shaken_lattice_explicit-phi.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "import Revise"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import QuantumCollocation as QC\n",
    "import NamedTrajectories as NT\n",
    "import TrajectoryIndexingUtils as NTidx\n",
    "import LinearAlgebra as LA\n",
    "import SparseArrays as SA\n",
    "import ForwardDiff as FD\n",
    "import Plots\n",
    "import Interpolations as IP\n",
    "using LaTeXStrings\n",
    "import JLD2"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "using FFTW:ifft, fft, fftshift, fftfreq"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "QuadraticObjective (generic function with 3 methods)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "include(\"utils.jl\")\n",
    "include(\"system.jl\")\n",
    "include(\"constraints.jl\")\n",
    "include(\"objectives.jl\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "V = 10.\n",
    "trunc = 13\n",
    "# E_R [kHz] found in Weidner thesis\n",
    "system = ShakenLatticeSystem1D(V, trunc; bloch_basis=true, bloch_transformation_trunc=3*trunc)\n",
    "# middle index of statevector where p = 0\n",
    "mid = system.params[:mid]\n",
    "dim = system.params[:dim]\n",
    "E_R = system.params[:E_R]\n",
    "#E_R = 1/0.05\n",
    "#print(\"time unit $(1/E_R) ms\\nE_R = $E_R kHz\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "system.params[:bloch_energies]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "system.H_drives_real[1]"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "df = DF.DataFrame(CSV.File(\"./paper_data/split_fig6_coarse.csv\"; header=0))"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "times = df[:,1] * E_R\n",
    "dts = times[2:end] - times[1:end-1]\n",
    "#push!(dts, dts[end])\n",
    "#push!(dts, 0.)\n",
    "phi = df[1:end-1,2]\n",
    "#push!(phi, 0.)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "duration = sum(dts) # in 1/E_R\n",
    "\n",
    "T = length(dts)\n",
    "dt_avg = duration / (T-1)\n",
    "#dts = zeros(T) .+ dt\n",
    "dt_bound = (minimum(dts), maximum(dts))\n",
    "times = cumsum(dts) - dts"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "a_bound = fill(1., 2)\n",
    "dda_bound = fill(50., 2)\n",
    "\n",
    "a = vcat(cos.(phi)', sin.(phi)')\n",
    "\n",
    "da = NT.derivative(a, dts)\n",
    "dda = NT.derivative(da, dts)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "duration = 2pi * 0.8 # in units of 1/E_R\n",
    "\n",
    "T = 801\n",
    "dt = duration / (T-1)\n",
    "dts = zeros(T) .+ dt\n",
    "dt_bound = (dt, dt)\n",
    "times = cumsum(dts) - dts\n",
    "duration"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "a_bound = fill(1.0, 2)\n",
    "phi_bound = [1.0 * pi]\n",
    "#dphi_bound = [100.]\n",
    "#ddphi_bound = [3000.]\n",
    "\n",
    "#phi = collect(sin.(11.5 *times)')\n",
    "phi = rand(1, T)\n",
    "a = vcat(cos.(phi), sin.(phi))\n",
    "\n",
    "dphi = NT.derivative(phi, dts)\n",
    "ddphi = NT.derivative(dphi, dts)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "Z = NT.load_traj(\"./interferometer/split_bloch78_time_study/0.6wr.jld2\")"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "NT.plot(Z, (:a, :phi), transformations=Dict(:psi_iso => x -> abs2.(QC.iso_to_ket(x))))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "a, phi, dts = Z.a, Z.phi, vec(Z.dts)\n",
    "# dts_new = fill(0.3*2pi/300, 301)\n",
    "# a = interpolate_controls(a, dts, dts_new)\n",
    "# dts = dts_new\n",
    "\n",
    "# phi = collect(atan.(a[2,:], a[1,:])')\n",
    "# phi_mod_clean!(phi)\n",
    "\n",
    "slice = 1:length(dts)\n",
    "a = a[:,slice]\n",
    "dts = dts[slice]\n",
    "phi = phi[:,slice]\n",
    "\n",
    "times = cumsum(dts) - dts\n",
    "T = length(times)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "duration = times[end]\n",
    "T = length(times)\n",
    "dt = duration/(T-1)\n",
    "dt_bound = (0.9*dt, dt)\n",
    "T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "a_bound = fill(1.0, 2)\n",
    "phi_bound = [1.0*pi]\n",
    "ddphi_bound = [1000.]\n",
    "\n",
    "dphi = NT.derivative(phi, dts)\n",
    "ddphi = NT.derivative(dphi, dts)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "duration/2pi"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "times"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "Plots.plot(times, a')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "Plots.plot(times, phi')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "Plots.plot(times, dphi')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "Plots.plot(times, ddphi')"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "psi0 = zeros(system.params[:dim])\n",
    "psi0[mid] = 0.\n",
    "psi0[mid-1] = sqrt(0.5)\n",
    "psi0[mid+1] = sqrt(0.5)\n",
    "normalize!(psi0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "#psi0 = get_bloch_state(system; lvl=0)\n",
    "psi0 = QC.cavity_state(0, dim)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Plots.bar(-p_max:p_max, abs2.(psi0))\n",
    "Plots.bar(0:dim-1, abs2.(psi0))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "psi0_iso = QC.ket_to_iso(psi0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "psi_iso = QC.rollout(psi0_iso, a, dts, system; integrator=exp)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "psi_iso += rand(size(psi_iso)...)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "psi = hcat([QC.iso_to_ket(psi_iso[:,t]) for t=1:T]...)\n",
    "pops = abs2.(psi)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Plots.plot(times, pops[:,:]', labels=(-p_max:1:p_max)', legend=:outertopright)#, xlim=(0.0, 2.0))\n",
    "Plots.plot(times, pops[:,:]', labels=(0:dim-1)', legend=:outertopright)#, xlim=(0.0, 2.0))"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "bloch_states = hcat([get_bloch_state(system; lvl=i) for i=0:dim-1]...)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "psi"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "blochs = bloch_states' * psi\n",
    "bloch_pops = abs2.(blochs)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Plots.plot(times, bloch_pops[:,:]', labels=(0:8)', legend=:outertopright)#, xlim=(0.0, 2.0))"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "pops[:, end]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "comps = (\n",
    "    psi_iso = psi_iso,\n",
    "    a = a,\n",
    "    phi = phi,\n",
    "    # dphi = dphi,\n",
    "    # ddphi = ddphi,\n",
    "    dts = dts\n",
    ")\n",
    "initial = (\n",
    "    psi_iso = psi0_iso,\n",
    "    phi = [0.],\n",
    "    #dphi = [0.]\n",
    ")\n",
    "final = (;\n",
    "    phi = [0.],\n",
    "    #dphi = [0.]\n",
    ")\n",
    "goal = (;)\n",
    "bounds = (\n",
    "    phi = phi_bound,\n",
    "    # ddphi = ddphi_bound,\n",
    "    dts = dt_bound\n",
    ")\n",
    "\n",
    "Z_guess = nothing\n",
    "GC.gc()\n",
    "Z_guess = NT.NamedTrajectory(\n",
    "    comps;\n",
    "    controls=(:phi),\n",
    "    timestep=:dts,\n",
    "    bounds=bounds,\n",
    "    initial=initial,\n",
    "    final=final,\n",
    "    goal=goal\n",
    ")"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "import JLD2"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "JLD2.save(\"./interferometer/mirror_victor2.jld2\", Z_guess)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Z_guess = NT.copy(Z_save)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "NT.update_bounds!(Z_guess, :dda, [-5000. -5000.; 5000. 5000.])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "dim = system.params[:dim]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "R = 1.0 * collect(LA.I(dim))\n",
    "R[10,10] = R[11,11] = 0.\n",
    "R = QC.QuantumSystems.iso(R)\n",
    "# R[8,8] = R[9+dim,9+dim] = 0. # this should get populations right AND fix y-z greatcircle\n",
    "R"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "kernel = sinc_kernel(50., vec(Z_guess.dts))\n",
    "convolver = LA.I(Z_guess.T) - kernel\n",
    "convolver = convolver' * convolver"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "Z_guess.psi_iso"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "state_goal = QC.cavity_state(3, dim)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "#J = NameComponentObjective(:psi_iso, [1:dim...], [1:T...], x -> 1 - abs2.(x' * state_goal), ([1:T...] ./ T) .* 100.; is_iso=true)\n",
    "# J1 = QC.QuantumObjective(name=:psi_iso, goals=QC.ket_to_iso(state_goal), loss=:InfidelityLoss, Q=100.0)\n",
    "#J += QC.QuadraticRegularizer(:dts, Z_guess, 0.01)\n",
    "#J += NameComponentQuadraticRegularizer(:a, [2], Z_guess, [0.001])\n",
    "\n",
    "J1 = QuadraticObjective(:psi_iso, Z_guess, R; Q=200.0)\n",
    "# J2 = NameComponentObjective(:psi_iso, [8, 9], [T], x -> real(x[1]'*x[2])^2, [100.0]; is_iso=true)\n",
    "# J4 = QC.QuadraticRegularizer(:ddphi, Z_guess, 1e-8/T)\n",
    "# J5 = QC.QuadraticRegularizer(:dts, Z_guess, 1e1/T)\n",
    "J5 = NameComponentQuadraticRegularizer(:psi_iso, [13], Z_guess, [1e1/T]; is_iso=true)\n",
    "\n",
    "# convolution\n",
    "J4 = QuadraticObjective(:phi, Z_guess, convolver, [1], 1:Z_guess.T; Q=50.0/T)\n",
    "\n",
    "J = J1 + J4 + J5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "J.L(Z_guess.datavec, Z_guess)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "integrators = nothing\n",
    "GC.gc()\n",
    "integrators = [\n",
    "    QC.QuantumStatePadeIntegrator(\n",
    "        system,\n",
    "        :psi_iso,\n",
    "        :a,\n",
    "        :dts;\n",
    "        order=4\n",
    "    ),\n",
    "    # QC.DerivativeIntegrator(\n",
    "    #     :phi,\n",
    "    #     :dphi,\n",
    "    #     :dts,\n",
    "    #     Z_guess\n",
    "    # ),\n",
    "    # QC.DerivativeIntegrator(\n",
    "    #     :dphi,\n",
    "    #     :ddphi,\n",
    "    #     :dts,\n",
    "    #     Z_guess\n",
    "    # )\n",
    "]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "constraints = [\n",
    "    IQPhiConstraint(:a, :phi, Z_guess),\n",
    "    FinalYZGreatCircleConstraint(:psi_iso, [10, 11], Z_guess)\n",
    "    #LinearSincConvolutionConstraint(:phi, :dts, Z_guess, 60.)\n",
    "    #OmegaAbsConstraint(1.0, Z_guess),\n",
    "    #PhiSincConvolutionConstraint(:a, :dts, Z_guess, 80.),\n",
    "    #PhiFunctionBoundConstraint(phase_bound, Z_guess),\n",
    "    #TimeSymmetricControlConstraint(:a, Z_guess)\n",
    "    #custom_bounds_constraint(:a, Z_guess, Int[], a_bound)\n",
    "]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Ipopt options\n",
    "options = QC.Options(\n",
    "    max_iter=200,\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# defining quantum control problem\n",
    "prob = nothing\n",
    "GC.gc()\n",
    "prob = QC.QuantumControlProblem(\n",
    "    system, \n",
    "    Z_guess, \n",
    "    J, \n",
    "    integrators;\n",
    "    constraints=constraints,\n",
    "    options=options,\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "QC.solve!(prob)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "Z = nothing\n",
    "GC.gc()\n",
    "Z = prob.trajectory"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "Z.psi_iso"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "psi_iso_rollout = QC.rollout(psi0_iso, Z.a, Z.dts, system; integrator=exp)\n",
    "psi = hcat([QC.iso_to_ket(psi_iso_rollout[:,t]) for t=1:T]...)\n",
    "pops = abs2.(psi)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "psi = hcat([QC.iso_to_ket(Z.psi_iso[:,t]) for t=1:T]...)\n",
    "pops = hcat([abs2.(QC.iso_to_ket(Z.psi_iso[:,t])) for t=1:T]...)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "psi[:,end]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "angle(psi[8,end]) - angle(psi[9,end])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "1 - J1.L(Z.datavec, Z)/100"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "J4.L(Z.datavec, Z)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "x = QC.iso_to_ket(Z.psi_iso[:,end])"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "x / exp(1im*angle(x[8]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "pops_goal"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "times = cumsum(Z.dts[1,:]) - Z.dts[1,:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "#p = Plots.plot(times, pops[:,:]', labels=(-p_max:1:p_max)', legend=:outertopright, size=(500, 300))\n",
    "p = Plots.plot(times, pops[:,:]', labels=(0:dim-1)', legend=:outertopright, size=(500, 300))\n",
    "Plots.xaxis!(p, \n",
    "    xlabel=L\"$t$ $[1/\\omega_R]$\"\n",
    ")\n",
    "Plots.yaxis!(p, \n",
    "    #ylabel=L\"population of momentum state $|p\\rangle$\"\n",
    "    ylabel=\"Bloch state population\"\n",
    ")\n",
    "Plots.title!(p, \"Splitting shaking sequence\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "Plots.plot(times, pops[end,:])"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "blochs = bloch_states' * psi\n",
    "bloch_pops = abs2.(blochs)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "p = Plots.plot(times, bloch_pops[:,:]', labels=(0:dim-1)', legend=:outertopright, size=(500, 300))\n",
    "Plots.xaxis!(p, \n",
    "    xlabel=L\"$t$ $[1/\\nu_R]$\"\n",
    ")\n",
    "Plots.yaxis!(p, \n",
    "    ylabel=L\"population of Bloch state $|B\\rangle$\"\n",
    ")\n",
    "Plots.title!(p, \"Splitting shaking sequence\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "Plots.plot(times, Z.a')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "Plots.plot(times, Z.phi')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "dphi = NT.derivative(Z.phi, dts)\n",
    "ddphi = NT.derivative(dphi, dts);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "Plots.plot(times, dphi')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "Plots.plot(times, ddphi')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "times_f1 = times[div(2*T,3):end]\n",
    "sin_f1 = pi/2*sin.(29.6*(times_f1 .- 0.27)) .- pi/2\n",
    "times_f2 = times[1:div(2*T,3)]\n",
    "sin_f2 = pi*sin.(11.5*(times_f2));"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "p = Plots.plot(times, Z.phi', linecolor=:blue, label=L\"\\varphi(t)\", size=(500, 300))\n",
    "Plots.plot!(p, times_f1, sin_f1, linecolor=:red, alpha=0.2, label=L\"\\omega=29.6\")\n",
    "Plots.plot!(p, times_f2, sin_f2, linecolor=:green, alpha=0.2, label=L\"\\omega=11.5\")\n",
    "# Plots.plot!(p, times, phase_bound.(times), linecolor=:grey, label=\"bound\")\n",
    "# Plots.plot!(p, times, -phase_bound.(times), linecolor=:grey, label=\"bound\")\n",
    "Plots.xaxis!(p, \n",
    "    xlabel=L\"$t$ $[1/\\omega_R]$\"\n",
    ")\n",
    "Plots.yaxis!(p, \n",
    "    ylabel=\"shaking amplitude\"\n",
    ")\n",
    "Plots.title!(p, \"Splitting shaking sequence\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "Z_guess = Z\n",
    "Z_save = NT.copy(Z)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "import JLD2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "duration_wr = round(duration/2pi; digits=2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "duration = sum(Z.dts) - Z.dts[end]\n",
    "duration_wr = round(duration/2pi; digits=2)\n",
    "s = \"\"\"\n",
    "Final infidelity (Bloch 3) in %:\n",
    "$(J1.L(Z.datavec, Z))\n",
    "\"\"\"\n",
    "write(\"$(duration_wr)wr.txt\", s)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "JLD2.save(\"interferometer/split_bloch910_time_study/$(duration_wr)wr.jld2\", Z)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "function fourier_time_freq(data_time, times, freqs)\n",
    "    dts = times[2:end] - times[1:end-1]\n",
    "    push!(dts, dts[end])\n",
    "    ft_mat = exp.(2im*pi*freqs*times')\n",
    "    data_freq = (dts' .* ft_mat) * data_time / sqrt.(2pi)\n",
    "    return data_freq\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "slice = 1:T #div(2*T,3):T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "freqs = collect(0:0.1:80)\n",
    "phi_ft = fourier_time_freq(Z.phi[1,slice], times[slice], freqs/2pi);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "p = Plots.plot(freqs, abs2.(phi_ft), size=(500, 300), label=nothing)\n",
    "Plots.xaxis!(p, \n",
    "    xlabel=L\"$\\omega$ $[\\omega_R]$\"\n",
    ")\n",
    "Plots.yaxis!(p, \n",
    "    ylabel=\"Fourier amplitude\"\n",
    ")\n",
    "Plots.title!(p, \"Shaking protocol spectrum\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "dphi = NT.derivative(Z.phi, dts)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "Plots.plot(times, dphi')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "ddphi = NT.derivative(dphi, dts)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "Plots.plot(times, ddphi')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# mirror (free rel phase)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "V = 10.\n",
    "trunc = 11\n",
    "# E_R [kHz] found in Weidner thesis\n",
    "system = ShakenLatticeSystem1D(V, trunc; bloch_basis=true, bloch_transformation_trunc=2*trunc)\n",
    "# middle index of statevector where p = 0\n",
    "mid = system.params[:mid]\n",
    "dim = system.params[:dim]\n",
    "E_R = system.params[:E_R]\n",
    "#E_R = 1/0.05\n",
    "#print(\"time unit $(1/E_R) ms\\nE_R = $E_R kHz\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "duration = 2pi * 1.0 # in units of 1/E_R\n",
    "\n",
    "T = 1001\n",
    "dt = duration / (T-1)\n",
    "dts = zeros(T) .+ dt\n",
    "dt_bound = (dt, dt)\n",
    "times = cumsum(dts) - dts\n",
    "duration"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "a_bound = fill(1.0, 2)\n",
    "phi_bound = [1.0 * pi]\n",
    "#dphi_bound = [100.]\n",
    "#ddphi_bound = [3000.]\n",
    "\n",
    "phi = collect((sin.(11.5 *times) + sin.(20.0 * times) + sin.(27.0 * times))')\n",
    "#phi = rand(1, T)\n",
    "a = vcat(cos.(phi), sin.(phi))\n",
    "\n",
    "dphi = NT.derivative(phi, dts)\n",
    "ddphi = NT.derivative(dphi, dts)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "Z1 = NT.load_traj(\"./interferometer/bloch_7_to_3.jld2\")\n",
    "Z2 = NT.load_traj(\"./interferometer/mirror_victor2.jld2\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "Z1.dts, Z2.dts"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "a, dts = get_interferometer(Z1, Z2, [])\n",
    "times = cumsum(dts) - dts\n",
    "T = length(times)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "Z = NT.load_traj(\"./interferometer/mirror_bloch7_bitshorter.jld2\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "a, dts = Z.a, vec(Z.dts)\n",
    "phi = collect(atan.(a[2,:], a[1,:])')\n",
    "\n",
    "slice = 1:length(dts)\n",
    "a = a[:,slice]\n",
    "dts = dts[slice]\n",
    "phi = phi[:,slice]\n",
    "\n",
    "times = cumsum(dts) - dts\n",
    "duration = times[end]\n",
    "T = length(times)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "T_new = 600\n",
    "dt_new = duration[end]/(T_new-1)\n",
    "dts_new = fill(dt_new, T_new);"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "a = interpolate_controls(a, dts, dts_new)\n",
    "times = cumsum(dts_new) - dts_new;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "duration = times[end]\n",
    "T = length(times)\n",
    "dt = duration/(T-1)\n",
    "dt_bound = (dt, dt)\n",
    "T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "a_bound = fill(1.0, 2)\n",
    "phi_bound = [1*pi]\n",
    "ddphi_bound = [1000.]\n",
    "\n",
    "dphi = NT.derivative(phi, dts)\n",
    "ddphi = NT.derivative(dphi, dts)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "Plots.plot(times, a')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "Plots.plot(times, phi')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "Plots.plot(times, dphi')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "Plots.plot(times, ddphi')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "p = Plots.plot(times, phi', linecolor=:blue, label=L\"\\varphi(t)\", size=(500, 300))\n",
    "Plots.xaxis!(p, \n",
    "    xlabel=L\"$t$ $[1/\\omega_R]$\"\n",
    ")\n",
    "Plots.yaxis!(p, \n",
    "    ylabel=\"shaking amplitude\"\n",
    ")\n",
    "Plots.title!(p, L\"Mirror $|7\\rangle$ (guess)\")"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "psi0 = zeros(system.params[:dim])\n",
    "psi0[mid] = 0.\n",
    "psi0[mid-1] = sqrt(0.5)\n",
    "psi0[mid+1] = sqrt(0.5)\n",
    "normalize!(psi0)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#####Victor solution\n",
    "function get_pw_sin(sin_amps, sin_dts)\n",
    "    N = length(sin_amps)\n",
    "    sin_T = length(sin_dts)\n",
    "    T = N*sin_T + 1\n",
    "    sin_times = cumsum(sin_dts) - sin_dts\n",
    "    sin_time = sin_times[end]\n",
    "    dts = repeat(sin_dts, N)\n",
    "    push!(dts, 0.)\n",
    "    phi = zeros(T)\n",
    "    for i=1:N\n",
    "        phi[(i-1)*sin_T+1:i*sin_T] = (-1)^(i-1) * sin_amps[i] * sin.(pi*sin_times/sin_time)\n",
    "    end\n",
    "    a = zeros(2, T)\n",
    "    a[1,:] = cos.(phi)\n",
    "    a[2,:] = sin.(phi)\n",
    "    return a, dts, cumsum(dts) - dts\n",
    "end\n",
    "\n",
    "sin_amps = [0.3926, 0.6872, 0.6872, 0.4908, 0.4908, 0.7853, 0.7853]\n",
    "append!(sin_amps, sin_amps[end:-1:1]) \n",
    "\n",
    "freq = 11.5\n",
    "sin_time = 2pi * 1/freq / 2\n",
    "sin_T = 20\n",
    "sin_dts = fill(sin_time / sin_T, sin_T)\n",
    "a, dts, times = get_pw_sin(sin_amps, sin_dts)\n",
    "T = length(times)\n",
    "\n",
    "a_bound = fill(1., 2)\n",
    "dda_bound = fill(10000., 2)\n",
    "dt_bound = (dts[1], dts[1])\n",
    "\n",
    "da = NT.derivative(a, dts)\n",
    "da[:, end] = da[:, end-1]\n",
    "dda = NT.derivative(da, dts)\n",
    "dda[:, end] = dda[:, end-1] = dda[:, end-2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "#psi0 = get_bloch_state(system; lvl=3)\n",
    "bloch_subspace = [7, 8]\n",
    "psip0 = QC.cavity_state(bloch_subspace[1], dim) + QC.cavity_state(bloch_subspace[2], dim)\n",
    "normalize!(psip0) \n",
    "psim0 = QC.cavity_state(bloch_subspace[1], dim) - QC.cavity_state(bloch_subspace[2], dim)\n",
    "normalize!(psim0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "system.params[:bloch_energies]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "psip0_iso = QC.ket_to_iso(psip0)\n",
    "psim0_iso = QC.ket_to_iso(psim0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "psip_iso = QC.rollout(psip0_iso, a, dts, system; integrator=exp)\n",
    "psim_iso = QC.rollout(psim0_iso, a, dts, system; integrator=exp)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "psip = hcat([QC.iso_to_ket(psip_iso[:,t]) for t=1:T]...)\n",
    "psip_pops = abs2.(psip)\n",
    "psim = hcat([QC.iso_to_ket(psim_iso[:,t]) for t=1:T]...)\n",
    "psim_pops = abs2.(psim)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = 3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "p = Plots.plot(times, psip_pops[:,:]', labels=(0:dim-1)', legend=:outertopright, size=(500, 300))\n",
    "Plots.xaxis!(p, \n",
    "    xlabel=L\"$t$ $[1/\\omega_R]$\"\n",
    ")\n",
    "Plots.yaxis!(p, \n",
    "    #ylabel=L\"population of momentum state $|p\\rangle$\"\n",
    "    ylabel=\"Bloch state population\"\n",
    ")\n",
    "Plots.title!(p, L\"Mirror $|%$(bloch_subspace[1])\\rangle+|%$(bloch_subspace[2])\\rangle \\rightarrow |%$(bloch_subspace[1])\\rangle-|%$(bloch_subspace[2])\\rangle$ (guess)\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "p = Plots.plot(times, psim_pops[:,:]', labels=(0:dim-1)', legend=:outertopright, size=(500, 300))\n",
    "Plots.xaxis!(p, \n",
    "    xlabel=L\"$t$ $[1/\\omega_R]$\"\n",
    ")\n",
    "Plots.yaxis!(p, \n",
    "    #ylabel=L\"population of momentum state $|p\\rangle$\"\n",
    "    ylabel=\"Bloch state population\"\n",
    ")\n",
    "Plots.title!(p, L\"Mirror $|%$(bloch_subspace[1])\\rangle-|%$(bloch_subspace[2])\\rangle \\rightarrow |%$(bloch_subspace[1])\\rangle+|%$(bloch_subspace[2])\\rangle$ (guess)\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "comps = (\n",
    "    psip_iso = psip_iso,\n",
    "    psim_iso = psim_iso,\n",
    "    a = a,\n",
    "    phi = phi,\n",
    "    dts = dts\n",
    ")\n",
    "initial = (\n",
    "    psip_iso = psip0_iso,\n",
    "    psim_iso = psim0_iso,\n",
    "    phi = [0.]\n",
    ")\n",
    "final = (;\n",
    "    phi = [0.]\n",
    ")\n",
    "goal = (;)\n",
    "bounds = (\n",
    "    phi = phi_bound,\n",
    "    dts = dt_bound\n",
    ")\n",
    "\n",
    "Z_guess = nothing\n",
    "GC.gc()\n",
    "Z_guess = NT.NamedTrajectory(\n",
    "    comps;\n",
    "    controls=(:phi),\n",
    "    timestep=:dts,\n",
    "    bounds=bounds,\n",
    "    initial=initial,\n",
    "    final=final,\n",
    "    goal=goal\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "kernel = sinc_kernel(40., vec(Z_guess.dts))\n",
    "convolver = LA.I(Z_guess.T) - kernel\n",
    "convolver = convolver' * convolver"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "dim = system.params[:dim]\n",
    "\n",
    "#J = NameComponentObjective(:psi_iso, [1:dim...], [1:T...], x -> 1 - abs2.(x' * state_goal), ([1:T...] ./ T) .* 100.; is_iso=true)\n",
    "J1 = QC.QuantumObjective(name=:psip_iso, goals=psim0_iso, loss=:InfidelityLoss, Q=100.0)\n",
    "J1 += QC.QuantumObjective(name=:psim_iso, goals=psip0_iso, loss=:InfidelityLoss, Q=100.0)\n",
    "#J += QC.QuadraticRegularizer(:dts, Z_guess, 0.01)\n",
    "#J += NameComponentQuadraticRegularizer(:a, [2], Z_guess, [0.001])\n",
    "#J += QC.QuadraticRegularizer(:ddphi, Z_guess, 1e-8/T)\n",
    "#J += QC.QuadraticRegularizer(:dts, Z_guess, 0.01)\n",
    "#J += NameComponentQuadraticRegularizer(:a, [2], Z_guess, [0.001])\n",
    "\n",
    "# J1 = QuadraticObjective(:psi_iso, Z_guess, R; Q=200.0)\n",
    "# J2 = NameComponentObjective(:psi_iso, [8, 9], [T], x -> real(x[1]'*x[2])^2, [100.0]; is_iso=true)\n",
    "# J3 = QC.QuadraticRegularizer(:ddphi, Z_guess, 1e-5/T)\n",
    "\n",
    "# convolution\n",
    "J4 = QuadraticObjective(:phi, Z_guess, convolver, [1], 1:Z_guess.T; Q=50.0/T)\n",
    "\n",
    "J = J1 + J4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "J.L(Z_guess.datavec, Z_guess)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "integrators = nothing\n",
    "GC.gc()\n",
    "integrators = [\n",
    "    QC.QuantumStatePadeIntegrator(\n",
    "        system,\n",
    "        :psip_iso,\n",
    "        :a,\n",
    "        :dts;\n",
    "        order=4\n",
    "    ),\n",
    "    QC.QuantumStatePadeIntegrator(\n",
    "        system,\n",
    "        :psim_iso,\n",
    "        :a,\n",
    "        :dts;\n",
    "        order=4\n",
    "    ),\n",
    "]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "constraints = [\n",
    "    IQPhiConstraint(:a, :phi, Z_guess),\n",
    "    #LinearSincConvolutionConstraint(:phi, :dts, Z_guess, 60.)\n",
    "    #OmegaAbsConstraint(1.0, Z_guess),\n",
    "    #PhiSincConvolutionConstraint(:a, :dts, Z_guess, 80.),\n",
    "    #PhiFunctionBoundConstraint(phase_bound, Z_guess),\n",
    "    #TimeSymmetricControlConstraint(:a, Z_guess)\n",
    "    #custom_bounds_constraint(:a, Z_guess, Int[], a_bound)\n",
    "]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Ipopt options\n",
    "options = QC.Options(\n",
    "    max_iter=200,\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# defining quantum control problem\n",
    "prob = nothing\n",
    "GC.gc()\n",
    "prob = QC.QuantumControlProblem(\n",
    "    system, \n",
    "    Z_guess, \n",
    "    J, \n",
    "    integrators;\n",
    "    constraints=constraints,\n",
    "    options=options,\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "QC.solve!(prob)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "Z = nothing\n",
    "GC.gc()\n",
    "Z = prob.trajectory"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "Z = NT.load_traj(\"interferometer/mirror_bloch78_freerelphase.jld2\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "psip_iso_rollout = QC.rollout(psip0_iso, Z.a, Z.dts, system; integrator=exp)\n",
    "psip = hcat([QC.iso_to_ket(psip_iso_rollout[:,t]) for t=1:Z.T]...)\n",
    "popsp = abs2.(psip)\n",
    "\n",
    "psim_iso_rollout = QC.rollout(psim0_iso, Z.a, Z.dts, system; integrator=exp)\n",
    "psim = hcat([QC.iso_to_ket(psim_iso_rollout[:,t]) for t=1:Z.T]...)\n",
    "popsm = abs2.(psim)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "psi = hcat([QC.iso_to_ket(Z.psi_iso[:,t]) for t=1:T]...)\n",
    "pops = hcat([abs2.(QC.iso_to_ket(Z.psi_iso[:,t])) for t=1:T]...)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "abs2.(psip[:,end]' * psim0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "abs2.(psim[:,end]' * psip0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "times = cumsum(Z.dts[1,:]) - Z.dts[1,:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "p = Plots.plot(times, popsp[:,:]', labels=(0:dim-1)', legend=:outertopright, size=(500, 300))\n",
    "Plots.xaxis!(p, \n",
    "    xlabel=L\"$t$ $[1/\\omega_R]$\"\n",
    ")\n",
    "Plots.yaxis!(p, \n",
    "    ylabel=\"Bloch state population\"\n",
    ")\n",
    "Plots.title!(p, L\"Mirror $|%$(bloch_subspace[1])\\rangle+|%$(bloch_subspace[2])\\rangle \\rightarrow |%$(bloch_subspace[1])\\rangle-|%$(bloch_subspace[2])\\rangle$\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "p = Plots.plot(times, popsm[:,:]', labels=(0:dim-1)', legend=:outertopright, size=(500, 300))\n",
    "Plots.xaxis!(p, \n",
    "    xlabel=L\"$t$ $[1/\\omega_R]$\"\n",
    ")\n",
    "Plots.yaxis!(p, \n",
    "    ylabel=\"Bloch state population\"\n",
    ")\n",
    "Plots.title!(p, L\"Mirror $|%$(bloch_subspace[1])\\rangle-|%$(bloch_subspace[2])\\rangle \\rightarrow |%$(bloch_subspace[1])\\rangle+|%$(bloch_subspace[2])\\rangle$\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "Plots.plot(times, Z.a')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "Plots.plot(times, Z.phi')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "Plots.plot(times, Z.dphi')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "Plots.plot(times, Z.ddphi')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "p = Plots.plot(times, Z.phi', linecolor=:blue, label=L\"\\varphi(t)\", size=(700, 300))\n",
    "# Plots.plot!(p, times, phase_bound.(times), linecolor=:grey, label=\"bound\")\n",
    "# Plots.plot!(p, times, -phase_bound.(times), linecolor=:grey, label=\"bound\")\n",
    "Plots.xaxis!(p, \n",
    "    xlabel=L\"$t$ $[1/\\omega_R]$\"\n",
    ")\n",
    "Plots.yaxis!(p, \n",
    "    ylabel=\"shaking amplitude\"\n",
    ")\n",
    "Plots.title!(p, L\"Mirror $|7\\rangle$\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "pops[:,end]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "Plots.plot(times, acos.(Z.a[1,:]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "Z_guess = Z\n",
    "Z_save = deepcopy(Z)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "Z_guess = trajectory_shrink_extend(Z, 1001)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "import JLD2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "JLD2.save(\"interferometer/mirror_bloch78_freerelphase.jld2\", Z)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "function fourier_time_freq(data_time, times, freqs)\n",
    "    dts = times[2:end] - times[1:end-1]\n",
    "    push!(dts, dts[end])\n",
    "    ft_mat = exp.(2im*pi*freqs*times')\n",
    "    data_freq = (dts' .* ft_mat) * data_time / sqrt.(2pi)\n",
    "    return data_freq\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "freqs = collect(0:0.1:60)\n",
    "phi_ft = fourier_time_freq(Z.a[2,:], times, freqs/(2pi));\n",
    "#phi_ft = fourier_time_freq(phi, times, freqs/(2pi));"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "Plots.plot(freqs, abs2.(phi_ft))#, ylims=(0.0, 0.01))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# mirror (Z gate)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "V = 10.\n",
    "trunc = 11\n",
    "# E_R [kHz] found in Weidner thesis\n",
    "system = ShakenLatticeSystem1D(V, trunc; bloch_basis=true, bloch_transformation_trunc=2*trunc, odd_even_fix_above_degeneracy_diff=1e-20)\n",
    "# middle index of statevector where p = 0\n",
    "mid = system.params[:mid]\n",
    "dim = system.params[:dim]\n",
    "E_R = system.params[:E_R]\n",
    "#E_R = 1/0.05\n",
    "#print(\"time unit $(1/E_R) ms\\nE_R = $E_R kHz\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "duration = 2pi * 1.0 # in units of 1/E_R\n",
    "\n",
    "T = 1001\n",
    "dt = duration / (T-1)\n",
    "dts = zeros(T) .+ dt\n",
    "dt_bound = (dt, dt)\n",
    "times = cumsum(dts) - dts\n",
    "duration"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "a_bound = fill(1.0, 2)\n",
    "phi_bound = [1.0 * pi]\n",
    "#dphi_bound = [100.]\n",
    "#ddphi_bound = [3000.]\n",
    "\n",
    "#phi = collect((sin.(11.5 *times) + sin.(20.0 * times) + sin.(27.0 * times))')\n",
    "phi = rand(1, T)\n",
    "phi = zeros(1, T)\n",
    "a = vcat(cos.(phi), sin.(phi))\n",
    "\n",
    "dphi = NT.derivative(phi, dts)\n",
    "ddphi = NT.derivative(dphi, dts)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "Plots.plot(times, a')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "Plots.plot(times, phi')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "Plots.plot(times, dphi')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "Plots.plot(times, ddphi')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "p = Plots.plot(times, phi', linecolor=:blue, label=L\"\\varphi(t)\", size=(500, 300))\n",
    "Plots.xaxis!(p, \n",
    "    xlabel=L\"$t$ $[1/\\omega_R]$\"\n",
    ")\n",
    "Plots.yaxis!(p, \n",
    "    ylabel=\"shaking amplitude\"\n",
    ")\n",
    "Plots.title!(p, L\"Mirror $|7\\rangle$ (guess)\")"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "psi0 = zeros(system.params[:dim])\n",
    "psi0[mid] = 0.\n",
    "psi0[mid-1] = sqrt(0.5)\n",
    "psi0[mid+1] = sqrt(0.5)\n",
    "normalize!(psi0)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#####Victor solution\n",
    "function get_pw_sin(sin_amps, sin_dts)\n",
    "    N = length(sin_amps)\n",
    "    sin_T = length(sin_dts)\n",
    "    T = N*sin_T + 1\n",
    "    sin_times = cumsum(sin_dts) - sin_dts\n",
    "    sin_time = sin_times[end]\n",
    "    dts = repeat(sin_dts, N)\n",
    "    push!(dts, 0.)\n",
    "    phi = zeros(T)\n",
    "    for i=1:N\n",
    "        phi[(i-1)*sin_T+1:i*sin_T] = (-1)^(i-1) * sin_amps[i] * sin.(pi*sin_times/sin_time)\n",
    "    end\n",
    "    a = zeros(2, T)\n",
    "    a[1,:] = cos.(phi)\n",
    "    a[2,:] = sin.(phi)\n",
    "    return a, dts, cumsum(dts) - dts\n",
    "end\n",
    "\n",
    "sin_amps = [0.3926, 0.6872, 0.6872, 0.4908, 0.4908, 0.7853, 0.7853]\n",
    "append!(sin_amps, sin_amps[end:-1:1]) \n",
    "\n",
    "freq = 11.5\n",
    "sin_time = 2pi * 1/freq / 2\n",
    "sin_T = 20\n",
    "sin_dts = fill(sin_time / sin_T, sin_T)\n",
    "a, dts, times = get_pw_sin(sin_amps, sin_dts)\n",
    "T = length(times)\n",
    "\n",
    "a_bound = fill(1., 2)\n",
    "dda_bound = fill(10000., 2)\n",
    "dt_bound = (dts[1], dts[1])\n",
    "\n",
    "da = NT.derivative(a, dts)\n",
    "da[:, end] = da[:, end-1]\n",
    "dda = NT.derivative(da, dts)\n",
    "dda[:, end] = dda[:, end-1] = dda[:, end-2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "#psi0 = get_bloch_state(system; lvl=3)\n",
    "bloch_subspace = [7, 8]\n",
    "psi0 = QC.cavity_state(bloch_subspace[1], dim)\n",
    "psip0 = QC.cavity_state(bloch_subspace[1], dim) + QC.cavity_state(bloch_subspace[2], dim)\n",
    "normalize!(psip0) \n",
    "psim0 = QC.cavity_state(bloch_subspace[1], dim) - QC.cavity_state(bloch_subspace[2], dim)\n",
    "normalize!(psim0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "system.params[:bloch_energies]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "psi0_iso = QC.ket_to_iso(psi0)\n",
    "psip0_iso = QC.ket_to_iso(psip0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "psi_iso = QC.rollout(psi0_iso, a, dts, system; integrator=exp)\n",
    "psip_iso = QC.rollout(psip0_iso, a, dts, system; integrator=exp)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "psi_iso += rand(size(psi_iso)...)\n",
    "psip_iso += rand(size(psip_iso)...)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "psi = hcat([QC.iso_to_ket(psi_iso[:,t]) for t=1:T]...)\n",
    "psi_pops = abs2.(psi)\n",
    "psip = hcat([QC.iso_to_ket(psip_iso[:,t]) for t=1:T]...)\n",
    "psip_pops = abs2.(psip)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "p = Plots.plot(times, psi_pops[:,:]', labels=(0:dim-1)', legend=:outertopright, size=(500, 300))\n",
    "Plots.xaxis!(p, \n",
    "    xlabel=L\"$t$ $[1/\\omega_R]$\"\n",
    ")\n",
    "Plots.yaxis!(p, \n",
    "    #ylabel=L\"population of momentum state $|p\\rangle$\"\n",
    "    ylabel=\"Bloch state population\"\n",
    ")\n",
    "Plots.title!(p, L\"Mirror $|%$(bloch_subspace[1])\\rangle \\rightarrow |%$(bloch_subspace[1])\\rangle$ (guess)\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "p = Plots.plot(times, psip_pops[:,:]', labels=(0:dim-1)', legend=:outertopright, size=(500, 300))\n",
    "Plots.xaxis!(p, \n",
    "    xlabel=L\"$t$ $[1/\\omega_R]$\"\n",
    ")\n",
    "Plots.yaxis!(p, \n",
    "    #ylabel=L\"population of momentum state $|p\\rangle$\"\n",
    "    ylabel=\"Bloch state population\"\n",
    ")\n",
    "Plots.title!(p, L\"Mirror $|%$(bloch_subspace[1])\\rangle+|%$(bloch_subspace[2])\\rangle \\rightarrow |%$(bloch_subspace[1])\\rangle-|%$(bloch_subspace[2])\\rangle$ (guess)\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "comps = (\n",
    "    psi_iso = psi_iso,\n",
    "    psip_iso = psip_iso,\n",
    "    a = a,\n",
    "    phi = phi,\n",
    "    dts = dts\n",
    ")\n",
    "initial = (\n",
    "    psi_iso = psi0_iso,\n",
    "    psip_iso = psip0_iso,\n",
    "    phi = [0.]\n",
    ")\n",
    "final = (;\n",
    "    phi = [0.]\n",
    ")\n",
    "goal = (;)\n",
    "bounds = (\n",
    "    phi = phi_bound,\n",
    "    dts = dt_bound\n",
    ")\n",
    "\n",
    "Z_guess = nothing\n",
    "GC.gc()\n",
    "Z_guess = NT.NamedTrajectory(\n",
    "    comps;\n",
    "    controls=(:phi),\n",
    "    timestep=:dts,\n",
    "    bounds=bounds,\n",
    "    initial=initial,\n",
    "    final=final,\n",
    "    goal=goal\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "kernel = sinc_kernel(40., vec(Z_guess.dts))\n",
    "convolver = LA.I(Z_guess.T) - kernel\n",
    "convolver = convolver' * convolver"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "dim = system.params[:dim]\n",
    "\n",
    "#J = NameComponentObjective(:psi_iso, [1:dim...], [1:T...], x -> 1 - abs2.(x' * state_goal), ([1:T...] ./ T) .* 100.; is_iso=true)\n",
    "J1 = QC.QuantumObjective(name=:psip_iso, goals=QC.ket_to_iso(psim0), loss=:InfidelityLoss, Q=100.0)\n",
    "J1 += QC.QuantumObjective(name=:psi_iso, goals=psi0_iso, loss=:InfidelityLoss, Q=100.0)\n",
    "#J += QC.QuadraticRegularizer(:dts, Z_guess, 0.01)\n",
    "#J += NameComponentQuadraticRegularizer(:a, [2], Z_guess, [0.001])\n",
    "#J += QC.QuadraticRegularizer(:ddphi, Z_guess, 1e-8/T)\n",
    "#J += QC.QuadraticRegularizer(:dts, Z_guess, 0.01)\n",
    "#J += NameComponentQuadraticRegularizer(:a, [2], Z_guess, [0.001])\n",
    "\n",
    "# J1 = QuadraticObjective(:psi_iso, Z_guess, R; Q=200.0)\n",
    "# J2 = NameComponentObjective(:psi_iso, [8, 9], [T], x -> real(x[1]'*x[2])^2, [100.0]; is_iso=true)\n",
    "# J3 = QC.QuadraticRegularizer(:ddphi, Z_guess, 1e-5/T)\n",
    "\n",
    "# convolution\n",
    "J4 = QuadraticObjective(:phi, Z_guess, convolver, [1], 1:Z_guess.T; Q=50.0/T)\n",
    "\n",
    "J = J1 + J4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "J.L(Z_guess.datavec, Z_guess)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "integrators = nothing\n",
    "GC.gc()\n",
    "integrators = [\n",
    "    QC.QuantumStatePadeIntegrator(\n",
    "        system,\n",
    "        :psi_iso,\n",
    "        :a,\n",
    "        :dts;\n",
    "        order=4\n",
    "    ),\n",
    "    QC.QuantumStatePadeIntegrator(\n",
    "        system,\n",
    "        :psip_iso,\n",
    "        :a,\n",
    "        :dts;\n",
    "        order=4\n",
    "    ),\n",
    "]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "constraints = [\n",
    "    IQPhiConstraint(:a, :phi, Z_guess),\n",
    "    QC.ComplexModulusContraint(\n",
    "        R=sqrt(0.1),\n",
    "        comps=Z_guess.components[:psi_iso][[3, 3+dim]],\n",
    "        times=[div(Z_guess.T, 2)],\n",
    "        zdim=Z_guess.dim,\n",
    "        T=Z_guess.T,\n",
    "        negated=true\n",
    "    )\n",
    "    #LinearSincConvolutionConstraint(:phi, :dts, Z_guess, 60.)\n",
    "    #OmegaAbsConstraint(1.0, Z_guess),\n",
    "    #PhiSincConvolutionConstraint(:a, :dts, Z_guess, 80.),\n",
    "    #PhiFunctionBoundConstraint(phase_bound, Z_guess),\n",
    "    #TimeSymmetricControlConstraint(:a, Z_guess)\n",
    "    #custom_bounds_constraint(:a, Z_guess, Int[], a_bound)\n",
    "]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Ipopt options\n",
    "options = QC.Options(\n",
    "    max_iter=200,\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# defining quantum control problem\n",
    "prob = nothing\n",
    "GC.gc()\n",
    "prob = QC.QuantumControlProblem(\n",
    "    system, \n",
    "    Z_guess, \n",
    "    J, \n",
    "    integrators;\n",
    "    constraints=constraints,\n",
    "    options=options,\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "QC.solve!(prob)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "Z = nothing\n",
    "GC.gc()\n",
    "Z = prob.trajectory"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "psi_iso_rollout = QC.rollout(psi0_iso, Z.a, Z.dts, system; integrator=exp)\n",
    "psi = hcat([QC.iso_to_ket(psi_iso_rollout[:,t]) for t=1:Z.T]...)\n",
    "pops = abs2.(psi)\n",
    "\n",
    "psip_iso_rollout = QC.rollout(psip0_iso, Z.a, Z.dts, system; integrator=exp)\n",
    "psip = hcat([QC.iso_to_ket(psip_iso_rollout[:,t]) for t=1:Z.T]...)\n",
    "popsp = abs2.(psip)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "psi = hcat([QC.iso_to_ket(Z.psi_iso[:,t]) for t=1:T]...)\n",
    "pops = hcat([abs2.(QC.iso_to_ket(Z.psi_iso[:,t])) for t=1:T]...)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "abs2.(psi[:,end]' * psi0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "abs2.(psip[:,end]' * psim0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "times = cumsum(Z.dts[1,:]) - Z.dts[1,:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "p = Plots.plot(times, pops[:,:]', labels=(0:dim-1)', legend=:outertopright, size=(500, 300))\n",
    "Plots.xaxis!(p, \n",
    "    xlabel=L\"$t$ $[1/\\omega_R]$\"\n",
    ")\n",
    "Plots.yaxis!(p, \n",
    "    ylabel=\"Bloch state population\"\n",
    ")\n",
    "Plots.title!(p, L\"Mirror $|%$(bloch_subspace[1])\\rangle \\rightarrow |%$(bloch_subspace[1])\\rangle$\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "p = Plots.plot(times, popsp[:,:]', labels=(0:dim-1)', legend=:outertopright, size=(500, 300))\n",
    "Plots.xaxis!(p, \n",
    "    xlabel=L\"$t$ $[1/\\omega_R]$\"\n",
    ")\n",
    "Plots.yaxis!(p, \n",
    "    ylabel=\"Bloch state population\"\n",
    ")\n",
    "Plots.title!(p, L\"Mirror $|%$(bloch_subspace[1])\\rangle+|%$(bloch_subspace[2])\\rangle \\rightarrow |%$(bloch_subspace[1])\\rangle-|%$(bloch_subspace[2])\\rangle$\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "Plots.plot(times, Z.a')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "Plots.plot(times, Z.phi')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "Plots.plot(times, Z.dphi')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "Plots.plot(times, Z.ddphi')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "p = Plots.plot(times, Z.phi', linecolor=:blue, label=L\"\\varphi(t)\", size=(500, 300))\n",
    "# Plots.plot!(p, times, phase_bound.(times), linecolor=:grey, label=\"bound\")\n",
    "# Plots.plot!(p, times, -phase_bound.(times), linecolor=:grey, label=\"bound\")\n",
    "Plots.xaxis!(p, \n",
    "    xlabel=L\"$t$ $[1/\\omega_R]$\"\n",
    ")\n",
    "Plots.yaxis!(p, \n",
    "    ylabel=\"shaking amplitude\"\n",
    ")\n",
    "Plots.title!(p, L\"Mirror $|7\\rangle$\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "pops[:,end]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "Plots.plot(times, acos.(Z.a[1,:]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "Z_guess = Z\n",
    "Z_save = deepcopy(Z)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "Z_guess = trajectory_shrink_extend(Z, 1001)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "import JLD2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "JLD2.save(\"interferometer/mirror_bloch78_Z.jld2\", Z)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "function fourier_time_freq(data_time, times, freqs)\n",
    "    dts = times[2:end] - times[1:end-1]\n",
    "    push!(dts, dts[end])\n",
    "    ft_mat = exp.(2im*pi*freqs*times')\n",
    "    data_freq = (dts' .* ft_mat) * data_time / sqrt.(2pi)\n",
    "    return data_freq\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "freqs = collect(0:0.1:60)\n",
    "phi_ft = fourier_time_freq(Z.a[2,:], times, freqs/(2pi));\n",
    "#phi_ft = fourier_time_freq(phi, times, freqs/(2pi));"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "Plots.plot(freqs, abs2.(phi_ft))#, ylims=(0.0, 0.01))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## convergence plot"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 163,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "catch\n",
      "catch\n",
      "catch\n",
      "catch\n",
      "catch\n",
      "catch\n",
      "catch\n",
      "catch\n",
      "catch\n",
      "catch\n",
      "catch\n",
      "catch\n",
      "catch\n",
      "catch\n",
      "catch\n",
      "catch\n",
      "catch\n",
      "catch\n",
      "catch\n",
      "catch\n",
      "catch\n",
      "catch\n",
      "catch\n",
      "catch\n",
      "catch\n",
      "catch\n",
      "catch\n",
      "catch\n",
      "catch\n",
      "catch\n",
      "catch\n",
      "catch\n",
      "catch\n",
      "catch\n",
      "catch\n",
      "catch\n",
      "catch\n",
      "catch\n",
      "catch\n",
      "catch\n",
      "catch\n",
      "catch\n",
      "catch\n",
      "catch\n",
      "catch\n",
      "catch\n",
      "catch\n",
      "catch\n",
      "catch\n",
      "catch\n",
      "catch\n",
      "catch\n",
      "catch\n",
      "catch\n",
      "catch\n",
      "catch\n",
      "catch\n",
      "catch\n",
      "catch\n"
     ]
    }
   ],
   "source": [
    "L = zeros(201)\n",
    "grad = zeros(201)\n",
    "open(\"convergence2.txt\") do f\n",
    "    global L, grad\n",
    "    while !eof(f)\n",
    "        s = strip(readline(f))\n",
    "        pcs = split(s, \" \")\n",
    "        pcs = filter(x -> x != \"\", pcs)\n",
    "        try\n",
    "            i = parse(Int, pcs[1])\n",
    "        catch\n",
    "            println(\"catch\")\n",
    "            continue\n",
    "        end\n",
    "        L[i+1] = parse(Float64, pcs[2])\n",
    "        grad[i+1] = parse(Float64, pcs[6])\n",
    "        i += 1\n",
    "    end\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 164,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "catch\n",
      "catch\n",
      "catch\n",
      "catch\n",
      "catch\n",
      "catch\n",
      "catch\n",
      "catch\n",
      "catch\n",
      "catch\n",
      "catch\n",
      "catch\n",
      "catch\n",
      "catch\n",
      "catch\n",
      "catch\n",
      "catch\n",
      "catch\n",
      "catch\n",
      "catch\n",
      "catch\n",
      "catch\n",
      "catch\n",
      "catch\n",
      "catch\n",
      "catch\n",
      "catch\n",
      "catch\n",
      "catch\n",
      "catch\n",
      "catch\n",
      "catch\n",
      "catch\n",
      "catch\n",
      "catch\n",
      "catch\n",
      "catch\n",
      "catch\n",
      "catch\n",
      "catch\n",
      "catch\n",
      "catch\n",
      "catch\n",
      "catch\n",
      "catch\n",
      "catch\n",
      "catch\n",
      "catch\n",
      "catch\n",
      "catch\n",
      "catch\n",
      "catch\n",
      "catch\n",
      "catch\n",
      "catch\n",
      "catch\n",
      "catch\n",
      "catch\n",
      "catch\n"
     ]
    }
   ],
   "source": [
    "L = hcat(L, zeros(201))\n",
    "grad = hcat(grad, zeros(201))\n",
    "open(\"convergence1.txt\") do f\n",
    "    global L, grad\n",
    "    while !eof(f)\n",
    "        s = strip(readline(f))\n",
    "        pcs = split(s, \" \")\n",
    "        pcs = filter(x -> x != \"\", pcs)\n",
    "        try\n",
    "            i = parse(Int, pcs[1])\n",
    "        catch\n",
    "            println(\"catch\")\n",
    "            continue\n",
    "        end\n",
    "        L[i+1,2] = parse(Float64, pcs[2])\n",
    "        grad[i+1,2] = parse(Float64, pcs[6])\n",
    "        i += 1\n",
    "    end\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 165,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "201×2 Matrix{Float64}:\n",
       " 126.28       126.28\n",
       " 109.415      116.074\n",
       " 108.783      101.327\n",
       " 122.668      100.826\n",
       " 122.594      100.525\n",
       " 120.363      100.635\n",
       " 119.947      100.51\n",
       " 122.265      100.42\n",
       " 123.537      100.334\n",
       " 122.958      100.258\n",
       "   ⋮          \n",
       "   0.101583   100.0\n",
       "   0.101547   100.0\n",
       "   0.094748   100.0\n",
       "   0.0906403  100.0\n",
       "   0.11058    100.0\n",
       "   0.0931546  100.0\n",
       "   0.0922879  100.0\n",
       "   0.103963   100.0\n",
       "   0.101276   100.0"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "L"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 173,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "p = Plots.plot(\n",
    "    log10.(grad),\n",
    "    size=(500,350),\n",
    "    label=[L\"with $B=2$ constraint\" \"standard\"], \n",
    "    legend=:topright,\n",
    "    xlabel=\"Iteration\",\n",
    "    ylabel=L\"\\log_{10}\\left(||\\!\\mathrm{step}\\,|\\!|_\\infty\\right)\",\n",
    "    ylim=(-7, 3),\n",
    "    xlim=(0, 201),\n",
    "    c=:black,\n",
    "    linestyle=[:solid :dot],\n",
    "    linewidth=1.5\n",
    "    )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 174,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\"/local/lmseifert/Infleqtion/research-superstaq/research_superstaq/theory/shaken_lattice/Max_QC/patent_figs/step_size.pdf\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Plots.savefig(p, \"patent_figs/step_size.pdf\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 175,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "p = Plots.plot(\n",
    "    L, \n",
    "    size=(500,350),\n",
    "    label=[L\"with $B=2$ constraint\" \"standard\" ], \n",
    "    legend=:topright,\n",
    "    xlabel=\"Iteration\",\n",
    "    ylabel=\"Objective value\",\n",
    "    xlim=(0, 201),\n",
    "    ylim=(0., 130.),\n",
    "    c=:black,\n",
    "    linestyle=[:solid :dot],\n",
    "    linewidth=1.5\n",
    "    )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 176,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\"/local/lmseifert/Infleqtion/research-superstaq/research_superstaq/theory/shaken_lattice/Max_QC/patent_figs/convergence.pdf\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Plots.savefig(p, \"patent_figs/convergence.pdf\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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   "file_extension": ".jl",
   "mimetype": "application/julia",
   "name": "julia",
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