examples/two_qubit_entangling_gate.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Entangling gate on two coupled qubits"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Imports"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [],
   "source": [
    "# !pip install -q -U pip\n",
    "# !pip install -q matplotlib"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-10T13:45:05.684014Z",
     "start_time": "2020-06-10T13:45:04.441825Z"
    }
   },
   "outputs": [],
   "source": [
    "# System imports\n",
    "import copy\n",
    "import numpy as np\n",
    "import time\n",
    "import itertools\n",
    "import matplotlib.pyplot as plt\n",
    "import tensorflow as tf\n",
    "import tensorflow_probability as tfp\n",
    "from typing import List\n",
    "\n",
    "# Main C3 objects\n",
    "from c3.c3objs import Quantity as Qty\n",
    "from c3.parametermap import ParameterMap as PMap\n",
    "from c3.experiment import Experiment as Exp\n",
    "from c3.model import Model as Mdl\n",
    "from c3.generator.generator import Generator as Gnr\n",
    "\n",
    "# Building blocks\n",
    "import c3.generator.devices as devices\n",
    "import c3.signal.gates as gates\n",
    "import c3.libraries.chip as chip\n",
    "import c3.signal.pulse as pulse\n",
    "import c3.libraries.tasks as tasks\n",
    "\n",
    "# Libs and helpers\n",
    "import c3.libraries.algorithms as algorithms\n",
    "import c3.libraries.hamiltonians as hamiltonians\n",
    "import c3.libraries.fidelities as fidelities\n",
    "import c3.libraries.envelopes as envelopes\n",
    "import c3.utils.qt_utils as qt_utils\n",
    "import c3.utils.tf_utils as tf_utils"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Model components\n",
    "The model consists of two qubits with 3 levels each and slightly different parameters:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-10T13:45:05.684014Z",
     "start_time": "2020-06-10T13:45:04.441825Z"
    }
   },
   "outputs": [],
   "source": [
    "qubit_lvls = 3\n",
    "freq_q1 = 5e9\n",
    "anhar_q1 = -210e6\n",
    "t1_q1 = 27e-6\n",
    "t2star_q1 = 39e-6\n",
    "qubit_temp = 50e-3\n",
    "\n",
    "q1 = chip.Qubit(\n",
    "    name=\"Q1\",\n",
    "    desc=\"Qubit 1\",\n",
    "    freq=Qty(value=freq_q1, min_val=4.995e9, max_val=5.005e9, unit='Hz 2pi'),\n",
    "    anhar=Qty(value=anhar_q1, min_val=-380e6, max_val=-120e6, unit='Hz 2pi'),\n",
    "    hilbert_dim=qubit_lvls,\n",
    "    t1=Qty(value=t1_q1, min_val=1e-6, max_val=90e-6, unit='s'),\n",
    "    t2star=Qty(value=t2star_q1, min_val=10e-6, max_val=90e-3, unit='s'),\n",
    "    temp=Qty(value=qubit_temp, min_val=0.0, max_val=0.12, unit='K')\n",
    ")\n",
    "\n",
    "freq_q2 = 5.6e9\n",
    "anhar_q2 = -240e6\n",
    "t1_q2 = 23e-6\n",
    "t2star_q2 = 31e-6\n",
    "q2 = chip.Qubit(\n",
    "    name=\"Q2\",\n",
    "    desc=\"Qubit 2\",\n",
    "    freq=Qty(value=freq_q2, min_val=5.595e9, max_val=5.605e9, unit='Hz 2pi'),\n",
    "    anhar=Qty(value=anhar_q2, min_val=-380e6, max_val=-120e6, unit='Hz 2pi'),\n",
    "    hilbert_dim=qubit_lvls,\n",
    "    t1=Qty(value=t1_q2, min_val=1e-6, max_val=90e-6,unit='s'),\n",
    "    t2star=Qty(value=t2star_q2, min_val=10e-6, max_val=90e-6, unit='s'),\n",
    "    temp=Qty(value=qubit_temp, min_val=0.0, max_val=0.12, unit='K')\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There is a static coupling in x-direction between them: $(b_1+b_1^\\dagger)(b_2+b_2^\\dagger)$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-10T13:45:05.684014Z",
     "start_time": "2020-06-10T13:45:04.441825Z"
    }
   },
   "outputs": [],
   "source": [
    "coupling_strength = 50e6\n",
    "q1q2 = chip.Coupling(\n",
    "    name=\"Q1-Q2\",\n",
    "    desc=\"coupling\",\n",
    "    comment=\"Coupling qubit 1 to qubit 2\",\n",
    "    connected=[\"Q1\", \"Q2\"],\n",
    "    strength=Qty(\n",
    "        value=coupling_strength,\n",
    "        min_val=-1 * 1e3 ,\n",
    "        max_val=200e6 ,\n",
    "        unit='Hz 2pi'\n",
    "    ),\n",
    "    hamiltonian_func=hamiltonians.int_XX\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "and each qubit has a drive line"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-10T13:45:05.684014Z",
     "start_time": "2020-06-10T13:45:04.441825Z"
    }
   },
   "outputs": [],
   "source": [
    "drive1 = chip.Drive(\n",
    "    name=\"d1\",\n",
    "    desc=\"Drive 1\",\n",
    "    comment=\"Drive line 1 on qubit 1\",\n",
    "    connected=[\"Q1\"],\n",
    "    hamiltonian_func=hamiltonians.x_drive\n",
    ")\n",
    "drive2 = chip.Drive(\n",
    "    name=\"d2\",\n",
    "    desc=\"Drive 2\",\n",
    "    comment=\"Drive line 2 on qubit 2\",\n",
    "    connected=[\"Q2\"],\n",
    "    hamiltonian_func=hamiltonians.x_drive\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "All parts are collected in the model. The initial state will be thermal at a non-vanishing temperature."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [],
   "source": [
    "init_temp = 50e-3\n",
    "init_ground = tasks.InitialiseGround(\n",
    "    init_temp=Qty(value=init_temp, min_val=-0.001, max_val=0.22, unit='K')\n",
    ")\n",
    "\n",
    "model = Mdl(\n",
    "    [q1, q2], # Individual, self-contained components\n",
    "    [drive1, drive2, q1q2],  # Interactions between components\n",
    "    [init_ground] # SPAM processing\n",
    ")\n",
    "model.set_lindbladian(False)\n",
    "model.set_dressed(True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Control signals\n",
    "The devices for the control line are set up"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-10T13:45:05.684014Z",
     "start_time": "2020-06-10T13:45:04.441825Z"
    }
   },
   "outputs": [],
   "source": [
    "sim_res = 100e9 # Resolution for numerical simulation\n",
    "awg_res = 2e9 # Realistic, limited resolution of an AWG\n",
    "v2hz = 1e9\n",
    "\n",
    "lo = devices.LO(name='lo', resolution=sim_res)\n",
    "awg = devices.AWG(name='awg', resolution=awg_res)\n",
    "mixer = devices.Mixer(name='mixer')\n",
    "resp = devices.Response(\n",
    "    name='resp',\n",
    "    rise_time=Qty(value=0.3e-9, min_val=0.05e-9, max_val=0.6e-9, unit='s'),\n",
    "    resolution=sim_res\n",
    ")\n",
    "dig_to_an = devices.DigitalToAnalog(name=\"dac\", resolution=sim_res)\n",
    "v_to_hz = devices.VoltsToHertz(\n",
    "    name='v_to_hz',\n",
    "    V_to_Hz=Qty(value=v2hz, min_val=0.9e9, max_val=1.1e9, unit='Hz/V')\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The generator combines the parts of the signal generation and assignes a signal chain to each control line."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-10T13:45:05.684014Z",
     "start_time": "2020-06-10T13:45:04.441825Z"
    }
   },
   "outputs": [],
   "source": [
    "generator = Gnr(\n",
    "        devices={\n",
    "            \"LO\": lo,\n",
    "            \"AWG\": awg,\n",
    "            \"DigitalToAnalog\": dig_to_an,\n",
    "            \"Response\": resp,\n",
    "            \"Mixer\": mixer,\n",
    "            \"VoltsToHertz\": v_to_hz\n",
    "        },\n",
    "        chains={\n",
    "            \"d1\": [\"LO\", \"AWG\", \"DigitalToAnalog\", \"Response\", \"Mixer\", \"VoltsToHertz\"],\n",
    "            \"d2\": [\"LO\", \"AWG\", \"DigitalToAnalog\", \"Response\", \"Mixer\", \"VoltsToHertz\"]\n",
    "        }\n",
    "    )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Gates-set and Parameter map\n",
    "Both qubits will be resonantly driven with a Gaussian envelope."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-10T13:45:05.684014Z",
     "start_time": "2020-06-10T13:45:04.441825Z"
    }
   },
   "outputs": [],
   "source": [
    "t_final = 7e-9\n",
    "sideband = 50e6 \n",
    "gauss_params_single = {\n",
    "    'amp': Qty(value=0.5, min_val=0.2, max_val=0.6, unit=\"V\"),\n",
    "    't_final': Qty(value=t_final, min_val=0.5 * t_final, max_val=1.5 * t_final, unit=\"s\"),\n",
    "    'sigma': Qty(value=t_final / 4, min_val=t_final / 8, max_val=t_final / 2, unit=\"s\"),\n",
    "    'xy_angle': Qty(value=0.0, min_val=-0.5 * np.pi, max_val=2.5 * np.pi, unit='rad'),\n",
    "    'freq_offset': Qty(value=-sideband - 3e6, min_val=-56 * 1e6, max_val=-52 * 1e6, unit='Hz 2pi'),\n",
    "    'delta': Qty(value=-1, min_val=-5, max_val=3, unit=\"\")\n",
    "}\n",
    "\n",
    "gauss_env_single_1 = pulse.Envelope(\n",
    "    name=\"gauss1\",\n",
    "    desc=\"Gaussian envelope on drive 1\",\n",
    "    params=gauss_params_single,\n",
    "    shape=envelopes.gaussian_nonorm\n",
    ")\n",
    "gauss_env_single_2 = pulse.Envelope(\n",
    "    name=\"gauss2\",\n",
    "    desc=\"Gaussian envelope on drive 2\",\n",
    "    params=copy.deepcopy(gauss_params_single),\n",
    "    shape=envelopes.gaussian_nonorm\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The carrier signal of each drive is set to the resonance frequency\n",
    "of the corresponding qubit."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-10T13:45:05.684014Z",
     "start_time": "2020-06-10T13:45:04.441825Z"
    }
   },
   "outputs": [],
   "source": [
    "lo_freq_q1 = freq_q1 + sideband\n",
    "carr_1 = pulse.Carrier(\n",
    "    name=\"carrier\",\n",
    "    desc=\"Carrier on drive 1\",\n",
    "    params={\n",
    "        'freq': Qty(value=lo_freq_q1, min_val=0.9 * lo_freq_q1, max_val=1.1 * lo_freq_q1, unit='Hz 2pi'),\n",
    "        'framechange': Qty(value=0.0, min_val=-np.pi, max_val=3 * np.pi, unit='rad')\n",
    "    }\n",
    ")\n",
    "\n",
    "lo_freq_q2 = freq_q2 + sideband\n",
    "carr_2 = pulse.Carrier(\n",
    "    name=\"carrier\",\n",
    "    desc=\"Carrier on drive 2\",\n",
    "    params={\n",
    "        'freq': Qty(value=lo_freq_q2, min_val=0.9 * lo_freq_q2, max_val=1.1 * lo_freq_q2, unit='Hz 2pi'),\n",
    "        'framechange': Qty(value=0.0, min_val=-np.pi, max_val=3 * np.pi, unit='rad')\n",
    "    }\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Instructions\n",
    "The instruction to be optimised is a CNOT gates controlled by qubit 1."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-10T13:45:05.684014Z",
     "start_time": "2020-06-10T13:45:04.441825Z"
    }
   },
   "outputs": [],
   "source": [
    "# CNOT comtrolled by qubit 1\n",
    "cnot12 = gates.Instruction(\n",
    "    name=\"cnot12\", targets=[0, 1], t_start=0.0, t_end=t_final, channels=[\"d1\", \"d2\"],\n",
    "    ideal=np.array([\n",
    "        [1,0,0,0],\n",
    "        [0,1,0,0],\n",
    "        [0,0,0,1],\n",
    "        [0,0,1,0]\n",
    "    ])\n",
    ")\n",
    "cnot12.add_component(gauss_env_single_1, \"d1\")\n",
    "cnot12.add_component(carr_1, \"d1\")\n",
    "cnot12.add_component(gauss_env_single_2, \"d2\")\n",
    "cnot12.add_component(carr_2, \"d2\")\n",
    "cnot12.comps[\"d1\"][\"carrier\"].params[\"framechange\"].set_value(\n",
    "    (-sideband * t_final) * 2 * np.pi % (2 * np.pi)\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### The experiment\n",
    "All components are collected in the parameter map and the experiment is set up."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-10T13:45:05.684014Z",
     "start_time": "2020-06-10T13:45:04.441825Z"
    }
   },
   "outputs": [],
   "source": [
    "parameter_map = PMap(instructions=[cnot12], model=model, generator=generator)\n",
    "exp = Exp(pmap=parameter_map)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Calculate and print the propagator before the optimisation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "tf.Tensor(\n",
      "[[ 2.90040286e-01+0.06796916j -9.05419295e-02-0.44005323j\n",
      "   3.32932691e-02+0.02624818j  1.83699230e-02-0.4519875j\n",
      "  -6.87075560e-01+0.11948446j  3.30388750e-02-0.07559797j\n",
      "   5.12968176e-02+0.03489245j  4.00691980e-02-0.06469375j\n",
      "   2.56872145e-03+0.01350305j]\n",
      " [-1.31456151e-01-0.43111727j  2.26936794e-01-0.20111687j\n",
      "   1.91084183e-02-0.01480484j -6.51684826e-01+0.24723886j\n",
      "  -2.47467811e-01-0.3840622j  -3.20181777e-02-0.00415827j\n",
      "   1.46942329e-02-0.08169747j  4.25011406e-02+0.00106457j\n",
      "  -4.06200000e-03+0.00186351j]\n",
      " [ 3.78678020e-02-0.00179018j  2.76809420e-03-0.02315965j\n",
      "  -4.13538094e-01-0.33772374j -9.69947972e-03-0.07244919j\n",
      "  -5.30975369e-02+0.01107233j -2.52346729e-01+0.79596642j\n",
      "   8.22126812e-03+0.00440004j -3.55403231e-04-0.00818356j\n",
      "  -3.93164689e-02-0.07564104j]\n",
      " [-3.46355245e-01+0.29125939j  5.89368247e-01+0.37203659j\n",
      "  -6.51961274e-02+0.00734386j -2.31070430e-01-0.182206j\n",
      "  -2.55521484e-01+0.38035364j -2.33895953e-02-0.05274812j\n",
      "  -2.81575528e-02+0.02641964j  3.08826166e-02+0.05269581j\n",
      "   3.29263144e-04+0.00563204j]\n",
      " [ 5.91929721e-01+0.36442811j -1.10400754e-01+0.44309809j\n",
      "   2.93850138e-02+0.04873209j -2.12723842e-01+0.40645443j\n",
      "  -2.76142184e-01-0.11497212j -2.11191992e-02+0.03398605j\n",
      "   3.62913577e-02+0.03056929j -2.37617310e-02+0.01633795j\n",
      "  -5.92571600e-03+0.01999525j]\n",
      " [-4.93145510e-02+0.07007041j  2.49429187e-02+0.00473892j\n",
      "   7.64049641e-01-0.33605327j -5.20743576e-02-0.03270246j\n",
      "   5.71777817e-03+0.0273477j   3.81010149e-01+0.37777146j\n",
      "   2.96257183e-03+0.00452817j -4.96636736e-03+0.00508481j\n",
      "   5.14540480e-02+0.01186775j]\n",
      " [-1.79229744e-02+0.06387697j  9.01881856e-02-0.00591019j\n",
      "  -7.40758132e-03+0.00576899j  2.92000888e-02-0.01302864j\n",
      "  -1.45902044e-02-0.03226958j  1.15117575e-03-0.00514899j\n",
      "   2.37089484e-01-0.46819796j -7.27638732e-01-0.41711908j\n",
      "   7.41651067e-02-0.0258729j ]\n",
      " [ 8.29132270e-02+0.00837308j  1.59064811e-02+0.04661615j\n",
      "   9.64368638e-03+0.00170216j -1.38408342e-02-0.04443097j\n",
      "   1.61003315e-02-0.00407821j  7.04992162e-03+0.00120346j\n",
      "  -7.71513780e-01-0.32662086j  2.32631427e-01-0.47838175j\n",
      "  -2.43539508e-02-0.05065904j]\n",
      " [-1.18817139e-03+0.00218983j  1.08118605e-02-0.00401908j\n",
      "   6.04382648e-02-0.06681276j  1.36747414e-02-0.00111907j\n",
      "   7.32825969e-03+0.01292438j -3.65918454e-02-0.02609693j\n",
      "   4.43034429e-02-0.07812736j -3.15525737e-02-0.01770467j\n",
      "  -9.41975117e-01+0.30433893j]], shape=(9, 9), dtype=complex128)\n"
     ]
    }
   ],
   "source": [
    "unitaries = exp.compute_propagators()\n",
    "print(unitaries[cnot12.get_key()])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Dynamics\n",
    "\n",
    "The system is initialised in the state $|0,1\\rangle$ so that a transition to $|1,1\\rangle$ should be visible."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "tf.Tensor(\n",
      "[[0.+0.j]\n",
      " [1.+0.j]\n",
      " [0.+0.j]\n",
      " [0.+0.j]\n",
      " [0.+0.j]\n",
      " [0.+0.j]\n",
      " [0.+0.j]\n",
      " [0.+0.j]\n",
      " [0.+0.j]], shape=(9, 1), dtype=complex128)\n"
     ]
    }
   ],
   "source": [
    "psi_init = [[0] * 9]\n",
    "psi_init[0][1] = 1\n",
    "init_state = tf.transpose(tf.constant(psi_init, tf.complex128))\n",
    "print(init_state)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "def plot_dynamics(exp, psi_init, seq, goal=-1):\n",
    "        \"\"\"\n",
    "        Plotting code for time-resolved populations.\n",
    "\n",
    "        Parameters\n",
    "        ----------\n",
    "        psi_init: tf.Tensor\n",
    "            Initial state or density matrix.\n",
    "        seq: list\n",
    "            List of operations to apply to the initial state.\n",
    "        goal: tf.float64\n",
    "            Value of the goal function, if used.\n",
    "        debug: boolean\n",
    "            If true, return a matplotlib figure instead of saving.\n",
    "        \"\"\"\n",
    "        model = exp.pmap.model\n",
    "        dUs = exp.partial_propagators\n",
    "        psi_t = psi_init.numpy()\n",
    "        pop_t = exp.populations(psi_t, model.lindbladian)\n",
    "        for gate in seq:\n",
    "            for du in dUs[gate]:\n",
    "                psi_t = np.matmul(du.numpy(), psi_t)\n",
    "                pops = exp.populations(psi_t, model.lindbladian)\n",
    "                pop_t = np.append(pop_t, pops, axis=1)\n",
    "\n",
    "        fig, axs = plt.subplots(1, 1)\n",
    "        ts = exp.ts\n",
    "        dt = ts[1] - ts[0]\n",
    "        ts = np.linspace(0.0, dt*pop_t.shape[1], pop_t.shape[1])\n",
    "        axs.plot(ts / 1e-9, pop_t.T)\n",
    "        axs.grid(linestyle=\"--\")\n",
    "        axs.tick_params(\n",
    "            direction=\"in\", left=True, right=True, top=True, bottom=True\n",
    "        )\n",
    "        axs.set_xlabel('Time [ns]')\n",
    "        axs.set_ylabel('Population')\n",
    "        plt.legend(model.state_labels)\n",
    "        pass\n",
    "\n",
    "def getQubitsPopulation(population: np.array, dims: List[int]) -> np.array:\n",
    "    \"\"\"\n",
    "    Splits the population of all levels of a system into the populations of levels per subsystem.\n",
    "    Parameters\n",
    "    ----------\n",
    "    population: np.array\n",
    "        The time dependent population of each energy level. First dimension: level index, second dimension: time.\n",
    "    dims: List[int]\n",
    "        The number of levels for each subsystem.\n",
    "    Returns\n",
    "    -------\n",
    "    np.array\n",
    "        The time-dependent population of energy levels for each subsystem. First dimension: subsystem index, second\n",
    "        dimension: level index, third dimension: time.\n",
    "    \"\"\"\n",
    "    numQubits = len(dims)\n",
    "\n",
    "    # create a list of all levels\n",
    "    qubit_levels = []\n",
    "    for dim in dims:\n",
    "        qubit_levels.append(list(range(dim)))\n",
    "    combined_levels = list(itertools.product(*qubit_levels))\n",
    "\n",
    "    # calculate populations\n",
    "    qubitsPopulations = np.zeros((numQubits, dims[0], population.shape[1]))\n",
    "    for idx, levels in enumerate(combined_levels):\n",
    "        for i in range(numQubits):\n",
    "            qubitsPopulations[i, levels[i]] += population[idx]\n",
    "    return qubitsPopulations\n",
    "\n",
    "def plotSplittedPopulation(\n",
    "    exp: Exp,\n",
    "    psi_init: tf.Tensor,\n",
    "    sequence: List[str],\n",
    "    filename: str = None\n",
    ") -> None:\n",
    "    \"\"\"\n",
    "    Plots time dependent populations for multiple qubits in separate plots.\n",
    "    Parameters\n",
    "    ----------\n",
    "    exp: Experiment\n",
    "        The experiment containing the model and propagators\n",
    "    psi_init: np.array\n",
    "        Initial state vector\n",
    "    sequence: List[str]\n",
    "        List of gate names that will be applied to the state\n",
    "    -------\n",
    "    \"\"\"\n",
    "    # calculate the time dependent level population\n",
    "    model = exp.pmap.model\n",
    "    dUs = exp.partial_propagators\n",
    "    psi_t = psi_init.numpy()\n",
    "    pop_t = exp.populations(psi_t, model.lindbladian)\n",
    "    for gate in sequence:\n",
    "        for du in dUs[gate]:\n",
    "            psi_t = np.matmul(du, psi_t)\n",
    "            pops = exp.populations(psi_t, model.lindbladian)\n",
    "            pop_t = np.append(pop_t, pops, axis=1)\n",
    "    dims = [s.hilbert_dim for s in model.subsystems.values()]\n",
    "    splitted = getQubitsPopulation(pop_t, dims)\n",
    "\n",
    "    # timestamps\n",
    "    dt = exp.ts[1] - exp.ts[0]\n",
    "    ts = np.linspace(0.0, dt * pop_t.shape[1], pop_t.shape[1])\n",
    "\n",
    "    # create both subplots\n",
    "    fig, axs = plt.subplots(1, len(splitted), sharey=\"all\")\n",
    "    for idx, ax in enumerate(axs):\n",
    "        ax.plot(ts / 1e-9, splitted[idx].T)\n",
    "        ax.tick_params(direction=\"in\", left=True, right=True, top=False, bottom=True)\n",
    "        ax.set_xlabel(\"Time [ns]\")\n",
    "        ax.set_ylabel(\"Population\")\n",
    "        ax.legend([str(x) for x in np.arange(dims[idx])])\n",
    "        ax.grid()\n",
    "\n",
    "    plt.tight_layout()\n",
    "    if filename:\n",
    "        plt.savefig(filename)\n",
    "    plt.show()\n",
    "\n",
    "sequence = [cnot12.get_key()]\n",
    "plot_dynamics(exp, init_state, sequence)\n",
    "#plot_dynamics(exp, init_state, sequence * 10)\n",
    "plotSplittedPopulation(exp, init_state, sequence, filename=\"dynamics_before.png\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Open-loop optimal control\n",
    "\n",
    "Now, open-loop optimisation with DRAG enabled is set up."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "cnot12[0, 1]-d1-gauss1-amp            : 500.000 mV \n",
      "cnot12[0, 1]-d1-gauss1-freq_offset    : -53.000 MHz 2pi \n",
      "cnot12[0, 1]-d1-gauss1-xy_angle       : -444.089 arad \n",
      "cnot12[0, 1]-d1-gauss1-delta          : -1.000  \n",
      "cnot12[0, 1]-d1-carrier-framechange   : 4.084 rad \n",
      "cnot12[0, 1]-d2-gauss2-amp            : 500.000 mV \n",
      "cnot12[0, 1]-d2-gauss2-freq_offset    : -53.000 MHz 2pi \n",
      "cnot12[0, 1]-d2-gauss2-xy_angle       : -444.089 arad \n",
      "cnot12[0, 1]-d2-gauss2-delta          : -1.000  \n",
      "cnot12[0, 1]-d2-carrier-framechange   : 0.000 rad \n",
      "\n"
     ]
    }
   ],
   "source": [
    "generator.devices['AWG'].enable_drag_2()\n",
    "\n",
    "opt_gates = [cnot12.get_key()]\n",
    "exp.set_opt_gates(opt_gates)\n",
    "\n",
    "gateset_opt_map=[\n",
    "    [(cnot12.get_key(), \"d1\", \"gauss1\", \"amp\")],\n",
    "    [(cnot12.get_key(), \"d1\", \"gauss1\", \"freq_offset\")],\n",
    "    [(cnot12.get_key(), \"d1\", \"gauss1\", \"xy_angle\")],\n",
    "    [(cnot12.get_key(), \"d1\", \"gauss1\", \"delta\")],\n",
    "    [(cnot12.get_key(), \"d1\", \"carrier\", \"framechange\")],\n",
    "    [(cnot12.get_key(), \"d2\", \"gauss2\", \"amp\")],\n",
    "    [(cnot12.get_key(), \"d2\", \"gauss2\", \"freq_offset\")],\n",
    "    [(cnot12.get_key(), \"d2\", \"gauss2\", \"xy_angle\")],\n",
    "    [(cnot12.get_key(), \"d2\", \"gauss2\", \"delta\")],\n",
    "    [(cnot12.get_key(), \"d2\", \"carrier\", \"framechange\")]\n",
    "]\n",
    "parameter_map.set_opt_map(gateset_opt_map)\n",
    "\n",
    "parameter_map.print_parameters()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As a fidelity function we choose average fidelity as well as LBFG-S (a wrapper of the scipy implementation) from our library."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "import os\n",
    "import tempfile\n",
    "from c3.optimizers.optimalcontrol import OptimalControl\n",
    "\n",
    "log_dir = os.path.join(tempfile.TemporaryDirectory().name, \"c3logs\")\n",
    "# increase maxfevals to 500+ for better results\n",
    "opt = OptimalControl(\n",
    "    dir_path=log_dir,\n",
    "    fid_func=fidelities.average_infid_set,\n",
    "    fid_subspace=[\"Q1\", \"Q2\"],\n",
    "    pmap=parameter_map,\n",
    "    algorithm=algorithms.cmaes,\n",
    "    options={\n",
    "        \"popsize\": 15,\n",
    "        \"maxfevals\": 100\n",
    "    },\n",
    "    run_name=\"cnot12\"\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Start the optimisation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "C3:STATUS:Saving as: /tmp/tmpskwo3xlm/c3logs/cnot12/2021_12_06_T_22_24_59/open_loop.log\n",
      "(7_w,15)-aCMA-ES (mu_w=4.5,w_1=34%) in dimension 10 (seed=964937, Mon Dec  6 22:24:59 2021)\n",
      "Iterat #Fevals   function value  axis ratio  sigma  min&max std  t[m:s]\n",
      "    1     15 7.326344256215179e-01 1.0e+00 8.85e-02  8e-02  9e-02 0:13.8\n",
      "    2     30 7.367559004446577e-01 1.2e+00 8.75e-02  8e-02  1e-01 0:27.4\n",
      "    3     45 7.139157246650509e-01 1.3e+00 9.55e-02  9e-02  1e-01 0:40.8\n",
      "    4     60 6.952586691625754e-01 1.5e+00 1.04e-01  9e-02  1e-01 0:54.5\n",
      "    5     75 6.691554889600820e-01 1.8e+00 1.13e-01  1e-01  2e-01 1:08.0\n",
      "    6     90 6.642503941891256e-01 1.9e+00 1.22e-01  1e-01  2e-01 1:21.7\n",
      "    7    105 6.754441193654891e-01 1.9e+00 1.22e-01  1e-01  2e-01 1:35.7\n",
      "termination on maxfevals=100\n",
      "final/bestever f-value = 6.754441e-01 6.642504e-01\n",
      "incumbent solution: [ 0.29354993  0.43400975 -0.62646119  0.04613593 -0.31716057  0.26852775\n",
      "  0.54834962 -0.64817835 ...]\n",
      "std deviations: [0.12406951 0.11915925 0.1206521  0.11160312 0.16109297 0.13345903\n",
      " 0.11291629 0.10293621 ...]\n"
     ]
    }
   ],
   "source": [
    "exp.set_opt_gates(opt_gates)\n",
    "opt.set_exp(exp)\n",
    "opt.optimize_controls()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The final parameters and the fidelity are"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "cnot12[0, 1]-d1-gauss1-amp            : 461.437 mV \n",
      "cnot12[0, 1]-d1-gauss1-freq_offset    : -52.704 MHz 2pi \n",
      "cnot12[0, 1]-d1-gauss1-xy_angle       : 355.730 mrad \n",
      "cnot12[0, 1]-d1-gauss1-delta          : -1.058  \n",
      "cnot12[0, 1]-d1-carrier-framechange   : 827.654 mrad \n",
      "cnot12[0, 1]-d2-gauss2-amp            : 428.475 mV \n",
      "cnot12[0, 1]-d2-gauss2-freq_offset    : -53.037 MHz 2pi \n",
      "cnot12[0, 1]-d2-gauss2-xy_angle       : 73.836 mrad \n",
      "cnot12[0, 1]-d2-gauss2-delta          : -484.207 m \n",
      "cnot12[0, 1]-d2-carrier-framechange   : 120.479 mrad \n",
      "\n",
      "0.6642503941891256\n"
     ]
    }
   ],
   "source": [
    "parameter_map.print_parameters()\n",
    "print(opt.current_best_goal)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Results of the optimisation\n",
    "Plotting the dynamics with the same initial state:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_dynamics(exp, init_state, sequence)\n",
    "plotSplittedPopulation(exp, init_state, sequence, filename=\"dynamics_after.png\")"
   ]
  }
 ],
 "metadata": {
  "interpreter": {
   "hash": "8fc56ae400e717d872a76f4d6b257151d16696a9d0a72e6998d355f9b43887c7"
  },
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.12"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}