lab7_ex1.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![image](resources/qgss-header.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Lab 7: Qubit Spectroscopy"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this lab, you will take what you learned about the interactions between qubits and resonators to perform transmon spectroscopy with the pulse simulator."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Installing Necessary Packages\n",
    "Before we begin, you will need to install some prerequisites into your environment. Run the cell below to complete these installations. At the end, the cell outputs will be cleared."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "!pip install -U -r grading_tools/requirements.txt\n",
    "\n",
    "from IPython.display import clear_output\n",
    "clear_output()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Simulating the Transmon as a Duffing Oscillator"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As you learned in Lecture 6, the transmon can be understood as a Duffing oscillator specified by a frequency $\\nu$, anharmonicity $\\alpha$, and drive strength $r$, which results in the Hamiltonian\n",
    "$$\n",
    "   \\hat{H}_{\\rm Duff}/\\hbar = 2\\pi\\nu a^\\dagger a + \\pi \\alpha a^\\dagger a(a^\\dagger a - 1) + 2 \\pi r (a + a^\\dagger) \\times D(t),\n",
    "$$\n",
    "\n",
    "where $D(t)$ is the signal on the drive channel for the qubit, and $a^\\dagger$ and $a$ are, respectively, the creation and annihilation operators for the qubit. Note that the drive strength $r$ sets the scaling of the control term, with $D(t)$ assumed to be a complex and unitless number satisfying $|D(t)| \\leq 1$. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Qiskit Pulse Overview\n",
    "\n",
    "As a brief overview, Qiskit Pulse schedules (experiments) consist of Instructions (i.e., Play) acting on Channels (i.e., the drive channel). Here is a summary table of available Instructions and Channels:\n",
    "\n",
    "![image](resources/pulse-instr.png)\n",
    "\n",
    "For more detail, this table summarizes the interaction of the channels with the actual quantum hardware:\n",
    "\n",
    "![image](resources/pulse-user-device-layers.png)\n",
    "\n",
    "However, we find it is more instructive to begin with guided programming in Pulse. Below you will learn how to create pulses, schedules, and run experiments on a simulator. These lessons can be immediately applied to actual pulse-enabled quantum hardware, in particular [`ibmq_armonk`](https://www.ibm.com/blogs/research/2019/12/qiskit-openpulse/)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Let's get started!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In most of the cells below, nothing needs to be modified. **However, you will need to execute the cells by pressing `shift+Enter` in each code block**. In order to keep things tidy and focus on the important aspects of Qiskit Pulse, the following cells make use of methods from the `helper` module. For the gory details, please refer back to the [Lab 7 notebook](lab7-jc-spect-readout.ipynb). Just as in Lab 6, before coming to the discussion of **Sideband Modulation**, the following code blocks\n",
    "\n",
    "- create backend pulse simulator and instantiate the transmon as a Duffing oscillator of frequency $\\sim 5$ GHz\n",
    "- import libraries for numerics and visualization, and define helpful constants\n",
    "- create the channels for the pulse schedule and define measurment schedule (we will only work with the drive channel)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# our backend is the Pulse Simulator\n",
    "from resources import helper\n",
    "from qiskit.providers.aer import PulseSimulator\n",
    "backend_sim = PulseSimulator()\n",
    "\n",
    "# sample duration for pulse instructions \n",
    "dt = 1e-9\n",
    "\n",
    "# create the model\n",
    "duffing_model = helper.get_transmon(dt)\n",
    "\n",
    "# get qubit frequency from Duffing model\n",
    "qubit_lo_freq = duffing_model.hamiltonian.get_qubit_lo_from_drift()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "\n",
    "# visualization tools\n",
    "import matplotlib.pyplot as plt\n",
    "plt.style.use('dark_background')\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",
    "kHz = 1.0e3 # kilohertz\n",
    "us = 1.0e-6 # microseconds\n",
    "ns = 1.0e-9 # nanoseconds"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Instantiate channels and create measurement schedule\n",
    "\n",
    "We will use the same measurement schedule throughout, whereas the drive schedules will vary. This must be built for the simulator, for a real backend we can ask for its default measurement pulse."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "from qiskit import pulse\n",
    "from qiskit.pulse import Play, Acquire\n",
    "from qiskit.pulse.pulse_lib import GaussianSquare\n",
    "\n",
    "# qubit to be used throughout the notebook\n",
    "qubit = 0\n",
    "\n",
    "### Collect the necessary channels\n",
    "drive_chan = pulse.DriveChannel(qubit)\n",
    "meas_chan = pulse.MeasureChannel(qubit)\n",
    "acq_chan = pulse.AcquireChannel(qubit)\n",
    "\n",
    "# Construct a measurement schedule and add it to an InstructionScheduleMap\n",
    "meas_samples = 1200\n",
    "meas_pulse = GaussianSquare(duration=meas_samples, amp=0.025, sigma=4, width=1150)\n",
    "measure_sched = Play(meas_pulse, meas_chan) | Acquire(meas_samples, acq_chan, pulse.MemorySlot(qubit))\n",
    "\n",
    "inst_map = pulse.InstructionScheduleMap()\n",
    "inst_map.add('measure', [qubit], measure_sched)\n",
    "\n",
    "# save the measurement/acquire pulse for later\n",
    "measure = inst_map.get('measure', qubits=[qubit])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Sideband Modulation\n",
    "\n",
    "Unlike the case of running on an actual device, with the simulator we can only set the (local) oscillator frequency of the drive, $f_{\\rm LO}$, to a single value. In order to sweep frequencies to perform spectroscopy, we use a trick called *sideband modulation*, where we modulate our spectroscopy pulse by a sideband frequency $f_{\\rm SB}$ so that the pulse applied to the qubit is of (radio) frequency\n",
    "\n",
    "$$ f_{\\rm RF} = f_{\\rm LO} + f_{\\rm SB}. $$\n",
    "\n",
    "This is achieved by multiplying each sample amplitude by a complex exponential \n",
    "\n",
    "$$ d_j^{\\rm SB} = \\sum_j e^{2\\pi f_{\\rm SB} t_j} d_j $$\n",
    "\n",
    "but we will tuck the details away in the `helper` module. The important thing is that we must apply the sideband for each pulse in order to change its frequency. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, instead of `assemble`'ing a single schedule with an array of schedule LO's as, we will create a schedule of the same pulse *sidebanded* by an array of sideband frequecies at a fixed LO frequency. Since we are now considering a transmon, we have multiple energy levels we can perform spectroscopy on. We will being with spectroscopy of the $|0\\rangle \\to |1\\rangle$ transition, which is the one used as the qubit, often called the *computational basis*."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "from qiskit.pulse import pulse_lib\n",
    "\n",
    "# the same spect pulse used in every schedule\n",
    "drive_amp = 0.9\n",
    "drive_sigma = 16\n",
    "drive_duration = 128\n",
    "spec_pulse = pulse_lib.gaussian(duration=drive_duration, amp=drive_amp, \n",
    "                                sigma=drive_sigma, name=f\"Spec drive amplitude = {drive_amp}\")\n",
    "\n",
    "# Construct an np array of the frequencies for our experiment\n",
    "spec_freqs_GHz = np.arange(5.0, 5.2, 0.005)\n",
    "\n",
    "# Create the base schedule\n",
    "# Start with drive pulse acting on the drive channel\n",
    "spec_schedules = []\n",
    "for freq in spec_freqs_GHz:\n",
    "    sb_spec_pulse = helper.apply_sideband(spec_pulse, qubit_lo_freq[0]-freq*GHz, dt)\n",
    "    \n",
    "    spec_schedule = pulse.Schedule(name='SB Frequency = {}'.format(freq))\n",
    "    spec_schedule += Play(sb_spec_pulse, drive_chan)\n",
    "    # The left shift `<<` is special syntax meaning to shift the start time of the schedule by some duration\n",
    "    spec_schedule += measure << spec_schedule.duration\n",
    "    spec_schedules.append(spec_schedule)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
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\n",
      "text/plain": [
       "<Figure size 720x864 with 1 Axes>"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "spec_schedules[0].draw()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "from qiskit import assemble\n",
    "\n",
    "# assemble the schedules into a Qobj\n",
    "spec01_qobj = assemble(**helper.get_params('spec01', globals()))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "# run the simulation\n",
    "spec01_result = backend_sim.run(spec01_qobj, duffing_model).result()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "# retrieve the data from the experiment\n",
    "spec01_values = helper.get_values_from_result(spec01_result, qubit)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We will fit the spectroscopy signal to a Lorentzian function of the form\n",
    "\n",
    "$$ \\frac{AB}{\\pi[(f-f_{01})^2 + B^2]} + C $$\n",
    "\n",
    "to find the qubit frequency $f_{01}$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "01 Spectroscopy yields 5.041685 GHz\n"
     ]
    }
   ],
   "source": [
    "fit_params, y_fit = helper.fit_lorentzian(spec_freqs_GHz, spec01_values, [5, 5, 1, 0])\n",
    "\n",
    "f01 = fit_params[1]\n",
    "\n",
    "plt.scatter(spec_freqs_GHz, np.real(spec01_values), color='white') # plot real part of sweep values\n",
    "plt.plot(spec_freqs_GHz, y_fit, color='red')\n",
    "plt.xlim([min(spec_freqs_GHz), max(spec_freqs_GHz)])\n",
    "\n",
    "plt.xlabel(\"Frequency [GHz]\")\n",
    "plt.ylabel(\"Measured Signal [a.u.]\")\n",
    "plt.show()\n",
    "\n",
    "print(\"01 Spectroscopy yields %f GHz\"%f01)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Exercise 1: Spectroscopy of 1->2 transition\n",
    "\n",
    "In order to observe the transition between the $|1\\rangle$ and $|2\\rangle$ states of the transmon, we must apply an $X_\\pi$ pulse to transition the qubit from $|0\\rangle$ to $|1\\rangle$ first. Because we are using the simulator, we must first define our $X_\\pi$ pulse from the Rabi experiment in Lab 6."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "x180_amp = 0.310160  #0.629070 #from lab 6 Rabi experiment\n",
    "\n",
    "x_pulse = pulse_lib.gaussian(duration=drive_duration,\n",
    "                             amp=x180_amp, \n",
    "                             sigma=drive_sigma,\n",
    "                             name='x_pulse')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The anharmonicity of our transmon qubits is typically around $-300$ MHz, so we will sweep around that value. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "anharmonicity_guess_GHz = -0.3\n",
    "\n",
    "def build_spec12_pulse_schedule(freq):\n",
    "    sb12_spec_pulse = helper.apply_sideband(spec_pulse, (freq + anharmonicity_guess_GHz)*GHz, dt)\n",
    "    \n",
    "    ### create a 12 spectroscopy pulse schedule spec12_schedule (already done)\n",
    "    ### play an x pulse on the drive channel\n",
    "    ### play sidebanded spec pulse on the drive channel\n",
    "    ### add measurement pulse to schedule\n",
    "    \n",
    "    spec12_schedule = pulse.Schedule()\n",
    "    \n",
    "    ### WRITE YOUR CODE BETWEEN THESE LINES - START\n",
    "    spec12_schedule += Play(x_pulse, drive_chan)\n",
    "    spec12_schedule += Play(sb12_spec_pulse, drive_chan)\n",
    "    spec12_schedule += measure << spec12_schedule.duration\n",
    "    \n",
    "    ### WRITE YOUR CODE BETWEEN THESE LINES - END\n",
    "    \n",
    "    return spec12_schedule"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "sb_freqs_GHz = np.arange(-.1, .1, 0.005) # sweep +/- 100 MHz around guess\n",
    "\n",
    "# now vary the sideband frequency for each spec pulse\n",
    "spec_schedules = []\n",
    "for freq in sb_freqs_GHz:\n",
    "    spec_schedules.append(build_spec12_pulse_schedule(freq))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x864 with 1 Axes>"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "spec_schedules[0].draw()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "# assemble the schedules into a Qobj\n",
    "spec12_qobj = assemble(**helper.get_params('spec12', globals()))\n",
    "answer1 = spec12_qobj"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "# run the simulation\n",
    "spec12_result = backend_sim.run(spec12_qobj, duffing_model).result()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "# retrieve the data from the experiment\n",
    "spec12_values = helper.get_values_from_result(spec12_result, qubit)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We will again fit the spectroscopy signal to a Lorentzian function of the form\n",
    "\n",
    "$$ \\frac{AB}{\\pi[(f-f_{12})^2 + B^2]} + C $$\n",
    "\n",
    "to find the frequency of the $|1\\rangle \\to |2\\rangle$ transition $f_{12}$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "12 Spectroscopy yields 4.714213 GHz\n",
      "Measured transmon anharmonicity is -327.471893 MHz\n"
     ]
    }
   ],
   "source": [
    "anharm_offset = qubit_lo_freq[0]/GHz + anharmonicity_guess_GHz\n",
    "\n",
    "fit_params, y_fit = helper.fit_lorentzian(anharm_offset + sb_freqs_GHz, spec12_values, [5, 4.5, .1, 3])\n",
    "\n",
    "f12 = fit_params[1]\n",
    "\n",
    "plt.scatter(anharm_offset + sb_freqs_GHz, np.real(spec12_values), color='white') # plot real part of sweep values\n",
    "plt.plot(anharm_offset + sb_freqs_GHz, y_fit, color='red')\n",
    "plt.xlim([anharm_offset + min(sb_freqs_GHz), anharm_offset + max(sb_freqs_GHz)])\n",
    "\n",
    "plt.xlabel(\"Frequency [GHz]\")\n",
    "plt.ylabel(\"Measured Signal [a.u.]\")\n",
    "plt.show()\n",
    "\n",
    "print(\"12 Spectroscopy yields %f GHz\"%f12)\n",
    "print(\"Measured transmon anharmonicity is %f MHz\"%((f12-f01)*GHz/MHz))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Help us improve our educational tools by submitting your code**<br>\n",
    "If you would like to help us learn how to improve our educational materials and offerings, you can opt in to send us a copy of your Jupyter notebook. By executing the cell below, you consent to sending us the code in your Jupyter notebook. All of the personal information will be anonymized."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/javascript": [
       "IPython.notebook.save_checkpoint();"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Sending ex1.ipynb ...\n",
      "Sent. Thanks!\n"
     ]
    }
   ],
   "source": [
    "from IPython.display import display, Javascript;display(Javascript('IPython.notebook.save_checkpoint();'));\n",
    "from grading_tools import send_code;send_code('ex1.ipynb')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Additional Resources\n",
    "\n",
    "- The Qiskit textbook sections that cover this material are\n",
    "  - [Circuit Quantum Electrodynamics](https://qiskit.org/textbook/ch-quantum-hardware/cQED-JC-SW.html)\n",
    "  - [Accessing Higher Energy States](https://qiskit.org/textbook/ch-quantum-hardware/accessing_higher_energy_states.html)\n",
    "\n",
    "- Watch the videos\n",
    "  - [Quantum Coding with Lauren Capelluto](https://www.youtube.com/watch?v=ZvipHRY-URs)\n",
    "  - [\"Qiskit Pulse: Programming Quantum Computers Through the Cloud with Pulses\"](https://www.youtube.com/watch?v=V_as5PufUiU) webinar at CQT by yours truly"
   ]
  }
 ],
 "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": 4
}