Fidelity of 2π rotations under various approximations across disk.ipynb

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      "text/plain": [
       "odf_time_evolution (generic function with 3 methods)"
      ]
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   "source": [
    "function fidelity(ρ, σ)\n",
    "    tr(sqrt(sqrt(ρ) * σ * sqrt(ρ)))^(1/2)\n",
    "end\n",
    "\n",
    "function R(n::Int64, m::Int64, ρ::Float64, scale::Float64=1E-6)\n",
    "    \"\"\"Following the naming convention on Wikipedia for R_n^m: https://en.wikipedia.org/wiki/Zernike_polynomials\"\"\"\n",
    "    if (n - m) % 2 != 0\n",
    "        0\n",
    "    else\n",
    "        function summand(k)\n",
    "            if ρ == 0\n",
    "                0\n",
    "            else\n",
    "                (-1)^k * factorial(n-k)/(factorial(k)*factorial(Int((n+m)/2) - k)*factorial(Int((n-m)/2) - k))*(ρ/scale)^(n-2*k)\n",
    "            end\n",
    "        end\n",
    "        mapreduce(summand, +, Array(range(0, stop=Int((n-m)/2), step=1)))\n",
    "    end\n",
    "end\n",
    "\n",
    "function Z(n::Int64, m::Int64)\n",
    "    \"\"\"In John's notes he includes a normalization, we have omitted that and are just following the conventions\n",
    "    on Wikipedia.\"\"\"\n",
    "    function Z_at_point(ρ::Float64, ϕ::Float64)\n",
    "        if m >= 0\n",
    "            R(n, m, ρ) * cos(m * ϕ)\n",
    "        else\n",
    "            R(n, -m, ρ) * sin(-m * ϕ)\n",
    "        end\n",
    "    end\n",
    "    Z_at_point\n",
    "end\n",
    "\n",
    "function plot_across_disk(f, discretization::Int64, radius::Float64)\n",
    "    x = y = Array(range(-radius, radius, length=discretization))\n",
    "    z = Array{typeof(f(0.,0.))}(UndefInitializer(), length(x), length(y))\n",
    "    for (i, xx) in enumerate(x)\n",
    "        for (j, yy) in enumerate(y)\n",
    "            if xx^2 + yy^2 > radius^2\n",
    "                if typeof(f(0.,0.)) == Tuple{Float64,Float64}\n",
    "                    z[i, j] = (0.,0.)\n",
    "                else\n",
    "                    z[i, j] = 0.\n",
    "                end\n",
    "            else\n",
    "                ρ = sqrt(xx^2 + yy^2)\n",
    "                ϕ = atan(yy, xx)\n",
    "                res = f(ρ, ϕ)\n",
    "                z[i, j] = res\n",
    "            end\n",
    "        end\n",
    "    end\n",
    "    x, y, z\n",
    "end\n",
    "\n",
    "using SpecialFunctions\n",
    "using QuantumOptics\n",
    "\n",
    "function H_odf(ρ::Float64, ϕ::Float64, t::Float64, zernike_coefficients_even::Array,\n",
    "        zernike_coefficients_odd::Array, U::Float64=2*π*10E3, ψ::Float64=0.;\n",
    "        μ::Float64=0.0, ω::Float64=2*π*43.8E3, bessel=false, small=false)\n",
    "    # For backwards compatibility - we might want different orders of Zernike terms.\n",
    "    if !isa(zernike_coefficients_even[1], Array)\n",
    "        zernike_coefficients_even = [zernike_coefficients_even]\n",
    "    end\n",
    "    if !isa(zernike_coefficients_odd[1], Array)\n",
    "        zernike_coefficients_odd = [zernike_coefficients_odd]\n",
    "    end\n",
    "    \n",
    "    eventuples = []\n",
    "    for zeven in zernike_coefficients_even\n",
    "        neven = length(zeven) - 1\n",
    "        Peven = reduce(+, [zeven[i] * R(neven, i-1, ρ) for i in Array(range(1, neven + 1, step=1))])\n",
    "        rotationeven = - (neven) * ω * t\n",
    "        push!(eventuples, (neven, Peven, rotationeven))\n",
    "    end\n",
    "    oddtuples = []\n",
    "    for zodd in zernike_coefficients_odd\n",
    "        nodd = length(zodd) - 1\n",
    "        Podd = reduce(+, [zodd[i] * R(nodd, i-1, ρ) for i in Array(range(1, nodd + 1, step=1))])\n",
    "        rotationodd = - (nodd) * ω * t\n",
    "        push!(oddtuples, (nodd, Podd, rotationodd))\n",
    "    end\n",
    "    \n",
    "    # any bessel approximation should only apply one order of zernike, this should error otherwise\n",
    "    if bessel && small\n",
    "        U * (1/2 * (mapreduce(x->x[2]*sin(x[1]*ϕ - ψ), +, oddtuples)\n",
    "            - mapreduce(x->x[2]*cos(x[1]*ϕ - ψ), +, eventuples))\n",
    "        - 1/16 * (mapreduce(x->x[1][2]^2*x[2][2]*cos(x[1][1]*ϕ - ψ), +, zip(eventuples, oddtuples))\n",
    "            + mapreduce(x->x[2][2]^2*x[1][2]*sin(x[1][1]*ϕ - ψ), +, zip(eventuples, oddtuples))))\n",
    "\n",
    "        #U/2 * (Peven * sin(neven * ϕ - ψ) - Podd * cos(nodd * ϕ - ψ))\n",
    "    elseif bessel && !small\n",
    "        U * (mapreduce(x->besselj1(x[2])*sin(x[1]*ϕ - ψ), +, oddtuples)\n",
    "            - mapreduce(x->besselj1(x[2])*cos(x[1]*ϕ - ψ), +, eventuples))\n",
    "        #U * (besselj1(Peven) * sin(neven * ϕ - ψ) - besselj1(Podd) * cos(nodd * ϕ - ψ))\n",
    "    else\n",
    "        U * sin(-μ*t + ψ + (mapreduce(x->x[2]*cos(x[1]*ϕ + x[3]), +, eventuples)\n",
    "                + mapreduce(x->x[2]*sin(x[1]*ϕ +x[3]), +, oddtuples)))\n",
    "        #U * sin(-μ*t + ψ + Peven * cos(neven * ϕ  + rotationeven) + Podd * sin(nodd * ϕ  + rotationodd))\n",
    "    end\n",
    "end\n",
    "\n",
    "function odf_time_evolution(ρ::Float64, ϕ::Float64, zernikeeven::Array, zernikeodd::Array,\n",
    "                            Γ::Float64=1/62, evolution_time::Float64=50.E-6;\n",
    "                            ω::Float64=2*π*43.8E3, μ::Float64=0.0, optimize=true, bessel=false, small=false)\n",
    "    b = SpinBasis(1//2)\n",
    "    ψ0 = 1/sqrt(2) * (spindown(b) + spinup(b))\n",
    "    T = [0:0.01E-6:evolution_time;]\n",
    "    H(t, ψ) = H_odf(ρ, ϕ, t, zernikeeven, zernikeodd, μ=μ, ω=ω, bessel=bessel, small=small)*sigmaz(b), [sigmam(b)], [dagger(sigmam(b))]\n",
    "    tout, ρ = timeevolution.master_dynamic(T, ψ0, H; rates=[Γ])\n",
    "    trace = Real.(expect(sigmax(b), ρ))\n",
    "    if optimize\n",
    "        minimum(trace), T[argmin(trace)]\n",
    "    else\n",
    "        trace\n",
    "    end\n",
    "end"
   ]
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   "execution_count": 2,
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     "data": {
      "text/plain": [
       "Ket(dim=2)\n",
       "  basis: Spin(1/2)\n",
       " 0.7071067811865475 + 0.0im\n",
       " 0.7071067811865475 + 0.0im"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
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   ],
   "source": [
    "zernike = [0, 1] # \n",
    "Γ = (1/62) \n",
    "rates = [Γ]\n",
    "b = SpinBasis(1//2)\n",
    "ω = 2 * π * 43.8E3\n",
    "μ = (length(zernike) - 1) * ω\n",
    "ψ0 = 1/sqrt(2) * (spindown(b) + spinup(b))"
   ]
  },
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      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "using Plots\n",
    "width = 1E-6\n",
    "discretization = 50\n",
    "function zernike_func(ρ, coefficients)\n",
    "    reduce(+, [coefficients[i] * R(length(coefficients)-1, i-1, ρ) for i in Array(range(1, length(coefficients), step=1))])\n",
    "end\n",
    "plot(\n",
    "    heatmap(plot_across_disk((ρ, ϕ) -> zernike_func(ρ, zernike) * sin((length(zernike) - 1) * ϕ), discretization, width)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
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     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plot(\n",
    "    heatmap(plot_across_disk((ρ, ϕ) -> zernike_func(ρ, zernike) * cos((length(zernike) - 1) * ϕ), discretization, width)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
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      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function zernike_func(ρ, coefficients)\n",
    "    reduce(+, [coefficients[i] * R(length(coefficients)-1, i-1, ρ) for i in Array(range(1, length(coefficients), step=1))])\n",
    "end\n",
    "plot(\n",
    "    heatmap(plot_across_disk((ρ, ϕ) -> zernike_func(ρ, zernike) * cos((length(zernike) - 1) * ϕ) + zernike_func(ρ, zernike) * sin((length(zernike) - 1) * ϕ), discretization, width)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Note that between notebooks we moved to used seconds, rather than microseconds.\n",
    "max_simulation_time = 50.E-6\n",
    "ρ = 1E-6\n",
    "ϕ = 0.\n",
    "pop, max_simulation_time = odf_time_evolution(ρ, ϕ, zernike, [0.], Γ, max_simulation_time, small=true, bessel=true, optimize=true)\n",
    "\n",
    "H(t, _) = H_odf(ρ, ϕ, t, zernike, zernike, small=true, bessel=true) * sigmaz(b), [sigmaz(b)], [dagger(sigmaz(b))]\n",
    "T = [0:0.01E-6:2*max_simulation_time;]\n",
    "tout, ψ = timeevolution.master_dynamic(T, ψ0, H; rates=rates)\n",
    "\n",
    "ω = 2 * π * 43.8E3\n",
    "μ = (length(zernike) - 1) * ω\n",
    "\n",
    "# Measure in the x basis\n",
    "excitation = Real.(expect(sigmax(b), ψ))\n",
    "large_bessel = odf_time_evolution(ρ, ϕ, zernike, [0.], Γ, 2*max_simulation_time; ω=ω, μ=μ, optimize=false, bessel=true, small=false)\n",
    "exact = odf_time_evolution(ρ, ϕ, zernike, [0.], Γ, 2*max_simulation_time; ω=ω, μ=μ, optimize=false, bessel=false, small=false);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "Figure(PyObject <Figure size 640x480 with 1 Axes>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "PyObject <matplotlib.legend.Legend object at 0x163405e50>"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "using PyPlot\n",
    "using LaTeXStrings\n",
    "plot(T*1E6, excitation, label=\"Approximate\")\n",
    "plot(T*1E6, large_bessel, label=\"RWA\")\n",
    "plot(T*1E6, exact, label=\"Exact\")\n",
    "xlabel(\"Evolution Time (μs)\")\n",
    "ylabel(L\"<\\sigma_x>\")\n",
    "title(L\"Evolution of $\\frac{1}{\\sqrt{2}}(\\psi_{up} + \\psi_{down})$\")\n",
    "legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "infidelity_across_disk (generic function with 1 method)"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function infidelity_across_disk(H1, H2)\n",
    "    function infidelity_polar(ρ, ϕ)\n",
    "        # We will assume that two times the π time is the 2π time.\n",
    "        initial_simulation_time = 100.E-6\n",
    "        max_simulation_time = 2 * last(odf_time_evolution(ρ, ϕ, zernike, [0.], Γ, initial_simulation_time, small=true, bessel=true, optimize=true))\n",
    "        H = H1(ρ, ϕ)\n",
    "        T = [0:.1E-6:max_simulation_time;]\n",
    "        _, ψTARGET = timeevolution.master_dynamic(T, ψ0, H; rates=[Γ])\n",
    "        ψTARGET = last(ψTARGET);\n",
    "        H3 = H2(ρ, ϕ)\n",
    "        # Why does naming something H below the first definition give an error?\n",
    "        _, ψRWA = timeevolution.master_dynamic(T, ψ0, H3; rates=[Γ])\n",
    "        ψRWA = last(ψRWA);\n",
    "        1-real(fidelity(ψRWA.data, ψTARGET.data))\n",
    "    end\n",
    "end"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Assuming just RWA"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "using Plots\n",
    "# Be _really_ careful with these names...\n",
    "function H1(ρ, ϕ)\n",
    "    # Should this be two zernike?\n",
    "    H(t, _) = H_odf(ρ, ϕ, t, zernike, [0.], μ=μ, ω=ω, bessel=true, small=true)*sigmaz(b), [sigmam(b)], [dagger(sigmam(b))]\n",
    "end\n",
    "function HRWA(ρ, ϕ)\n",
    "    H(t, _) = H_odf(ρ, ϕ, t, zernike, [0.], μ=μ, ω=ω, bessel=true, small=false)*sigmaz(b), [sigmam(b)], [dagger(sigmam(b))]\n",
    "end\n",
    "RWA_infidelity = plot_across_disk(infidelity_across_disk(H1, HRWA), discretization, width);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/svg+xml": [
       "<?xml version=\"1.0\" encoding=\"utf-8\"?>\n",
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       "<defs>\n",
       "  <clipPath id=\"clip070\">\n",
       "    <rect x=\"0\" y=\"0\" width=\"2400\" height=\"1600\"/>\n",
       "  </clipPath>\n",
       "</defs>\n",
       "<path clip-path=\"url(#clip070)\" d=\"\n",
       "M0 1600 L2400 1600 L2400 0 L0 0  Z\n",
       "  \" fill=\"#ffffff\" fill-rule=\"evenodd\" fill-opacity=\"1\"/>\n",
       "<defs>\n",
       "  <clipPath id=\"clip071\">\n",
       "    <rect x=\"480\" y=\"0\" width=\"1681\" height=\"1600\"/>\n",
       "  </clipPath>\n",
       "</defs>\n",
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      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plot(heatmap(RWA_infidelity), title=\"Infidelity from Target State Assuming only RWA\", axis=nothing)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Exact Dynamics"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Be _really_ careful with these names...\n",
    "function H3(ρ, ϕ)\n",
    "    H(t, _) = H_odf(ρ, ϕ, t, zernike, [0.], μ=μ, ω=ω, bessel=false, small=false)*sigmaz(b), [sigmam(b)], [dagger(sigmam(b))]\n",
    "end\n",
    "exact_infidelity = plot_across_disk(infidelity_across_disk(H1, H3), discretization, width);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
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       "  2256.76,643.501 2232.76,643.501 2232.76,497.25 2256.76,497.25 2232.76,497.25 2232.76,350.999 2256.76,350.999 2232.76,350.999 2232.76,204.748 2256.76,204.748 \n",
       "  2232.76,204.748 2232.76,123.472 \n",
       "  \"/>\n",
       "</svg>\n"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plot(heatmap(exact_infidelity), title=\"Infidelity from Target State with Exact Dynamics\", axis=nothing)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "function evolve(T, ψ0, ρ, ϕ)\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {
    "scrolled": false
   },
   "outputs": [],
   "source": [
    "function infidelity_polar(ρ, ϕ)\n",
    "    # We will assume that two times the π time is the 2π time.\n",
    "    initial_simulation_time = 100.E-6\n",
    "    max_simulation_time = 2 * last(odf_time_evolution(ρ, ϕ, zernike, zernike, Γ, initial_simulation_time, small=false, bessel=false, optimize=true))\n",
    "    H = H1(ρ, ϕ)\n",
    "    T = [0:.1E-6:max_simulation_time;]\n",
    "    _, ψTARGET = timeevolution.master_dynamic(T, ψ0, H; rates=[Γ])\n",
    "    ψTARGET = last(ψTARGET);\n",
    "    H(t, _) = H_odf(ρ, ϕ, t, zernike, [0], μ=μ, ω=ω, bessel=false, small=false)*sigmaz(b), [sigmam(b)], [dagger(sigmam(b))]\n",
    "    _, ψEVEN = timeevolution.master_dynamic(T, ψ0, H; rates=[Γ])\n",
    "    ψEVEN = last(ψEVEN);\n",
    "    H(t, _) = H_odf(ρ, ϕ, t, [0], zernike, μ=μ, ω=ω, bessel=false, small=false)*sigmaz(b), [sigmam(b)], [dagger(sigmam(b))]\n",
    "    _, ψEVENODD = timeevolution.master_dynamic(T, ψEVEN, H; rates=[Γ]);\n",
    "    ψEVENODD = last(ψEVENODD);\n",
    "    1-real(fidelity(ψEVENODD.data, ψTARGET.data))\n",
    "end\n",
    "\n",
    "evenodd_infidelity = plot_across_disk(infidelity_polar, discretization*2, width);"
   ]
  },
  {
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      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plot(heatmap(evenodd_infidelity), title=\"Infidelity from Target State with Exact Dynamics,\\n Alternating Even then Odd Zernike\", axis=nothing)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Simultaneous two terms, Exact"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Be _really_ careful with these names...\n",
    "function H1(ρ, ϕ)\n",
    "    # Should this be two zernike?\n",
    "    H(t, _) = H_odf(ρ, ϕ, t, zernike, zernike, μ=μ, ω=ω, bessel=true, small=true)*sigmaz(b), [sigmam(b)], [dagger(sigmam(b))]\n",
    "end\n",
    "function H3(ρ, ϕ)\n",
    "    H(t, _) = H_odf(ρ, ϕ, t, zernike, zernike, μ=μ, ω=ω, bessel=false, small=false)*sigmaz(b), [sigmam(b)], [dagger(sigmam(b))]\n",
    "end\n",
    "exact_infidelity = plot_across_disk(infidelity_across_disk(H1, H3), discretization, width);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
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     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plot(heatmap(exact_infidelity), title=\"Infidelity from Target State with Exact Dynamics,\\n Even and Odd Terms\", axis=nothing)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Be _really_ careful with these names...\n",
    "function H1(ρ, ϕ)\n",
    "    # Should this be two zernike?\n",
    "    H(t, _) = H_odf(ρ, ϕ, t, zernike, zernike, μ=μ, ω=ω, bessel=true, small=true)*sigmaz(b), [sigmam(b)], [dagger(sigmam(b))]\n",
    "end\n",
    "function H3(ρ, ϕ)\n",
    "    H(t, _) = H_odf(ρ, ϕ, t, zernike, zernike, μ=μ, ω=ω, bessel=false, small=false)*sigmaz(b), [sigmam(b)], [dagger(sigmam(b))]\n",
    "end\n",
    "exact_infidelity = plot_across_disk(infidelity_across_disk(H1, H3), discretization, width);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [
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      ]
     },
     "execution_count": 63,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plot(heatmap(exact_infidelity), title=\"Infidelity from Target State with Exact Dynamics,\\n Even and Odd, Including Second Order Terms\", axis=nothing)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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