CrossResonance_Tomography_SIMULATED.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import time\n",
    "from collections import namedtuple\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "import qiskit as q\n",
    "import qiskit.tools.jupyter\n",
    "from qiskit.pulse import pulse_lib as _  # only want to call pulse_lib as q.pulse.pulse_lib\n",
    "from qiskit.test.mock import FakeAlmaden\n",
    "from qiskit.ignis.verification.tomography.data import marginal_counts"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pulse_compiler_helper_fns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/pranavgokhale/Developer/qiskit/qiskit-terra/qiskit/pulse/channels/pulse_channel_spec.py:87: DeprecationWarning: The PulseChannelSpec is deprecated. Use backend.configuration() instead. The supported methods require some migrations; check out the release notes for the complete details.\n",
      "  DeprecationWarning)\n",
      "/Users/pranavgokhale/Developer/qiskit/qiskit-terra/qiskit/providers/models/backendconfiguration.py:363: UserWarning: `dt` and `dtm` now have units of seconds(s) rather than nanoseconds(ns).\n",
      "  warnings.warn('`dt` and `dtm` now have units of seconds(s) rather '\n",
      "/Users/pranavgokhale/Developer/qiskit/qiskit-terra/qiskit/pulse/cmd_def.py:66: DeprecationWarning: The CmdDef is being deprecated. All CmdDef methods are now supported by `InstructionScheduleMap` accessible as `backend.defaults().circuit_instruction_map` for any Pulse enabled system.\n",
      "  DeprecationWarning)\n"
     ]
    }
   ],
   "source": [
    "backend = FakeAlmaden()\n",
    "system = q.pulse.PulseChannelSpec.from_backend(backend)\n",
    "back_config = backend.configuration().to_dict()\n",
    "cmd_def = q.pulse.CmdDef.from_defaults(backend.defaults().cmd_def, backend.defaults().pulse_library)\n",
    "measure = cmd_def.get('measure', qubits=backend.configuration().meas_map[0])\n",
    "backend_sim = qiskit.Aer.get_backend('pulse_simulator')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "hamiltonian = {}\n",
    "hamiltonian['h_str'] = ['_SUM[i,0,1,wq{i}/2*(I{i}-Z{i})]', '_SUM[i,0,1,omegad{i}*X{i}||D{i}]',\n",
    "                        'jq0q1*Sp0*Sm1', 'jq0q1*Sm0*Sp1', 'omegad1*X0||U0', 'omegad0*X1||U1']\n",
    "hamiltonian['qub'] = {'0': 2, '1': 2}\n",
    "hamiltonian['vars'] = {'wq0': 30.518812656662774, 'wq1': 31.238229295532093,\n",
    "                       'omegad0': 0.1675, 'omegad1': 0.176,\n",
    "                       'jq0q1': -0.0069}\n",
    "\n",
    "back_config['hamiltonian'] = hamiltonian\n",
    "back_config['noise'] = {}\n",
    "back_config['dt'] = 1.0\n",
    "back_config['ode_options'] = {}\n",
    "back_config['qubit_list'] = [0,1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Measure X on target\n",
    "x_schedules = []\n",
    "for theta in np.linspace(0, np.pi, 41, endpoint=True):\n",
    "    schedule = pulse_compiler_helper_fns.get_cr_schedule(theta, 0, 1, cmd_def, system) \n",
    "    schedule |= cmd_def.get('u2', qubits=[1], P0=0, P1=np.pi) << schedule.duration\n",
    "    schedule = schedule.filter(channels=[system.qubits[0].drive, system.qubits[1].drive, system.controls[0]])\n",
    "    schedule |= measure << schedule.duration\n",
    "    x_schedules.append(schedule)\n",
    "    \n",
    "# do same thing, but first flip \n",
    "for theta in np.linspace(0, np.pi, 41, endpoint=True):\n",
    "    schedule = cmd_def.get('x', qubits=[0])\n",
    "    schedule |= pulse_compiler_helper_fns.get_cr_schedule(theta, 0, 1, cmd_def, system) << schedule.duration\n",
    "    schedule |= cmd_def.get('u2', qubits=[1], P0=0, P1=np.pi) << schedule.duration\n",
    "    schedule = schedule.filter(channels=[system.qubits[0].drive, system.qubits[1].drive, system.controls[0]])\n",
    "    schedule |= measure << schedule.duration\n",
    "    x_schedules.append(schedule)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "shots = 1000"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "qobj = q.assemble(x_schedules, backend, \n",
    "                       meas_level=1, meas_return='avg', \n",
    "                       memory_slots=2,\n",
    "                       shots=shots, sim_config = back_config)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.        , 4.85720941, 4.97172909, 9.82893851])"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "evals, estates = backend_sim.get_dressed_energies(qobj)\n",
    "evals/2/np.pi"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Measure Y on target\n",
    "y_schedules = []\n",
    "for theta in np.linspace(0, np.pi, 41, endpoint=True):\n",
    "    schedule = pulse_compiler_helper_fns.get_cr_schedule(theta, 0, 1, cmd_def, system)\n",
    "    schedule |= cmd_def.get('u1', qubits=[1], P0=-np.pi/2) << schedule.duration\n",
    "    schedule |= cmd_def.get('u2', qubits=[1], P0=0, P1=np.pi) << schedule.duration\n",
    "    schedule = schedule.filter(channels=[system.qubits[0].drive, system.qubits[1].drive, system.controls[0]])\n",
    "    schedule |= measure << schedule.duration\n",
    "    y_schedules.append(schedule)\n",
    "    \n",
    "# do same thing, but first flip \n",
    "for theta in np.linspace(0, np.pi, 41, endpoint=True):\n",
    "    schedule = cmd_def.get('x', qubits=[0])\n",
    "    schedule |= pulse_compiler_helper_fns.get_cr_schedule(theta, 0, 1, cmd_def, system) << schedule.duration\n",
    "    schedule |= cmd_def.get('u1', qubits=[1], P0=-np.pi/2) << schedule.duration\n",
    "    schedule |= cmd_def.get('u2', qubits=[1], P0=0, P1=np.pi) << schedule.duration\n",
    "    schedule = schedule.filter(channels=[system.qubits[0].drive, system.qubits[1].drive, system.controls[0]])\n",
    "    schedule |= measure << schedule.duration\n",
    "    y_schedules.append(schedule)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Measure Z on target\n",
    "z_schedules = []\n",
    "for theta in np.linspace(0, np.pi, 41, endpoint=True):\n",
    "    schedule = pulse_compiler_helper_fns.get_cr_schedule(theta, 0, 1, cmd_def, system)\n",
    "    schedule = schedule.filter(channels=[system.qubits[0].drive, system.qubits[1].drive, system.controls[0]])\n",
    "    schedule |= measure << schedule.duration\n",
    "    z_schedules.append(schedule)\n",
    "    \n",
    "# do same thing, but first flip \n",
    "for theta in np.linspace(0, np.pi, 41, endpoint=True):\n",
    "    schedule = cmd_def.get('x', qubits=[0])\n",
    "    schedule |= pulse_compiler_helper_fns.get_cr_schedule(theta, 0, 1, cmd_def, system) << schedule.duration\n",
    "    schedule = schedule.filter(channels=[system.qubits[0].drive, system.qubits[1].drive, system.controls[0]])\n",
    "    schedule |= measure << schedule.duration\n",
    "    z_schedules.append(schedule)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "shots = 10000\n",
    "\n",
    "qobj = q.assemble(x_schedules, backend, \n",
    "                     qubit_lo_freq = [evals[1]/2/np.pi, evals[2]/2/np.pi],\n",
    "                     shots=shots, sim_config = back_config)\n",
    "x_result = backend_sim.run(qobj).result()\n",
    "\n",
    "qobj = q.assemble(y_schedules, backend, \n",
    "                     qubit_lo_freq = [evals[1]/2/np.pi, evals[2]/2/np.pi],\n",
    "                     shots=shots, sim_config = back_config)\n",
    "y_result = backend_sim.run(qobj).result()\n",
    "\n",
    "qobj = q.assemble(z_schedules, backend, \n",
    "                     qubit_lo_freq = [evals[1]/2/np.pi, evals[2]/2/np.pi],\n",
    "                     shots=shots, sim_config = back_config)\n",
    "z_result = backend_sim.run(qobj).result()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "from qiskit.ignis.verification.tomography.data import marginal_counts"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[-0.01959999999999995, 0.01760000000000006, 0.045600000000000085, 0.0616000000000001, 0.07919999999999994, 0.0633999999999999, 0.05380000000000007, 0.04519999999999991, 0.02320000000000011, -0.0016000000000000458, -0.03979999999999995, -0.07040000000000002, -0.0806, -0.10799999999999998, -0.12980000000000003, -0.14680000000000004, -0.15080000000000005, -0.135, -0.12780000000000002, -0.09040000000000004, -0.06620000000000004, -0.045399999999999996, -0.028200000000000003, -0.018000000000000016, -0.0010000000000000009, 0.024799999999999933, 0.023600000000000065, -0.00039999999999995595, -0.027599999999999958, -0.009199999999999986, -0.041200000000000014, -0.0746, -0.09960000000000002, -0.12160000000000004, -0.123, -0.12139999999999995, -0.10860000000000003, -0.08699999999999997, -0.08440000000000003, -0.05379999999999996, -0.025800000000000045]\n",
      "[0.0023999999999999577, -0.015199999999999991, -0.04479999999999995, -0.06000000000000005, -0.09219999999999995, -0.08479999999999999, -0.10260000000000002, -0.10699999999999998, -0.07820000000000005, -0.10160000000000002, -0.07540000000000002, -0.06000000000000005, -0.058599999999999985, -0.03520000000000001, -0.014599999999999946, -0.0033999999999999586, 0.013600000000000056, 0.040999999999999925, 0.052999999999999936, 0.04919999999999991, 0.05840000000000001, 0.05360000000000009, 0.031400000000000095, 0.05139999999999989, 0.023600000000000065, -0.0030000000000000027, -0.007199999999999984, -0.018199999999999994, -0.043200000000000016, -0.039000000000000035, -0.09219999999999995, -0.09060000000000001, -0.09360000000000002, -0.09899999999999998, -0.10219999999999996, -0.0766, -0.07679999999999998, -0.0494, -0.041000000000000036, -0.031200000000000006, -0.016599999999999948]\n"
     ]
    }
   ],
   "source": [
    "x_vals_control_off = []\n",
    "for i in range(41):\n",
    "    x_counts = marginal_counts(x_result.get_counts(i), meas_qubits=[1])\n",
    "    x_vals_control_off.append((x_counts.get('0', 0) / shots - 0.5) * 2)\n",
    "\n",
    "x_vals_control_on = []\n",
    "for i in range(41, 82):\n",
    "    x_counts = marginal_counts(x_result.get_counts(i), meas_qubits=[1])\n",
    "    x_vals_control_on.append((x_counts.get('0', 0) / shots - 0.5) * 2)\n",
    "\n",
    "print(x_vals_control_off)\n",
    "print(x_vals_control_on)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.004999999999999893, -0.08340000000000003, -0.17459999999999998, -0.23839999999999995, -0.31679999999999997, -0.3808, -0.482, -0.5254, -0.6033999999999999, -0.6562, -0.7014, -0.7598, -0.7946, -0.848, -0.8852, -0.9164, -0.9446, -0.9626, -0.981, -0.9898, -0.9982, -0.996, -0.9902, -0.9746, -0.9518, -0.9186, -0.889, -0.8642, -0.819, -0.7654, -0.7034, -0.6496, -0.5813999999999999, -0.521, -0.4646, -0.3862, -0.31120000000000003, -0.23740000000000006, -0.15600000000000003, -0.07999999999999996, 0.005800000000000027]\n",
      "[-0.0048000000000000265, 0.07679999999999998, 0.18179999999999996, 0.258, 0.30000000000000004, 0.3824000000000001, 0.46120000000000005, 0.5434000000000001, 0.5878000000000001, 0.6654, 0.7165999999999999, 0.7672000000000001, 0.812, 0.8566, 0.8957999999999999, 0.9328000000000001, 0.9548000000000001, 0.9742, 0.9876, 0.9956, 0.9974000000000001, 0.994, 0.9867999999999999, 0.9683999999999999, 0.95, 0.9204000000000001, 0.8928, 0.8500000000000001, 0.8056000000000001, 0.7547999999999999, 0.7092, 0.6464000000000001, 0.5788, 0.506, 0.4363999999999999, 0.3839999999999999, 0.3086, 0.24760000000000004, 0.17300000000000004, 0.06800000000000006, 0.011200000000000099]\n"
     ]
    }
   ],
   "source": [
    "y_vals_control_off = []\n",
    "for i in range(41):\n",
    "    y_counts = marginal_counts(y_result.get_counts(i), meas_qubits=[1])\n",
    "    y_vals_control_off.append((y_counts.get('0', 0) / shots - 0.5) * 2)\n",
    "\n",
    "y_vals_control_on = []\n",
    "for i in range(41, 82):\n",
    "    y_counts = marginal_counts(y_result.get_counts(i), meas_qubits=[1])\n",
    "    y_vals_control_on.append((y_counts.get('0', 0) / shots - 0.5) * 2)\n",
    "\n",
    "print(y_vals_control_off)\n",
    "print(y_vals_control_on)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1.0, 0.9967999999999999, 0.986, 0.9621999999999999, 0.937, 0.9179999999999999, 0.8854, 0.8582000000000001, 0.7969999999999999, 0.7647999999999999, 0.6943999999999999, 0.6414, 0.5884, 0.5138, 0.44520000000000004, 0.3819999999999999, 0.32200000000000006, 0.23459999999999992, 0.15860000000000007, 0.06879999999999997, 0.00019999999999997797, -0.08379999999999999, -0.17079999999999995, -0.24319999999999997, -0.3104, -0.3862, -0.44199999999999995, -0.525, -0.5800000000000001, -0.6492, -0.7083999999999999, -0.7662, -0.8, -0.8496, -0.8868, -0.9144, -0.9462, -0.9704, -0.9858, -0.9968, -0.9998]\n",
      "[1.0, 0.9956, 0.9872000000000001, 0.9718, 0.9505999999999999, 0.9184000000000001, 0.8844000000000001, 0.8395999999999999, 0.8033999999999999, 0.7502, 0.702, 0.6661999999999999, 0.5738000000000001, 0.51, 0.4628000000000001, 0.3972, 0.31820000000000004, 0.23140000000000005, 0.14100000000000001, 0.07499999999999996, 0.011200000000000099, -0.09099999999999997, -0.14780000000000004, -0.23399999999999999, -0.3134, -0.3954, -0.46199999999999997, -0.5184, -0.5798, -0.6606000000000001, -0.7026, -0.7584, -0.8118, -0.8476, -0.8896, -0.9174, -0.9518, -0.969, -0.9864, -0.9958, -1.0]\n"
     ]
    }
   ],
   "source": [
    "z_vals_control_off = []\n",
    "for i in range(41):\n",
    "    z_counts = marginal_counts(z_result.get_counts(i), meas_qubits=[1])\n",
    "    z_vals_control_off.append((z_counts.get('0', 0) / shots - 0.5) * 2)\n",
    "\n",
    "z_vals_control_on = []\n",
    "for i in range(41, 82):\n",
    "    z_counts = marginal_counts(z_result.get_counts(i), meas_qubits=[1])\n",
    "    z_vals_control_on.append((z_counts.get('0', 0) / shots - 0.5) * 2)\n",
    "\n",
    "print(z_vals_control_off)\n",
    "print(z_vals_control_on)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "x_vals_control_off = [-0.01959999999999995, 0.01760000000000006, 0.045600000000000085, 0.0616000000000001, 0.07919999999999994, 0.0633999999999999, 0.05380000000000007, 0.04519999999999991, 0.02320000000000011, -0.0016000000000000458, -0.03979999999999995, -0.07040000000000002, -0.0806, -0.10799999999999998, -0.12980000000000003, -0.14680000000000004, -0.15080000000000005, -0.135, -0.12780000000000002, -0.09040000000000004, -0.06620000000000004, -0.045399999999999996, -0.028200000000000003, -0.018000000000000016, -0.0010000000000000009, 0.024799999999999933, 0.023600000000000065, -0.00039999999999995595, -0.027599999999999958, -0.009199999999999986, -0.041200000000000014, -0.0746, -0.09960000000000002, -0.12160000000000004, -0.123, -0.12139999999999995, -0.10860000000000003, -0.08699999999999997, -0.08440000000000003, -0.05379999999999996, -0.025800000000000045]\n",
    "x_vals_control_on = [0.0023999999999999577, -0.015199999999999991, -0.04479999999999995, -0.06000000000000005, -0.09219999999999995, -0.08479999999999999, -0.10260000000000002, -0.10699999999999998, -0.07820000000000005, -0.10160000000000002, -0.07540000000000002, -0.06000000000000005, -0.058599999999999985, -0.03520000000000001, -0.014599999999999946, -0.0033999999999999586, 0.013600000000000056, 0.040999999999999925, 0.052999999999999936, 0.04919999999999991, 0.05840000000000001, 0.05360000000000009, 0.031400000000000095, 0.05139999999999989, 0.023600000000000065, -0.0030000000000000027, -0.007199999999999984, -0.018199999999999994, -0.043200000000000016, -0.039000000000000035, -0.09219999999999995, -0.09060000000000001, -0.09360000000000002, -0.09899999999999998, -0.10219999999999996, -0.0766, -0.07679999999999998, -0.0494, -0.041000000000000036, -0.031200000000000006, -0.016599999999999948]\n",
    "y_vals_control_off = [0.004999999999999893, -0.08340000000000003, -0.17459999999999998, -0.23839999999999995, -0.31679999999999997, -0.3808, -0.482, -0.5254, -0.6033999999999999, -0.6562, -0.7014, -0.7598, -0.7946, -0.848, -0.8852, -0.9164, -0.9446, -0.9626, -0.981, -0.9898, -0.9982, -0.996, -0.9902, -0.9746, -0.9518, -0.9186, -0.889, -0.8642, -0.819, -0.7654, -0.7034, -0.6496, -0.5813999999999999, -0.521, -0.4646, -0.3862, -0.31120000000000003, -0.23740000000000006, -0.15600000000000003, -0.07999999999999996, 0.005800000000000027]\n",
    "y_vals_control_on = [-0.0048000000000000265, 0.07679999999999998, 0.18179999999999996, 0.258, 0.30000000000000004, 0.3824000000000001, 0.46120000000000005, 0.5434000000000001, 0.5878000000000001, 0.6654, 0.7165999999999999, 0.7672000000000001, 0.812, 0.8566, 0.8957999999999999, 0.9328000000000001, 0.9548000000000001, 0.9742, 0.9876, 0.9956, 0.9974000000000001, 0.994, 0.9867999999999999, 0.9683999999999999, 0.95, 0.9204000000000001, 0.8928, 0.8500000000000001, 0.8056000000000001, 0.7547999999999999, 0.7092, 0.6464000000000001, 0.5788, 0.506, 0.4363999999999999, 0.3839999999999999, 0.3086, 0.24760000000000004, 0.17300000000000004, 0.06800000000000006, 0.011200000000000099]\n",
    "z_vals_control_off = [1.0, 0.9967999999999999, 0.986, 0.9621999999999999, 0.937, 0.9179999999999999, 0.8854, 0.8582000000000001, 0.7969999999999999, 0.7647999999999999, 0.6943999999999999, 0.6414, 0.5884, 0.5138, 0.44520000000000004, 0.3819999999999999, 0.32200000000000006, 0.23459999999999992, 0.15860000000000007, 0.06879999999999997, 0.00019999999999997797, -0.08379999999999999, -0.17079999999999995, -0.24319999999999997, -0.3104, -0.3862, -0.44199999999999995, -0.525, -0.5800000000000001, -0.6492, -0.7083999999999999, -0.7662, -0.8, -0.8496, -0.8868, -0.9144, -0.9462, -0.9704, -0.9858, -0.9968, -0.9998]\n",
    "z_vals_control_on = [1.0, 0.9956, 0.9872000000000001, 0.9718, 0.9505999999999999, 0.9184000000000001, 0.8844000000000001, 0.8395999999999999, 0.8033999999999999, 0.7502, 0.702, 0.6661999999999999, 0.5738000000000001, 0.51, 0.4628000000000001, 0.3972, 0.31820000000000004, 0.23140000000000005, 0.14100000000000001, 0.07499999999999996, 0.011200000000000099, -0.09099999999999997, -0.14780000000000004, -0.23399999999999999, -0.3134, -0.3954, -0.46199999999999997, -0.5184, -0.5798, -0.6606000000000001, -0.7026, -0.7584, -0.8118, -0.8476, -0.8896, -0.9174, -0.9518, -0.969, -0.9864, -0.9958, -1.0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "thetas = np.linspace(0, 180, 41, endpoint=True)\n",
    "dense_thetas = np.linspace(0, 180, 101, endpoint=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "plt.rcParams.update({'font.size': 14})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x180 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(6, 2.5))\n",
    "plt.plot(thetas, x_vals_control_off, label='Control |0>', linewidth=3)\n",
    "plt.plot(thetas, x_vals_control_on, label='Control |1>', linewidth=3)\n",
    "plt.plot(dense_thetas, [0] * 101, label='Ideal', color='black', linestyle='dashed', linewidth=3)\n",
    "plt.axis([0, 180, -1, 1])\n",
    "plt.yticks([-1, -.5, 0, .5, 1])\n",
    "plt.xticks([0, 45, 90, 135, 180])\n",
    "plt.legend(mode='expand', ncol=2, loc=2)\n",
    "plt.ylabel('<X> on Target')\n",
    "plt.savefig('Figures/CR_X_SIMULATED.svg', bbox_inches = \"tight\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x144 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(6, 2))\n",
    "plt.plot(thetas, y_vals_control_off, label='Control |0>', linewidth=3)\n",
    "plt.plot(thetas, y_vals_control_on, label='Control |1>', linewidth=3)\n",
    "plt.plot(dense_thetas, np.sin(dense_thetas*np.pi/180), label='Ideal', color='black', linestyle='dashed', linewidth=3)\n",
    "plt.plot(dense_thetas, -np.sin(dense_thetas*np.pi/180), label='Ideal', color='black', linestyle='dashed', linewidth=3)\n",
    "plt.axis([0, 180, -1, 1])\n",
    "plt.ylabel('<Y> on Target')\n",
    "plt.yticks([-1, -.5, 0, .5, 1])\n",
    "_=plt.xticks([0, 45, 90, 135, 180])\n",
    "plt.savefig('Figures/CR_Y_SIMULATED.svg', bbox_inches = \"tight\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x172.8 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(6, 2.4))\n",
    "plt.plot(thetas, [val - 0.05 for val in z_vals_control_off], label='Control |0>', linewidth=3)  # slightly offset to show color\n",
    "plt.plot(thetas, z_vals_control_on, label='Control |1>', linewidth=3)\n",
    "plt.plot(dense_thetas, np.cos(dense_thetas*np.pi/180), label='Ideal', color='black', linestyle='dashed', linewidth=3)\n",
    "plt.axis([0, 180, -1, 1])\n",
    "plt.ylabel('<Z> on Target')\n",
    "plt.yticks([-1, -.5, 0, .5, 1])\n",
    "_=plt.xticks([0, 45, 90, 135, 180])\n",
    "plt.xlabel('Θ in degrees')\n",
    "plt.gcf().subplots_adjust(bottom=.2)\n",
    "plt.savefig('Figures/CR_Z_SIMULATED.svg', bbox_inches = \"tight\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "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": "3.7.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}