rabi-flopping.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "d50d3c95",
   "metadata": {},
   "source": [
    "# Simulating Rabi flopping on a quantum computer"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4cec2002",
   "metadata": {},
   "source": [
    "## Setup\n",
    "\n",
    "First, make sure that you have the latest version of Qiskit installed. To upgrade your Qiskit package, run the following command:\n",
    "\n",
    "```bash\n",
    "pip install --upgrade qiskit\n",
    "```\n",
    "\n",
    "Get an API key from IonQ. This will be used by the IonQ provider inside Qiskit to submit circuits to the IonQ platform.\n",
    "\n",
    "After securing an API key, install the python package `qiskit_ionq` using `pip`:\n",
    "\n",
    "```bash\n",
    "pip install qiskit_ionq\n",
    "```\n",
    "\n",
    "(IonQ's adapter for Qiskit is currently in private beta -- your feedback is welcomed!)\n",
    "\n",
    "### (Optional) Extra Dependencies\n",
    "\n",
    "Some examples use additional Python dependencies; please make sure to `pip install` them as needed.\n",
    "\n",
    "Dependencies:\n",
    "* `matplotlib`: To run `qiskit.visualization.plot_histogram`.\n",
    "\n",
    "**NOTE**: The provider expects an API key to be supplied via the `token` keyword argument to its constructor. If no token is directly provided, the provider will check for one in the `QISKIT_IONQ_API_TOKEN` environment variable.\n",
    "\n",
    "Now that the Python package has been installed, you can import and instantiate the provider:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "id": "91ffee1a",
   "metadata": {},
   "outputs": [],
   "source": [
    "#import Aer here, before calling qiskit_ionq_provider\n",
    "from qiskit import Aer\n",
    "\n",
    "from qiskit_ionq import IonQProvider \n",
    "\n",
    "#Call provider and set token value\n",
    "provider = IonQProvider(token='my token')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bcbafdc0",
   "metadata": {},
   "source": [
    "The `provider` instance can now be used to create and submit circuits to IonQ.\n",
    "\n",
    "### Backend Types\n",
    "\n",
    "The IonQ provider supports two backend types:\n",
    "* `ionq_simulator`: IonQ's simulator backend.\n",
    "* `ionq_qpu`: IonQ's QPU backend.\n",
    "\n",
    "To view all current backend types, use the `.backends` property on the provider instance:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "id": "20e5ea5f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<IonQSimulatorBackend('ionq_simulator')>, <IonQQPUBackend('ionq_qpu')>]"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "provider.backends()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "86aa5fcb",
   "metadata": {},
   "source": [
    "### Let's create some circuits\n",
    "\n",
    "To simulate Rabi flopping on a quantum computing we need to apply single-qubit rotations of varying angle to a qubit. To avoid submitting multiple single-qubit circuits, we can utilize all availablbe ions and apply single-qubit rotations to each of them at once. The probability of the $\\left|1\\right>$ state will oscillate with the angle of rotation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "id": "aba7a97c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<pre style=\"word-wrap: normal;white-space: pre;background: #fff0;line-height: 1.1;font-family: &quot;Courier New&quot;,Courier,monospace\">       ┌─────────┐ \n",
       " q_0: ─┤ RX(π/3) ├─\n",
       "       ├─────────┴┐\n",
       " q_1: ─┤ RX(2π/3) ├\n",
       "       └┬───────┬─┘\n",
       " q_2: ──┤ RX(π) ├──\n",
       "       ┌┴───────┴─┐\n",
       " q_3: ─┤ RX(4π/3) ├\n",
       "       ├──────────┤\n",
       " q_4: ─┤ RX(5π/3) ├\n",
       "       └┬────────┬┘\n",
       " q_5: ──┤ RX(2π) ├─\n",
       "       ┌┴────────┴┐\n",
       " q_6: ─┤ RX(7π/3) ├\n",
       "       ├──────────┤\n",
       " q_7: ─┤ RX(8π/3) ├\n",
       "       └┬────────┬┘\n",
       " q_8: ──┤ RX(3π) ├─\n",
       "      ┌─┴────────┴┐\n",
       " q_9: ┤ RX(10π/3) ├\n",
       "      ├───────────┤\n",
       "q_10: ┤ RX(11π/3) ├\n",
       "      └───────────┘</pre>"
      ],
      "text/plain": [
       "       ┌─────────┐ \n",
       " q_0: ─┤ RX(π/3) ├─\n",
       "       ├─────────┴┐\n",
       " q_1: ─┤ RX(2π/3) ├\n",
       "       └┬───────┬─┘\n",
       " q_2: ──┤ RX(π) ├──\n",
       "       ┌┴───────┴─┐\n",
       " q_3: ─┤ RX(4π/3) ├\n",
       "       ├──────────┤\n",
       " q_4: ─┤ RX(5π/3) ├\n",
       "       └┬────────┬┘\n",
       " q_5: ──┤ RX(2π) ├─\n",
       "       ┌┴────────┴┐\n",
       " q_6: ─┤ RX(7π/3) ├\n",
       "       ├──────────┤\n",
       " q_7: ─┤ RX(8π/3) ├\n",
       "       └┬────────┬┘\n",
       " q_8: ──┤ RX(3π) ├─\n",
       "      ┌─┴────────┴┐\n",
       " q_9: ┤ RX(10π/3) ├\n",
       "      ├───────────┤\n",
       "q_10: ┤ RX(11π/3) ├\n",
       "      └───────────┘"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from qiskit import QuantumCircuit, QuantumRegister\n",
    "from math import pi\n",
    "\n",
    "def get_qc(p):\n",
    "    qr = QuantumRegister(11,'q')\n",
    "    qc = QuantumCircuit(qr)\n",
    "\n",
    "    for i in range(1,12):\n",
    "        qc.rx(i*p,i-1)\n",
    "    \n",
    "    return qc\n",
    "\n",
    "qci = get_qc(pi/3)\n",
    "qci.draw()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "38e2951d",
   "metadata": {},
   "source": [
    "To study the effect of decoherence, let's generate two more similar circuits with artificially added over and under rotations."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "id": "cb24294c",
   "metadata": {},
   "outputs": [],
   "source": [
    "qca = get_qc(pi/3+pi/18)\n",
    "qcr = get_qc(pi/3-pi/18)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4d2ee0cf",
   "metadata": {},
   "source": [
    "### Let's look at the ideal results"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cea23aaa",
   "metadata": {},
   "source": [
    "Let's add a 11-bit measurement register for qubits 0,1,2,3,4,5,6,7,8,9,10."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "id": "970d7916",
   "metadata": {},
   "outputs": [],
   "source": [
    "from qiskit import ClassicalRegister\n",
    "\n",
    "# Add the measurement register\n",
    "circs = [qci,qca,qcr]\n",
    "cr = ClassicalRegister(11,'c')\n",
    "for qc in circs:\n",
    "    qc.add_register(cr)\n",
    "    qc.measure(range(11),range(11))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9b09b833",
   "metadata": {},
   "source": [
    "We can now simulate these circuits. If we look at the individual $\\left|1\\right>$ state probability of each ion, we'll observe oscillations with different periods. The averaged result oscillates with the same period of the ideal circuit but the amplitude is damp due to the introduced decoherence (artificial over and under rotations)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "id": "ea3912b6",
   "metadata": {},
   "outputs": [],
   "source": [
    "from qiskit.providers.jobstatus import JobStatus\n",
    "from qiskit import Aer, execute\n",
    "\n",
    "# Choose the simulator backend \n",
    "backend = provider.get_backend(\"ionq_simulator\")\n",
    "#backend = Aer.get_backend(\"qasm_simulator\")\n",
    "\n",
    "# Run the circuit:\n",
    "def run_jobs(backend,circs,nshots):\n",
    "    jobs = []\n",
    "    job_ids = []\n",
    "    qcs = []\n",
    "\n",
    "    for qc in circs:\n",
    "        qcs.append(qc)\n",
    "        job = backend.run(qc, shots=nshots)\n",
    "        #job = execute(qc, backend, shots=nshots, memory=True)\n",
    "        jobs.append(job)\n",
    "        #job_ids.append(job.job_id())\n",
    "    \n",
    "    return jobs\n",
    "\n",
    "jobs = run_jobs(backend,circs,1000)\n",
    "\n",
    "# Calculate output state populations\n",
    "def get_pops(res,nn,n):\n",
    "    #print(res)\n",
    "    pops = [0 for i in range(2**nn)]\n",
    "    for key in res.keys():\n",
    "        pops[int(key,16)] = res[key]/n\n",
    "        #pops[int(key,2)] = res[key]/n\n",
    "    return pops\n",
    "\n",
    "# Fetch the result\n",
    "def get_jobs(jobs,nshots):\n",
    "    results = []\n",
    "    for i in range(len(jobs)):\n",
    "        result = jobs[i].result()\n",
    "        #print(result.data()['counts'])\n",
    "        #print(get_pops(result.data()['counts'],11,nshots))\n",
    "        results.append(get_pops(result.data()['counts'],11,nshots))\n",
    "    \n",
    "    return results\n",
    "\n",
    "results = get_jobs(jobs,1000)\n",
    "\n",
    "def get_ion(res,ion):\n",
    "    p1 = 0\n",
    "    for x in range(2**11):\n",
    "        if (x&(2**ion)):\n",
    "            p1 += res[x]\n",
    "    return p1\n",
    "\n",
    "prbi = [get_ion(results[0],i) for i in range(11)]\n",
    "prba = [get_ion(results[1],i) for i in range(11)]\n",
    "prbr = [get_ion(results[2],i) for i in range(11)]\n",
    "avres = [sum([results[i][j] for i in range(3)])/3 for j in range(2**11)]\n",
    "prbs = [get_ion(avres,i) for i in range(11)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "id": "88712eeb",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x11f307bd0>"
      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "plt.plot(range(12),[0]+prbi,label=\"Ideal\")\n",
    "plt.plot(range(12),[0]+prba,label=\"Over-rotation\")\n",
    "plt.plot(range(12),[0]+prbr,label=\"Under-rotation\")\n",
    "plt.plot(range(12),[0]+prbs,label=\"Average\",linewidth=3)\n",
    "plt.ylim([0,1])\n",
    "plt.ylabel(\"State |1> probability\")\n",
    "plt.xlabel(\"Qubit (*time*)\")\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a2c7a991",
   "metadata": {},
   "source": [
    "### Running jobs on a quantum computer"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b1a2d2a6",
   "metadata": {},
   "source": [
    "We are now ready to submit the jobs on IonQ's QPUs. Since actual quantum computers are noisy, the quality of the output state probabilities decreases with the number of gates favoring fully connected architectures over the ones with limited connectivity."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "id": "530ba3e8",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Switch the backend to run circuits on a quantum computer\n",
    "qpu_backend = provider.get_backend(\"ionq_qpu\")\n",
    "\n",
    "jobs = run_jobs(qpu_backend,circs,1000)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "265e9657",
   "metadata": {},
   "source": [
    "The job will queue, and results will arrive once it's executed!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "cb4e5f38",
   "metadata": {},
   "outputs": [],
   "source": [
    "#Check if jobs are done\n",
    "for i in range(len(jobs)):\n",
    "    print(jobs[i].status())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "id": "cac54458",
   "metadata": {},
   "outputs": [
    {
     "ename": "KeyboardInterrupt",
     "evalue": "",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mKeyboardInterrupt\u001b[0m                         Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-64-899603904bb0>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m      1\u001b[0m \u001b[0;31m# Fetch the result\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 2\u001b[0;31m \u001b[0mresults\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mget_jobs\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mjobs\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m1000\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      3\u001b[0m \u001b[0mprbi_m\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0mget_ion\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mresults\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mi\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mi\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mrange\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m11\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      4\u001b[0m \u001b[0mprba_m\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0mget_ion\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mresults\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mi\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mi\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mrange\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m11\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      5\u001b[0m \u001b[0mprbr_m\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0mget_ion\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mresults\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m2\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mi\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mi\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mrange\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m11\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m<ipython-input-60-eedb6e68c6f8>\u001b[0m in \u001b[0;36mget_jobs\u001b[0;34m(jobs, nshots)\u001b[0m\n\u001b[1;32m     36\u001b[0m     \u001b[0mresults\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     37\u001b[0m     \u001b[0;32mfor\u001b[0m \u001b[0mi\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mrange\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mjobs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 38\u001b[0;31m         \u001b[0mresult\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mjobs\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mi\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mresult\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     39\u001b[0m         \u001b[0;31m#print(result.data()['counts'])\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     40\u001b[0m         \u001b[0;31m#print(get_pops(result.data()['counts'],11,nshots))\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/anaconda3/envs/tflow/lib/python3.7/site-packages/qiskit_ionq/ionq_job.py\u001b[0m in \u001b[0;36mresult\u001b[0;34m(self)\u001b[0m\n\u001b[1;32m    247\u001b[0m         \u001b[0;31m# Wait for the job to complete.\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    248\u001b[0m         \u001b[0;32mtry\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 249\u001b[0;31m             \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mwait_for_final_state\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    250\u001b[0m         \u001b[0;32mexcept\u001b[0m \u001b[0mJobTimeoutError\u001b[0m \u001b[0;32mas\u001b[0m \u001b[0mex\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    251\u001b[0m             \u001b[0;32mraise\u001b[0m \u001b[0mexceptions\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mIonQJobTimeoutError\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"Timed out waiting for job to complete.\"\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mfrom\u001b[0m \u001b[0mex\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/anaconda3/envs/tflow/lib/python3.7/site-packages/qiskit/providers/job.py\u001b[0m in \u001b[0;36mwait_for_final_state\u001b[0;34m(self, timeout, wait, callback)\u001b[0m\n\u001b[1;32m    118\u001b[0m             \u001b[0;32mif\u001b[0m \u001b[0mcallback\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    119\u001b[0m                 \u001b[0mcallback\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mjob_id\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mstatus\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 120\u001b[0;31m             \u001b[0mtime\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msleep\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mwait\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    121\u001b[0m             \u001b[0mstatus\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mstatus\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    122\u001b[0m         \u001b[0;32mreturn\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mKeyboardInterrupt\u001b[0m: "
     ]
    }
   ],
   "source": [
    "# Fetch the result\n",
    "results = get_jobs(jobs,1000)\n",
    "prbi_m = [get_ion(results[0],i) for i in range(11)]\n",
    "prba_m = [get_ion(results[1],i) for i in range(11)]\n",
    "prbr_m = [get_ion(results[2],i) for i in range(11)]\n",
    "avres = [sum([results[i][j] for i in range(3)])/3 for j in range(2**11)]\n",
    "prbs_m = [get_ion(avres,i) for i in range(11)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "d8966d6c",
   "metadata": {},
   "outputs": [],
   "source": [
    "plt.plot(range(12),[0]+prbi_m,label=\"Ideal\")\n",
    "plt.plot(range(12),[0]+prba_m,label=\"Over-rotation\")\n",
    "plt.plot(range(12),[0]+prbr_m,label=\"Under-rotation\")\n",
    "plt.plot(range(12),[0]+prbs_m,label=\"Average\",linewidth=3)\n",
    "plt.ylim([0,1])\n",
    "plt.ylabel(\"State |1> probability\")\n",
    "plt.legend()"
   ]
  }
 ],
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