "2024-03-24T15:52:51.597",
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"shell.execute_reply": "2024-03-24T15:52:51.858"
}
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"outputs": [
{
"data": {
"text/plain": [
"3-element view(::Vector{Float64}, 1:3) with eltype Float64:\n",
" 0.2\n",
" 0.4\n",
" 0.3"
]
},
"execution_count": 8,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"parameters.ΔT"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"or [unpack](https://github.com/mauro3/UnPack.jl) the entire array (or part of the array) into variables:"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {
"execution": {
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"shell.execute_reply": "2024-03-24T15:52:51.886"
}
},
"outputs": [],
"source": [
"@unpack ΔT, E₀ = parameters;"
]
},
{
"cell_type": "markdown",
"metadata": {
"execution": {
"iopub.execute_input": "2024-03-24T11:24:48.169",
"iopub.status.busy": "2024-03-24T11:24:48.169",
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"shell.execute_reply": "2024-03-24T11:24:48.251"
}
},
"source": [
"The `total_enantiomer_ham` function also uses the following keyword arguments:\n",
"\n",
"* `sign`: The string `+` or `-` specifies which Hamiltonian, i.e., $H_{I}^{(+)}(t)$ or $H_{I}^{(-)}(t)$, is retuned.\n",
"* `a`: Numerical parameter that controls how smooth each field is turned on and off. The larger `a` becomes, the more the field shapes $E_{i0}(t)$ resemble a rectangle."
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {
"execution": {
"iopub.execute_input": "2024-03-24T15:52:51.887",
"iopub.status.busy": "2024-03-24T15:52:51.887",
"iopub.status.idle": "2024-03-24T15:52:51.960",
"shell.execute_reply": "2024-03-24T15:52:51.960"
}
},
"outputs": [
{
"data": {
"text/plain": [
"total_enantiomer_ham (generic function with 1 method)"
]
},
"execution_count": 10,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"function total_enantiomer_ham(parameters; sign, a)\n",
"\n",
" @unpack ϕ, ΔT, E₀ = parameters\n",
" ϕ₁, ϕ₂, ϕ₃ = ϕ[1:3]\n",
" μ = (sign == \"-\" ? -1 : 1)\n",
"\n",
" H₁ = μ * [\n",
" 0 exp(𝕚*ϕ₁) 0\n",
" exp(-𝕚*ϕ₁) 0 0\n",
" 0 0 0\n",
" ]\n",
"\n",
" H₂ = μ * [\n",
" 0 0 0\n",
" 0 0 exp(𝕚*ϕ₂)\n",
" 0 exp(-𝕚*ϕ₂) 0\n",
" ]\n",
"\n",
" H₃ = μ * [\n",
" 0 0 exp(𝕚*ϕ₃)\n",
" 0 0 0\n",
" exp(-𝕚*ϕ₃) 0 0\n",
" ]\n",
"\n",
" # times where pulses end\n",
" T₁ = sum(ΔT[1:1])\n",
" T₂ = sum(ΔT[1:2])\n",
" T₃ = sum(ΔT[1:3])\n",
"\n",
" return hamiltonian(\n",
" (H₁, t -> E(t; E₀=E₀[1], t₁=0.0, t₂=T₁, a)),\n",
" (H₂, t -> E(t; E₀=E₀[2], t₁=T₁, t₂=T₂, a)),\n",
" (H₃, t -> E(t; E₀=E₀[3], t₁=T₂, t₂=T₃, a)),\n",
" )\n",
"end"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {
"execution": {
"iopub.execute_input": "2024-03-24T15:52:51.960",
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"shell.execute_reply": "2024-03-24T15:52:52.159"
}
},
"outputs": [],
"source": [
"H₊ = total_enantiomer_ham(parameters; sign=\"+\", a=100);"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We define the initial state as\n",
"\n",
"$$\n",
"\\Psi_{\\pm}(0)\n",
"=\n",
"\\begin{pmatrix}\n",
" 1 \\\\ 0 \\\\ 0\n",
"\\end{pmatrix}.\n",
"$$"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {
"execution": {
"iopub.execute_input": "2024-03-24T15:52:52.160",
"iopub.status.busy": "2024-03-24T15:52:52.160",
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"shell.execute_reply": "2024-03-24T15:52:52.163"
}
},
"outputs": [],
"source": [
"# the initial state consists of three levels with population initially in the ground state\n",
"Ψ₀ = ComplexF64[1, 0, 0];"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Our time grid is obtained by dividing $$t \\in \\left[0,1\\right]$$ into 100 equal intervals (100 intervals means 101 points)."
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {
"execution": {
"iopub.execute_input": "2024-03-24T15:52:52.164",
"iopub.status.busy": "2024-03-24T15:52:52.164",
"iopub.status.idle": "2024-03-24T15:52:52.170",
"shell.execute_reply": "2024-03-24T15:52:52.170"
},
"lines_to_next_cell": 2
},
"outputs": [],
"source": [
"tlist = collect(range(0, 1; length=101));"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Problem 0 - Pulse parameterisation\n",
"\n",
"Familiarise yourself with the concept of pulse parameterisation. The pulses we will be looking at in this script are shaped as the difference between two hyperbolic tangent functions.\n",
"`E₀` controls the pulse amplitude, `a` controls how rectangular the pulse appears and `t₁` and `t₂` determine when the pulse starts and ends.\n",
"Try changing the arguments of `plot_parameterised_pulse`, such that the two curves match (an exact fit is difficult, aim for a calculated mismatch of below one)."
]
},
{
"cell_type": "code",
"execution_count": 14,
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"outputs": [
{
"data": {
"image/png": 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]
},
"execution_count": 14,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"function plot_parameterised_pulse(tlist; E₀, a, t₁, t₂)\n",
" pulse = t -> E(t; E₀, a, t₁, t₂)\n",
" target_pulse = t -> 20 * exp(-20 * (t - 0.5)^2)\n",
" mismatch = sum(abs.(pulse.(tlist) .- target_pulse.(tlist))) / length(tlist)\n",
" plot(tlist, pulse , label=\"your pulse\", color=(mismatch < 1 ? \"green\" : \"blue\"))\n",
" plot!(tlist, target_pulse; label=\"target pulse\", color=\"orange\")\n",
" annotate!(\n",
" 0, 20,\n",
" (\"mismatch: $(round(mismatch; digits=3))\", 10, :left)\n",
" )\n",
"end\n",
"\n",
"plot_parameterised_pulse(tlist; E₀=3.14, a=500, t₁=0.15, t₂=0.85)"
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {
"execution": {
"iopub.execute_input": "2024-03-24T15:52:53.891",
"iopub.status.busy": "2024-03-24T15:52:53.891",
"iopub.status.idle": "2024-03-24T15:52:53.892",
"shell.execute_reply": "2024-03-24T15:52:53.892"
}
},
"outputs": [],
"source": [
"#step0.hint"
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {
"execution": {
"iopub.execute_input": "2024-03-24T15:52:53.892",
"iopub.status.busy": "2024-03-24T15:52:53.892",
"iopub.status.idle": "2024-03-24T15:52:53.892",
"shell.execute_reply": "2024-03-24T15:52:53.892"
}
},
"outputs": [],
"source": [
"#step0.solution"
]
},
{
"cell_type": "markdown",
"metadata": {
"execution": {
"iopub.execute_input": "2024-03-14T15:40:57.490",
"iopub.status.busy": "2024-03-14T15:40:57.488",
"iopub.status.idle": "2024-03-14T15:40:58.088",
"shell.execute_reply": "2024-03-14T15:40:58.088"
}
},
"source": [
"**Bonus**: After you go through the \"Problem 1\" below, come back here and use the `Optimization` package to determine even better parameters."
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {
"execution": {
"iopub.execute_input": "2024-03-24T15:52:53.892",
"iopub.status.busy": "2024-03-24T15:52:53.892",
"iopub.status.idle": "2024-03-24T15:52:53.893",
"shell.execute_reply": "2024-03-24T15:52:53.892"
}
},
"outputs": [],
"source": [
"#bonus.hint"
]
},
{
"cell_type": "code",
"execution_count": 18,
"metadata": {
"execution": {
"iopub.execute_input": "2024-03-24T15:52:53.893",
"iopub.status.busy": "2024-03-24T15:52:53.893",
"iopub.status.idle": "2024-03-24T15:52:53.893",
"shell.execute_reply": "2024-03-24T15:52:53.893"
}
},
"outputs": [],
"source": [
"#bonus.solution"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Initialise optimization\n",
"\n",
"Now we can turn towards optimization. To this end, we use the optimization methods provided by the [`NLOpt` package](https://nlopt.readthedocs.io/en/latest/). This package has a [Julia wrapper](https://github.com/JuliaOpt/NLopt.jl) which we could use directly, but there is also a package [Optimization.jl](https://docs.sciml.ai/Optimization/stable/) that provides a common API for defining and solving optimization problems not just via `NLOpt` but also a dozen other optimization toolboxes. For simplicity, we also use the standard Nelder-Mead method here, although it should be noted that `NLOpt` provides a whole lot of different methods (as do the other toolboxes wrapped by Optimization.jl).\n",
"\n",
"The Optimization.jl interface requires to provide a `loss` function that takes a vector `x` of (real) control parameters as well as an object `constants` containing static parameters. This could be another vector, but a [`NamedTuple`](https://docs.julialang.org/en/v1/base/base/#Core.NamedTuple) is often cleaner. Note that for less trivial problems, the function to be optimized would be a more general [`OptimizationFunction`](https://docs.sciml.ai/Optimization/stable/API/optimization_function/) object that also contains information for how to calculate gradients. See the [Optimization.jl manual](https://docs.sciml.ai/Optimization/stable/API/optimization_problem/) for details. Nelder-Mead being a \"gradient-free\" method, we will not need this here.\n",
"\n",
"Our `loss` function gets the list `x`, which contains our optimization parameters, i.e., all pulse durations, all phases $\\phi_{i}$ and all amplitudes $E_{i,0}$, on input and returns the error of the enantio-selective process. In detail, `loss` returns zero if and only if the dynamics (governed by the parameters from set `x`) transfer the initial state $\\Psi(0)$ into the respective target states, i.e.,\n",
"\n",
"$$\n",
"\\Psi_{+}(0)\n",
"\\longrightarrow\n",
"\\Psi_{+}\\left(T\\right) =\n",
"\\begin{pmatrix}\n",
" 1 \\\\ 0 \\\\ 0\n",
"\\end{pmatrix}\n",
"$$\n",
"\n",
"for enantiomer `+` and\n",
"\n",
"$$\n",
"\\Psi_{-}(0)\n",
"\\longrightarrow\n",
"\\Psi_{-}\\left(T\\right) =\n",
"\\begin{pmatrix}\n",
" 0 \\\\ 0 \\\\ 1\n",
"\\end{pmatrix}\n",
"$$\n",
"\n",
"for enantiomer `-`."
]
},
{
"cell_type": "code",
"execution_count": 19,
"metadata": {
"execution": {
"iopub.execute_input": "2024-03-24T15:52:53.893",
"iopub.status.busy": "2024-03-24T15:52:53.893",
"iopub.status.idle": "2024-03-24T15:52:53.900",
"shell.execute_reply": "2024-03-24T15:52:53.899"
}
},
"outputs": [
{
"data": {
"text/plain": [
"loss (generic function with 1 method)"
]
},
"execution_count": 19,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"function loss(x, constants)\n",
"\n",
" # The optimizer will usually pass in `x` as a standard vector,\n",
" # so we have to repack it into a `ComponentVector` for\n",
" # `total_enantiomer_ham`\n",
" parameters = ComponentVector(ΔT=x[1:3], ϕ=x[4:6], E₀=x[7:9])\n",
"\n",
" H₊ = total_enantiomer_ham(parameters; sign=\"+\", a=constants.a)\n",
" H₋ = total_enantiomer_ham(parameters; sign=\"-\", a=constants.a)\n",
"\n",
" Ψ₀ = ComplexF64[1, 0, 0];\n",
" tlist = collect(range(0, constants.T; length=constants.nt));\n",
"\n",
" Ψ₊ = propagate(Ψ₀, H₊, tlist; method=OrdinaryDiffEq)\n",
" Ψ₋ = propagate(Ψ₀, H₋, tlist; method=OrdinaryDiffEq)\n",
"\n",
" fid = (abs2(Ψ₊[1]) + abs2(Ψ₋[3])) / 2\n",
" return 1 - fid\n",
"\n",
"end"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Problem 1 - Run optimization\n",
"\n",
"Next, we can run the actual optimization. It requires us to define lower and upper bounds for all parameters that should be optimized. In our case, we choose\n",
"\n",
"$$\n",
"0 \\leq t_{i,2} \\leq T=1,\n",
"\\qquad\n",
"0 \\leq \\phi_{i} \\leq 2 \\pi,\n",
"\\qquad\n",
"0 \\leq E_{i,0} \\leq 10.\n",
"$$\n",
"\n",
"Note that we need to provide guess values for all nine parameters, in the order `ΔT₁`, `ΔT₂`, `ΔT₃`, `ϕ₁`, `ϕ₂`, `ϕ₃`, `E₀₁`, `E₀₂`, `E₀₃`.\n",
"\n",
"Their choice will have a significant impact on the general success and form of the optimized solution. Your task is to fill in the upper optimization bounds and to try different guesses and evaluate their impact on the optimization."
]
},
{
"cell_type": "code",
"execution_count": 20,
"metadata": {
"execution": {
"iopub.execute_input": "2024-03-24T15:52:53.900",
"iopub.status.busy": "2024-03-24T15:52:53.900",
"iopub.status.idle": "2024-03-24T15:52:54.144",
"shell.execute_reply": "2024-03-24T15:52:54.143"
}
},
"outputs": [],
"source": [
"guess = ComponentVector(\n",
" ΔT=[#= insert values =#],\n",
" ϕ=[#= insert values =#],\n",
" E₀=[#= insert values =#]\n",
");\n",
"\n",
"prob = OptimizationProblem(\n",
" loss,\n",
" guess,\n",
" (a=1000.0, T=1, nt=100); # this is a NamedTuple\n",
" lb=zeros(length(guess)),\n",
" ub=ComponentVector(\n",
" ΔT=[#= insert values =#],\n",
" ϕ=[#= insert values =#],\n",
" E₀=[#= insert values =#]\n",
" ),\n",
" stopval=(1-0.99),\n",
");"
]
},
{
"cell_type": "code",
"execution_count": 21,
"metadata": {
"execution": {
"iopub.execute_input": "2024-03-24T15:52:54.144",
"iopub.status.busy": "2024-03-24T15:52:54.144",
"iopub.status.idle": "2024-03-24T15:52:54.144",
"shell.execute_reply": "2024-03-24T15:52:54.144"
}
},
"outputs": [],
"source": [
"#step1.hint"
]
},
{
"cell_type": "code",
"execution_count": 22,
"metadata": {
"execution": {
"iopub.execute_input": "2024-03-24T15:52:54.145",
"iopub.status.busy": "2024-03-24T15:52:54.144",
"iopub.status.idle": "2024-03-24T15:52:54.145",
"shell.execute_reply": "2024-03-24T15:52:54.145"
}
},
"outputs": [],
"source": [
"#step1.solution"
]
},
{
"cell_type": "code",
"execution_count": 23,
"metadata": {
"execution": {
"iopub.execute_input": "2024-03-24T15:52:54.145",
"iopub.status.busy": "2024-03-24T15:52:54.145",
"iopub.status.idle": "2024-03-24T15:52:54.201",
"shell.execute_reply": "2024-03-24T15:52:54.201"
}
},
"outputs": [],
"source": [
"# step1.solution\n",
"obtained_fidelities = Float64[];\n",
"guess = ComponentVector(\n",
" ΔT=[0.2, 0.4, 0.3],\n",
" ϕ=[π, π, π],\n",
" E₀=[5.0, 5.0, 5.0]\n",
");\n",
"\n",
"prob = OptimizationProblem(\n",
" loss,\n",
" guess,\n",
" (a=1000.0, T=1, nt=100); # this is a NamedTuple\n",
" lb=zeros(9),\n",
" ub=ComponentVector(\n",
" ΔT=[1.0, 1.0, 1.0],\n",
" ϕ=[2π, 2π, 2π],\n",
" E₀=[10.0, 10.0, 10.0]\n",
" ),\n",
" stopval=(1-0.99),\n",
");"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We can check the quality of the guess pulse:"
]
},
{
"cell_type": "code",
"execution_count": 24,
"metadata": {
"execution": {
"iopub.execute_input": "2024-03-24T15:52:54.201",
"iopub.status.busy": "2024-03-24T15:52:54.201",
"iopub.status.idle": "2024-03-24T15:52:57.405",
"shell.execute_reply": "2024-03-24T15:52:57.405"
}
},
"outputs": [
{
"data": {
"text/plain": [
"0.5614917779915963"
]
},
"execution_count": 24,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"loss(guess, (a=1000.0, T=tlist[end], nt=length(tlist)))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"In the optimization, we'll want to keep track of the fidelity after each iteration. To this end, we define a [\"callback\" function](https://docs.sciml.ai/Optimization/stable/API/solve/#CommonSolve.solve-Tuple%7BOptimizationProblem,%20Any%7D) that the optimizer will run after each step."
]
},
{
"cell_type": "code",
"execution_count": 25,
"metadata": {
"execution": {
"iopub.execute_input": "2024-03-24T15:52:57.406",
"iopub.status.busy": "2024-03-24T15:52:57.406",
"iopub.status.idle": "2024-03-24T15:52:57.411",
"shell.execute_reply": "2024-03-24T15:52:57.411"
}
},
"outputs": [
{
"data": {
"text/plain": [
"callback (generic function with 1 method)"
]
},
"execution_count": 25,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"obtained_fidelities = Float64[]; # for keeping track of the fidelity in each iteration\n",
"\n",
"function callback(state, loss_val)\n",
" global obtained_fidelities\n",
" fid = 1 - loss_val\n",
" push!(obtained_fidelities, fid)\n",
" print(\"Iteration: $(length(obtained_fidelities)), current fidelity $(round(fid; digits=4))\\r\")\n",
" return false\n",
"end"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Lastly, we call `Optimization.solve` to run the optimization:"
]
},
{
"cell_type": "code",
"execution_count": 26,
"metadata": {
"execution": {
"iopub.execute_input": "2024-03-24T15:52:57.411",
"iopub.status.busy": "2024-03-24T15:52:57.411",
"iopub.status.idle": "2024-03-24T15:52:59.675",
"shell.execute_reply": "2024-03-24T15:52:59.675"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Iteration: 136, current fidelity 0.9966\r"
]
},
{
"data": {
"text/plain": [
"retcode: Success\n",
"u: 9-element Vector{Float64}:\n",
" 0.2686912766492031\n",
" 0.30246351309282327\n",
" 0.44434934847416263\n",
" 2.028084270278409\n",
" 3.7190624690870195\n",
" 4.142238519916371\n",
" 8.771945622785278\n",
" 4.945397804716041\n",
" 5.460732815160975"
]
},
"execution_count": 26,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"obtained_fidelities = Float64[];\n",
"res = Optimization.solve(prob, NLopt.LN_NELDERMEAD(); maxiters=500, callback)"
]
},
{
"cell_type": "code",
"execution_count": 27,
"metadata": {
"execution": {
"iopub.execute_input": "2024-03-24T15:52:59.675",
"iopub.status.busy": "2024-03-24T15:52:59.675",
"iopub.status.idle": "2024-03-24T15:52:59.861",
"shell.execute_reply": "2024-03-24T15:52:59.861"
}
},
"outputs": [
{
"data": {
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"</svg>\n"
]
},
"execution_count": 27,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"plot(obtained_fidelities; marker=:cross, label=\"\", xlabel=\"optimization iteration\", ylabel=\"fidelity\")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Analyse optimization results\n",
"After optimiziation we can verify the optimization result by plotting the pulses\n",
"as well as the resulting dynamics.\n",
"To this end, we define the Hamiltonians of the two enantiomers given the optimized parameters."
]
},
{
"cell_type": "code",
"execution_count": 28,
"metadata": {
"execution": {
"iopub.execute_input": "2024-03-24T15:52:59.861",
"iopub.status.busy": "2024-03-24T15:52:59.861",
"iopub.status.idle": "2024-03-24T15:52:59.871",
"shell.execute_reply": "2024-03-24T15:52:59.871"
}
},
"outputs": [],
"source": [
"opt_params = convert(typeof(guess), res.u)\n",
"\n",
"H₊opt = total_enantiomer_ham(opt_params; sign=\"+\", a=1000.0);\n",
"H₋opt = total_enantiomer_ham(opt_params; sign=\"-\", a=1000.0);"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"In order to visualize the optimized pulses, we plot them in the following. We'll use"
]
},
{
"cell_type": "code",
"execution_count": 29,
"metadata": {
"execution": {
"iopub.execute_input": "2024-03-24T15:52:59.872",
"iopub.status.busy": "2024-03-24T15:52:59.871",
"iopub.status.idle": "2024-03-24T15:52:59.872",
"shell.execute_reply": "2024-03-24T15:52:59.872"
}
},
"outputs": [],
"source": [
"using QuantumPropagators.Controls: get_controls"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"to extract the functions with the optimized parameters from the optimal Hamiltonians."
]
},
{
"cell_type": "code",
"execution_count": 30,
"metadata": {
"execution": {
"iopub.execute_input": "2024-03-24T15:52:59.872",
"iopub.status.busy": "2024-03-24T15:52:59.872",
"iopub.status.idle": "2024-03-24T15:53:00.134",
"shell.execute_reply": "2024-03-24T15:53:00.134"
}
},
"outputs": [
{
"data": {
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]
},
"execution_count": 30,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"function plot_pulse(H, tlist; kwargs...)\n",
" fig = plot(; xlabel=\"time\", ylabel=\"amplitude\", kwargs...)\n",
" sub = [\"₁\", \"₂\", \"₃\"]\n",
" for (i, E) in enumerate(get_controls(H))\n",
" plot!(fig, tlist, E; label=\"E$(sub[i])\")\n",
" end\n",
" return fig\n",
"end\n",
"\n",
"plot_pulse(H₊opt, range(0, 1; length=500); legend=:right)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Lastly, we solve the dynamics of the two enantiomers (now using the optimized parameters) and plot their population dynamics."
]
},
{
"cell_type": "code",
"execution_count": 31,
"metadata": {
"execution": {
"iopub.execute_input": "2024-03-24T15:53:00.134",
"iopub.status.busy": "2024-03-24T15:53:00.134",
"iopub.status.idle": "2024-03-24T15:53:00.142",
"shell.execute_reply": "2024-03-24T15:53:00.141"
}
},
"outputs": [
{
"data": {
"text/plain": [
"propagate_system (generic function with 1 method)"
]
},
"execution_count": 31,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"function propagate_system(Htot, title; tlist=tlist)\n",
" Ψ₀ = ComplexF64[1, 0, 0];\n",
" states = propagate(Ψ₀, Htot, tlist; method=OrdinaryDiffEq, storage=true)\n",
" pops = abs2.(states)\n",
" plot(; title, xlabel=\"time\", ylabel=\"population\", legend=:top)\n",
" plot!(tlist, pops[1,:]; label=\"|c₁|²\")\n",
" plot!(tlist, pops[2,:]; label=\"|c₂|²\")\n",
" plot!(tlist, pops[3,:]; label=\"|c₃|²\")\n",
"end"
]
},
{
"cell_type": "code",
"execution_count": 32,
"metadata": {
"execution": {
"iopub.execute_input": "2024-03-24T15:53:00.142",
"iopub.status.busy": "2024-03-24T15:53:00.142",
"iopub.status.idle": "2024-03-24T15:53:00.316",
"shell.execute_reply": "2024-03-24T15:53:00.316"
}
},
"outputs": [
{
"data": {
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]
},
"execution_count": 32,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"propagate_system(H₊opt, \"enantiomer +\")"
]
},
{
"cell_type": "code",
"execution_count": 33,
"metadata": {
"execution": {
"iopub.execute_input": "2024-03-24T15:53:00.316",
"iopub.status.busy": "2024-03-24T15:53:00.316",
"iopub.status.idle": "2024-03-24T15:53:00.354",
"shell.execute_reply": "2024-03-24T15:53:00.354"
}
},
"outputs": [
{
"data": {
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