OpenPulse Tutorial.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from qiskit.tools.jupyter import *\n",
    "%config InlineBackend.figure_format = 'svg' # Makes the images look nice\n",
    "\n",
    "from qiskit import IBMQ\n",
    "IBMQ.load_account()\n",
    "provider = IBMQ.get_provider(hub='ibm-q', group='open', project='main')\n",
    "backend = provider.get_backend('ibmq_armonk')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# get backend information\n",
    "backend_config = backend.configuration()\n",
    "assert backend_config.open_pulse, \"Backend doesn't support Pulse\" # check for OpenPulse support"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Sampling time: 0.2222222222222222 ns\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/opt/conda/lib/python3.7/site-packages/qiskit/providers/models/backendconfiguration.py:355: 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"
     ]
    }
   ],
   "source": [
    "# can find sampling times for backend pulses within backend configuration\n",
    "dt = backend_config.dt\n",
    "print(f\"Sampling time: {dt*1e9} ns\") # dt is returned in seconds, convert to nanoseconds\n",
    "## Warnings can be safely ignored"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# backend defaults give starting point for how to use backend, contains estimates for qubit\n",
    "# frequencies and default programs to enact basic quantum operators\n",
    "backend_defaults = backend.defaults()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Part 1\n",
    "1 Finding the qubit frequency using frequency sweep\n",
    "\n",
    "* qubit frequency is difference in E b/w |0>, |1>\n",
    "* need frequency for pulses to perform quantum operations on qubits\n",
    "* superconducting qubits - higher energies also available, but anharmonic so we can control which transition we are exciting -> Allows us to isolate two energy levels and treat each qubit as basic two-level system (distance between energy levels *non-linear*, scrunches up as you go to |2>, |3> but very wide for |0>, |1>\n",
    "* typically sweep through range of frequencies and look for signs of absorption \n",
    "  * define a frequency range that will be swept, then a \"step amount\" (ex: +/- 40 Mhz w/ 1Mhz stepping\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Qubit 0 has an estimated frequency of 4.974290529121356 GHz.\n",
      "The sweep will go from 4.954290529121356 GHz to 4.994290529121356 GHz in steps of 1.0 MHz.\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "\n",
    "# unit conversion factors -> all backend properties returned in SI (Hz, sec, etc)\n",
    "GHz = 1.0e9 # Gigahertz\n",
    "MHz = 1.0e6 # Megahertz\n",
    "us = 1.0e-6 # Microseconds\n",
    "ns = 1.0e-9 # Nanoseconds\n",
    "\n",
    "# We will find the qubit frequency for the following (only) qubit.\n",
    "qubit = 0\n",
    "\n",
    "# The sweep will be centered around the estimated qubit frequency.\n",
    "center_frequency_Hz = backend_defaults.qubit_freq_est[qubit]        # The default frequency is given in Hz\n",
    "                                                                    # warning: this will change in a future release\n",
    "print(f\"Qubit {qubit} has an estimated frequency of {center_frequency_Hz / GHz} GHz.\")\n",
    "\n",
    "# scale factor to remove factors of 10 from the data\n",
    "scale_factor = 1e-14\n",
    "\n",
    "# We will sweep 40 MHz around the estimated frequency\n",
    "frequency_span_Hz = 40 * MHz\n",
    "# in steps of 1 MHz.\n",
    "frequency_step_Hz = 1 * MHz\n",
    "\n",
    "# We will sweep 20 MHz above and 20 MHz below the estimated frequency\n",
    "## take the central frequency, then subtrac by half the span to est. min-max bounds\n",
    "frequency_min = center_frequency_Hz - frequency_span_Hz / 2 \n",
    "frequency_max = center_frequency_Hz + frequency_span_Hz / 2\n",
    "# Construct an np array of the frequencies for our experiment\n",
    "## np.arange, return evenly spaced values within given interval. If step is non-integer, consider\n",
    "## using np.linspace\n",
    "frequencies_GHz = np.arange(frequency_min / GHz, \n",
    "                            frequency_max / GHz, \n",
    "                            frequency_step_Hz / GHz)\n",
    "\n",
    "print(f\"The sweep will go from {frequency_min / GHz} GHz to {frequency_max / GHz} GHz \\\n",
    "in steps of {frequency_step_Hz / MHz} MHz.\")\n",
    "# Safe to ignore warnings"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* start by defining *drive pulse*, a kind of Gaussian pulse\n",
    "* all pulse durations are given in `dt` units."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "# samples need to be multiples of 16\n",
    "def get_closest_multiple_of_16(num):\n",
    "    return int(num + 8 ) - (int(num + 8 ) % 16)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "from qiskit import pulse            # This is where we access all of our Pulse features!\n",
    "from qiskit.pulse import pulse_lib  # This Pulse module helps us build sampled pulses for common pulse shapes\n",
    "\n",
    "\n",
    "# Drive pulse parameters (us = microseconds)\n",
    "drive_sigma_us = 0.075                     # This determines the actual width of the gaussian\n",
    "drive_samples_us = drive_sigma_us*8        # This is a truncating parameter, because gaussians don't have \n",
    "                                           # a natural finite length\n",
    "\n",
    "drive_sigma = get_closest_multiple_of_16(drive_sigma_us * us /dt)       # The width of the gaussian in units of dt\n",
    "drive_samples = get_closest_multiple_of_16(drive_samples_us * us /dt)   # The truncating parameter in units of dt\n",
    "drive_amp = 0.3\n",
    "# Drive pulse samples\n",
    "drive_pulse = pulse_lib.gaussian(duration=drive_samples,\n",
    "                                 sigma=drive_sigma,\n",
    "                                 amp=drive_amp,\n",
    "                                 name='freq_sweep_excitation_pulse')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* When acquisition is done for one qubit, it is also done on other qubits\n",
    "* acquisition seems to mean triggering the ADC associated with a qubit, triggers data collection for channel associated with a qubit "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Find out which group of qubits need to be acquired with this qubit\n",
    "meas_map_idx = None\n",
    "for i, measure_group in enumerate(backend_config.meas_map): #meas_map = list of sets of qubits that must be measured together\n",
    "    if qubit in measure_group: # pick one qubit from the measure group\n",
    "        meas_map_idx = i\n",
    "        break\n",
    "assert meas_map_idx is not None, f\"Couldn't find qubit {qubit} in the meas_map!\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "# define measurement pulse\n",
    "# Instead of hardcoding, obtain a calibrated measurement pulse from backend default instruction schedule map\n",
    "inst_sched_map = backend_defaults.instruction_schedule_map\n",
    "measure = inst_sched_map.get('measure', qubits=backend_config.meas_map[meas_map_idx])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Specify channels on which we apply pulses\n",
    "# channels indexed by qubit number \n",
    "## According to arxiv paper, each qubit has two channels\n",
    "## * drive channel + measurement input (stimulus) channel\n",
    "## * signal on drive channel for qubit i is mixed with user-specificed local oscillator at\n",
    "##   certain frequency -> interacts with qubit through hamiltonian\n",
    "## * measurement channel also gets \"mixed\" with local oscillator\n",
    "## https://arxiv.org/pdf/1809.03452.pdf\n",
    "drive_chan = pulse.DriveChannel(qubit)\n",
    "meas_chan = pulse.MeasureChannel(qubit)\n",
    "acq_chan = pulse.AcquireChannel(qubit)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "## w/ pulse params + pulse shapes, can create pulse schedule\n",
    "## at each frequency, send drive pulse of frequency to qubit and perform measurement\n",
    "## immediately after pulse.\n",
    "\n",
    "## pulse envelopes independent of frequency so can build reusable schedule\n",
    "## specify drive pulse frequency with a frequency configuration array\n",
    "\n",
    "# Create the base schedule\n",
    "# Start with drive pulse acting on the drive channel\n",
    "schedule = pulse.Schedule(name='Frequency sweep')\n",
    "schedule += drive_pulse(drive_chan)\n",
    "# The left shift `<<` is special syntax meaning to shift the start time of the schedule by some duration\n",
    "schedule += measure << schedule.duration\n",
    "\n",
    "# Create the frequency settings for the sweep (MUST BE IN HZ)\n",
    "frequencies_Hz = frequencies_GHz*GHz\n",
    "schedule_frequencies = [{drive_chan: freq} for freq in frequencies_Hz]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
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     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "schedule.draw(channels=[drive_chan, meas_chan, acq_chan], label=True, scaling=1.0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/opt/conda/lib/python3.7/site-packages/qiskit/providers/models/backendconfiguration.py:377: UserWarning: `rep_time` now has units of seconds(s) rather than microseconds(mu s).\n",
      "  warnings.warn('`rep_time` now has units of seconds(s) rather '\n"
     ]
    }
   ],
   "source": [
    "from qiskit import assemble\n",
    "\n",
    "num_shots_per_frequency = 1024\n",
    "# assemble into a Qobj sent to quantum device\n",
    "## meas_level = 0 raw data (array of cmplx vals per shot)\n",
    "## meas_level = 1 kerneled data (kerneled data, 1 cmplex val per shot)\n",
    "## meas_level = 2 returns classified (0/1 per shot)\n",
    "## choose meas_level = 1 to replicate lab conditions, where discriminator hasn't been calibrated\n",
    "frequency_sweep_program = assemble(schedule,\n",
    "                                   backend=backend, \n",
    "                                   meas_level=1,\n",
    "                                   meas_return='avg', # ask for average of results\n",
    "                                   shots=num_shots_per_frequency,\n",
    "                                   schedule_los=schedule_frequencies)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "job = backend.run(frequency_sweep_program)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "5eb106826d2c84001180a97e\n"
     ]
    }
   ],
   "source": [
    "print(job.job_id())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Job Status: job has successfully run\n"
     ]
    }
   ],
   "source": [
    "from qiskit.tools.monitor import job_monitor\n",
    "job_monitor(job)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "frequency_sweep_results = job.result(timeout=120)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
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   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "sweep_values = []\n",
    "for i in range(len(frequency_sweep_results.results)):\n",
    "    # Get the results from the ith experiment\n",
    "    res = frequency_sweep_results.get_memory(i)*scale_factor\n",
    "    # Get the results for `qubit` from this experiment\n",
    "    sweep_values.append(res[qubit])\n",
    "\n",
    "plt.scatter(frequencies_GHz, np.real(sweep_values), color='black') # plot real part of sweep values\n",
    "plt.xlim([min(frequencies_GHz), max(frequencies_GHz)])\n",
    "plt.xlabel(\"Frequency [GHz]\")\n",
    "plt.ylabel(\"Measured signal [a.u.]\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
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   "source": [
    "# to get value of peak frequency, fit values to resonance response curve, typically a lorentzian shape\n",
    "from scipy.optimize import curve_fit\n",
    "\n",
    "def fit_function(x_values, y_values, function, init_params):\n",
    "    fitparams, conv = curve_fit(function, x_values, y_values, init_params)\n",
    "    y_fit = function(x_values, *fitparams)\n",
    "    \n",
    "    return fitparams, y_fit\n",
    "\n",
    "fit_params, y_fit = fit_function(frequencies_GHz,\n",
    "                                 np.real(sweep_values), \n",
    "                                 lambda x, A, q_freq, B, C: (A / np.pi) * (B / ((x - q_freq)**2 + B**2)) + C,\n",
    "                                 [5, 4.975, 1, 3] # initial parameters for curve_fit\n",
    "                                )\n",
    "\n",
    "plt.scatter(frequencies_GHz, np.real(sweep_values), color='black')\n",
    "plt.plot(frequencies_GHz, y_fit, color='red')\n",
    "plt.xlim([min(frequencies_GHz), max(frequencies_GHz)])\n",
    "\n",
    "plt.xlabel(\"Frequency [GHz]\")\n",
    "plt.ylabel(\"Measured Signal [a.u.]\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "We've updated our qubit frequency estimate from 4.97429 GHz to 4.97441 GHz.\n"
     ]
    }
   ],
   "source": [
    "A, rough_qubit_frequency, B, C = fit_params\n",
    "rough_qubit_frequency = rough_qubit_frequency*GHz # make sure qubit freq is in Hz\n",
    "print(f\"We've updated our qubit frequency estimate from \"\n",
    "      f\"{round(backend_defaults.qubit_freq_est[qubit] / GHz, 5)} GHz to {round(rough_qubit_frequency/GHz, 5)} GHz.\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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