lab_1_(1).ipynb

{
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        "id": "view-in-github",
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      "source": [
        "<a href=\"https://colab.research.google.com/github/NSPFD/IBM_QUANTUM-_COMPUTING-_CHALLENGE-2024/blob/main/lab_1_(1).ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "2d04489a",
      "metadata": {
        "id": "2d04489a"
      },
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      ]
    },
    {
      "cell_type": "markdown",
      "id": "6526012d",
      "metadata": {
        "id": "6526012d"
      },
      "source": [
        "# Lab 1: Introduction to Qiskit 1.0"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "69483aa5",
      "metadata": {
        "id": "69483aa5"
      },
      "source": [
        "# Table of Contents\n",
        "- [Introduction](#intro)\n",
        "- [Part I: Qiskit states, the new and the old](#pt1)\n",
        "  - [Exercise 1: Create and draw a singlet Bell state circuit](#exercise1)\n",
        "  - [Exercise 2: Use Sampler.run](#exercise2)\n",
        "  - [Exercise 3: Create and draw a W-state circuit](#exercise3)   \n",
        "- [Part II: VQE with Qiskit 1.0](#pt2)\n",
        "  - [Exercise 4: Create a parameterized circuit to serve as the ansatz](#exercise4)    \n",
        "  - [Exercise 5: Transpile to ISA circuits](#exercise5)\n",
        "  - [Exercise 6: Defining the cost function](#exercise6)\n",
        "  - [Exercise 7: QiskitRuntimeService V2 Primitives, local testing mode and Sessions, a first look](#exercise7)\n"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "vDDPUSL8DRLr",
      "metadata": {
        "id": "vDDPUSL8DRLr"
      },
      "source": [
        "## Setup"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "NngrjOs8PWJ_",
      "metadata": {
        "id": "NngrjOs8PWJ_"
      },
      "outputs": [],
      "source": [
        "### Install Qiskit, if needed\n",
        "\n",
        "%pip install qiskit[visualization]==1.0.2\n",
        "%pip install qiskit_aer\n",
        "%pip install qiskit_ibm_runtime\n",
        "%pip install matplotlib\n",
        "%pip install pylatexenc\n",
        "%pip install qiskit-transpiler-service\n",
        "%pip install git+https://github.com/qiskit-community/Quantum-Challenge-Grader.git"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "_tm3sSUEPbYp",
      "metadata": {
        "id": "_tm3sSUEPbYp"
      },
      "outputs": [],
      "source": [
        "### Save API Token, if needed\n",
        "\n",
        "%set_env QXToken=deleteThisAndPasteYourTokenHere\n",
        "\n",
        "# Make sure there is no space between the equal sign\n",
        "# and the beginning of your token"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "zbO8kneGPW7h",
      "metadata": {
        "id": "zbO8kneGPW7h"
      },
      "outputs": [],
      "source": [
        "# imports\n",
        "import numpy as np\n",
        "from typing import List, Callable\n",
        "from scipy.optimize import minimize\n",
        "from scipy.optimize._optimize import OptimizeResult\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "from qiskit import QuantumCircuit\n",
        "from qiskit.quantum_info import Statevector, Operator, SparsePauliOp\n",
        "from qiskit.primitives import StatevectorSampler, PrimitiveJob\n",
        "from qiskit.circuit.library import TwoLocal\n",
        "from qiskit.transpiler.preset_passmanagers import generate_preset_pass_manager\n",
        "from qiskit.visualization import plot_histogram\n",
        "from qiskit_ibm_runtime.fake_provider import FakeSherbrooke\n",
        "from qiskit_ibm_runtime import Session, EstimatorV2 as Estimator\n",
        "from qiskit_aer import AerSimulator"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "NwnHYrYsCw29",
      "metadata": {
        "id": "NwnHYrYsCw29"
      },
      "outputs": [],
      "source": [
        "# Setup the grader\n",
        "from qc_grader.challenges.iqc_2024 import (\n",
        "    grade_lab1_ex1,\n",
        "    grade_lab1_ex2,\n",
        "    grade_lab1_ex3,\n",
        "    grade_lab1_ex4,\n",
        "    grade_lab1_ex5,\n",
        "    grade_lab1_ex6,\n",
        "    grade_lab1_ex7,\n",
        ")"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "2c18d993",
      "metadata": {
        "id": "2c18d993"
      },
      "source": [
        "## Introduction <a name=\"intro\"></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "726fd3f5",
      "metadata": {
        "id": "726fd3f5"
      },
      "source": [
        "Welcome to lab one! This lab is designed to introduce you to some of the new capabilities and functions of Qiskit 1.0. Later challenges will develop on these capabilities further and introduce the more complex new Qiskit functionalities.\n",
        "\n",
        "Through this lab you will learn how to set up quantum states using Qiskit, and how to implement an optimization algorithm using VQE. These two tasks will be set in two sections:\n",
        "\n",
        "\n",
        "1.   Qiskit states, the new and the old\n",
        "2.   VQE with Qiskit 1.0\n",
        "\n",
        "Let's get started!"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "01caf8c3",
      "metadata": {
        "id": "01caf8c3"
      },
      "source": [
        "## Part I: Qiskit states, the new and the old  <a name=\"pt1\"></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "3ad35e28",
      "metadata": {
        "id": "3ad35e28"
      },
      "source": [
        "<a id=\"exercise1\"></a>\n",
        "<a name=\"exercise1\"></a>\n",
        "<div class=\"alert alert-block alert-success\">\n",
        "    \n",
        "<b> Exercise 1: Create and draw a singlet Bell state circuit</b>\n",
        "    \n",
        "Bell circuits are specific circuits which generate Bell states, or EPR pairs, a form of entangled and normalized basis vectors. In other words, they are the circuits we use to generate entangled states, a key ingredient in quantum computations.\n",
        "\n",
        "There exist 4 different Bell states. You can learn about each from the [Basics of Quantum Information page](https://learning.quantum.ibm.com/course/basics-of-quantum-information/multiple-systems#bell-states)\n",
        "\n",
        "**Your Task:** please build a circuit that generates the $| \\psi ^- \\rangle$ Bell state.\n",
        "    \n",
        "</div>"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "c2d85fb4",
      "metadata": {
        "id": "c2d85fb4"
      },
      "outputs": [],
      "source": [
        "# Build a circuit to form a psi-minus Bell state\n",
        "# Apply gates to the provided QuantumCircuit, qc\n",
        "\n",
        "qc = QuantumCircuit(2)\n",
        "\n",
        "### Write your code below here ###\n",
        "\n",
        "\n",
        "\n",
        "### Don't change any code past this line ###\n",
        "qc.measure_all()\n",
        "qc.draw('mpl')"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "fBVD5zLiokQ5",
      "metadata": {
        "id": "fBVD5zLiokQ5"
      },
      "source": [
        "<div class=\"alert alert-block alert-warning\">\n",
        "\n",
        "**Hint:** The $| \\psi ^- \\rangle$ Bell state uses a single Z gate, and a single X gate, both of which occur after the CNOT.\n",
        "\n",
        "</div>"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "3167dc62",
      "metadata": {
        "id": "3167dc62"
      },
      "outputs": [],
      "source": [
        "# Submit your answer using following code\n",
        "\n",
        "grade_lab1_ex1(qc) # Expected result type: QuantumCircuit"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "059ab0ac",
      "metadata": {
        "id": "059ab0ac"
      },
      "source": [
        "To observe the resulting entangled state that this circuit produces, we'll run our circuit a number of times and collect statistics on the final qubit measurements. That is the goal of the next exercise."
      ]
    },
    {
      "cell_type": "markdown",
      "id": "d7c977fa",
      "metadata": {
        "id": "d7c977fa"
      },
      "source": [
        "<a id=\"exercise2\"></a>\n",
        "<a name=\"exercise2\"></a>\n",
        "<div class=\"alert alert-block alert-success\">\n",
        "    \n",
        "<b> Exercise 2: Use Sampler.run</b>\n",
        "    \n",
        "The [Qiskit Sampler](https://docs.quantum.ibm.com/api/qiskit/qiskit.primitives.StatevectorSampler) primitive ([more info on Primitives here](https://docs.quantum.ibm.com/run/primitives-get-started)) returns the sampled result according to the specified output type. It allows us to efficiently sample quantum states by executing quantum circuits and providing probability distributions of the quantum states.\n",
        "\n",
        "**Your Task:** use the Qiskit StatevectorSampler to obtain the counts resulting from our circuit.\n",
        "    \n",
        "</div>"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "866634d6",
      "metadata": {
        "id": "866634d6"
      },
      "outputs": [],
      "source": [
        "qc.measure_all()\n",
        "\n",
        "### Write your code below here ###\n",
        "\n",
        "\n",
        "sampler = #Add your code here\n",
        "pub = #Add your code here\n",
        "job_sampler = #Add your code here\n",
        "\n",
        "\n",
        "### Don't change any code past this line ###\n",
        "\n",
        "result_sampler = job_sampler.result()\n",
        "counts_sampler = result_sampler[0].data.meas.get_counts()\n",
        "\n",
        "print(counts_sampler)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "819ca0b9",
      "metadata": {
        "id": "819ca0b9"
      },
      "outputs": [],
      "source": [
        "# Submit your answer using following code\n",
        "\n",
        "grade_lab1_ex2(job_sampler) # Expected result type: PrimitiveJob"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "114afe5a",
      "metadata": {
        "id": "114afe5a"
      },
      "outputs": [],
      "source": [
        "plot_histogram(counts_sampler)"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "e7a7d98e",
      "metadata": {
        "id": "e7a7d98e"
      },
      "source": [
        "The histogram shows an approximately even probability of finding our qubits in the `01` and the `10` states, suggesting that entanglement was performed as expected."
      ]
    },
    {
      "cell_type": "markdown",
      "id": "32181b27",
      "metadata": {
        "id": "32181b27"
      },
      "source": [
        "<a id=\"exercise3\"></a>\n",
        "<a name=\"exercise3\"></a>\n",
        "<div class=\"alert alert-block alert-success\">\n",
        "    \n",
        "<b> Exercise 3: Create and draw a W-state circuit</b>\n",
        "    \n",
        "Next, we will develop a slightly more complicated circuit. Similarly to Bell states circuit producing Bell states, W-state circuits produce W states. Although Bell states entangle two qubits, W-states entangle three qubits.\n",
        "To build our W-state, we will follow 6 simple steps:\n",
        "\n",
        "1.  Initialize our 3 qubit circuit\n",
        "2.  Perform an Ry rotation on our qubit. The specifics of this operation are provided.\n",
        "3.  Perform a controlled hadamard gate on qubit 1, with control qubit 0\n",
        "4.  Add a CNOT gate with control qubit 1 and target qubit 2\n",
        "5.  Add a CNOT gate with control qubit 0 and target qubit 1\n",
        "6.  Add a X gate on qubit 0\n",
        "\n",
        "**Your Task:** Follow the steps to build the W-state circuit\n",
        "    \n",
        "</div>"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "642af102",
      "metadata": {
        "id": "642af102"
      },
      "outputs": [],
      "source": [
        "# Step 1\n",
        "qc = #your_code_here\n",
        "\n",
        "# Step 2 (provided)\n",
        "qc.ry(1.91063324, 0)\n",
        "\n",
        "# Add steps 3-6 below\n",
        "\n",
        "\n",
        "\n",
        "\n",
        "### Don't change any code past this line ###\n",
        "qc.measure_all()\n",
        "qc.draw('mpl')"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "bd4eebc9",
      "metadata": {
        "id": "bd4eebc9"
      },
      "outputs": [],
      "source": [
        "# Submit your answer using following code\n",
        "\n",
        "grade_lab1_ex3(qc) # Expected result type: # Expected result type: QuantumCircuit"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "8f37ffcc",
      "metadata": {
        "id": "8f37ffcc"
      },
      "source": [
        "Once again, let's visualize our results:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "4cf1070b",
      "metadata": {
        "id": "4cf1070b"
      },
      "outputs": [],
      "source": [
        "sampler = StatevectorSampler()\n",
        "pub = (qc)\n",
        "job_sampler = sampler.run([pub], shots=10000)\n",
        "\n",
        "result_sampler = job_sampler.result()\n",
        "counts_sampler = result_sampler[0].data.meas.get_counts()\n",
        "\n",
        "print(counts_sampler)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "f6bf02e4",
      "metadata": {
        "id": "f6bf02e4"
      },
      "outputs": [],
      "source": [
        "plot_histogram(counts_sampler)"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "668598e4",
      "metadata": {
        "id": "668598e4"
      },
      "source": [
        "We observe our total counts distributed in three similarly sized bins in three states, which are the three desired states for the successful creation of a W-state. Good work!\n",
        "\n",
        "Now that we have basic circuits down, we'll start introducing and developing more complex codes with Qiskit 1.0."
      ]
    },
    {
      "cell_type": "markdown",
      "id": "6196753d",
      "metadata": {
        "id": "6196753d"
      },
      "source": [
        "## Part II: VQE with Qiskit 1.0\n",
        "<a name=\"pt2\"></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "15698c4c-b0c8-4152-921d-f7f3d8c17d6c",
      "metadata": {
        "id": "15698c4c-b0c8-4152-921d-f7f3d8c17d6c"
      },
      "source": [
        "The core of this challenge will leverage Qiskit Runtime and a Variational Quantum Eigensolver (VQE). We will be using the Qiskit Runtime Estimator to calculate expectation values for combinations of qubits, and Qiskit Runtime Sessions to facilitate running a VQE algorithm. The challenge draws upon code from an example that experimental physicist & IBM Quantum researcher Nick Bronn created for the [Coding with Qiskit Runtime video series](https://www.youtube.com/playlist?list=PLOFEBzvs-VvqAC8DnVoLOzg2bKE4C7ARM), specifically in [Episode 05 Primitives & Sessions](https://youtu.be/yxuH8eb4MS4?si=e3trSORNjooWlQXu), and implements it using the newest Qiskit 1.0 version."
      ]
    },
    {
      "cell_type": "markdown",
      "id": "3dc99a7d-dd22-4dd8-a706-f9316dfd79a4",
      "metadata": {
        "id": "3dc99a7d-dd22-4dd8-a706-f9316dfd79a4"
      },
      "source": [
        "### Let's start by creating a Pauli operator\n",
        "A Pauli operator is a matrix representing a quantum mechanical observable corresponding to a measurement of spin along a particular axis (x, y, z). Let's build one:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "c1fb098b-bcb9-4c51-a7d3-31c7d9cdf560",
      "metadata": {
        "id": "c1fb098b-bcb9-4c51-a7d3-31c7d9cdf560",
        "tags": []
      },
      "outputs": [],
      "source": [
        "pauli_op = SparsePauliOp(['ZII', 'IZI', 'IIZ'])\n",
        "print(pauli_op.to_matrix())"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "7c82bfe0",
      "metadata": {
        "id": "7c82bfe0"
      },
      "source": [
        "Feel free to experiment with various Pauli operators and see what resulting possible combinantions you obtain!"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "58adaccf-0198-462b-92dd-973ac13fca19",
      "metadata": {
        "id": "58adaccf-0198-462b-92dd-973ac13fca19",
        "tags": []
      },
      "source": [
        "### Setup and run a VQE algorithm"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "87714a07",
      "metadata": {
        "id": "87714a07"
      },
      "source": [
        "Now, we'll start setting up our VQE algorithm. Variational quantum eigensolvers (VQEs), are hybrid algorithms that utilize quantum and classical techniques to find the ground state of a given physical system. They are often used in quantum chemistry and optimization problems, and are promising candidates for hybrid-algorithms in noisy near-term devices."
      ]
    },
    {
      "cell_type": "markdown",
      "id": "9f8c5410",
      "metadata": {
        "id": "9f8c5410"
      },
      "source": [
        "VQEs are characterized by the use of a classical optimization algorithm to iteratively improve upon a parameterized trial solution, called an \"ansatz\". The aim is to solve for the ground state of a given Hamiltonian represented as a linear combination of Pauli terms."
      ]
    },
    {
      "cell_type": "markdown",
      "id": "d4d2b52b",
      "metadata": {
        "id": "d4d2b52b"
      },
      "source": [
        "Executing a VQE algorithm requires these three steps:\n",
        "\n",
        "1. Setting up the Hamiltonian and ansatz (problem specification)\n",
        "2. Implementing the Qiskit Runtime estimator\n",
        "3. Adding the Classical optimizer and running our program\n",
        "\n",
        "We we will follow these steps."
      ]
    },
    {
      "cell_type": "markdown",
      "id": "84bcedc8",
      "metadata": {
        "id": "84bcedc8"
      },
      "source": [
        "<a id=\"exercise4\"></a>\n",
        "<a name=\"exercise4\"></a>\n",
        "<div class=\"alert alert-block alert-success\">\n",
        "    \n",
        "<b> Exercise 4: Create a parameterized circuit to serve as the ansatz</b>\n",
        "    \n",
        "Our first task will be to set up our ansatz, or a trial solution, for our problem which we will compare against.\n",
        "\n",
        "For this we can use Qiskit's `TwoLocal` circuit, a pre-built circuit that can be used to prepare trial wave functions for variational quantum algorithms or classification circuits for machine learning. TwoLocal circuits are parameterized circuits consisting of alternating rotation layers and entanglement layers. You can find more information about them in [Qiskit's documentation](https://docs.quantum.ibm.com/api/qiskit/circuit_library).\n",
        "\n",
        "**Your Task:** Set up a 3-qubit TwoLocal circuit using [Ry](https://docs.quantum.ibm.com/api/qiskit/qiskit.circuit.library.RYGate) and [Rz](https://docs.quantum.ibm.com/api/qiskit/qiskit.circuit.library.RZGate) rotations. Entanglement should be set to full, and entanglement blocks should use the Cz gate. Make sure you set `reps=1` and `insert_barriers=True`.\n",
        "\n",
        "</div>"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "7932c40f",
      "metadata": {
        "id": "7932c40f",
        "tags": []
      },
      "outputs": [],
      "source": [
        "num_qubits = #Add your code here\n",
        "rotation_blocks = #Add your code here\n",
        "entanglement_blocks = #Add your code here\n",
        "entanglement = #Add your code here\n",
        "\n",
        "ansatz = #Add your code here\n",
        "\n",
        "\n",
        "### Don't change any code past this line ###\n",
        "ansatz.decompose().draw('mpl')"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "7da61e7d",
      "metadata": {
        "id": "7da61e7d"
      },
      "outputs": [],
      "source": [
        "# Submit your answer using following code\n",
        "\n",
        "grade_lab1_ex4(num_qubits, rotation_blocks, entanglement_blocks, entanglement) # Expected result type: int, List[str], str, str"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "360e6651",
      "metadata": {
        "id": "360e6651"
      },
      "source": [
        "From the previous figure we see that our ansatz circuit is defined by a vector of parameters θ, with the total number given by:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "6cf998bc",
      "metadata": {
        "id": "6cf998bc"
      },
      "outputs": [],
      "source": [
        "num_params = ansatz.num_parameters\n",
        "num_params"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "0cefbb00",
      "metadata": {
        "id": "0cefbb00"
      },
      "source": [
        "<a id=\"exercise5\"></a>\n",
        "<a name=\"exercise5\"></a>\n",
        "<div class=\"alert alert-block alert-success\">\n",
        "    \n",
        "<b> Exercise 5: Transpile to ISA circuits </b>\n",
        "    \n",
        "In this example we will use the [FakeSherbrooke](https://docs.quantum.ibm.com/api/qiskit-ibm-runtime/qiskit_ibm_runtime.fake_provider.FakeSherbrooke), a fake  (simulated) 127-qubit backend, useful for testing the transpiler and other backend-facing functionalities.\n",
        "\n",
        "Preset pass managers are the default pass managers used by the `transpile()` function. `transpile()` provides a convenient and simple method to construct a standalone `PassManager` object that mirrors what the transpile function does when optimizing and transforming a quantum circuit for execution on a specific backend.\n",
        "\n",
        "**Your Task:** Define the pass manager. Reference the [Qiskit documentation](https://docs.quantum.ibm.com/api/qiskit/0.42/qiskit.transpiler.preset_passmanagers.generate_preset_pass_manager) for more info.\n",
        "\n",
        "\n",
        "</div>"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "43c88439",
      "metadata": {
        "id": "43c88439"
      },
      "outputs": [],
      "source": [
        "backend_answer = #Add your code\n",
        "optimization_level_answer = #Add your code\n",
        "pm = generate_preset_pass_manager(backend=backend_answer,optimization_level=optimization_level_answer)\n",
        "isa_circuit = # Add your code"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "c8d3e796",
      "metadata": {
        "id": "c8d3e796"
      },
      "source": [
        "<div class=\"alert alert-block alert-info\">\n",
        "    \n",
        "<b>Tip: Make sure you are using the right backend! </b>\n",
        "\n",
        "The grader was designed with **FakeSherbrooke** in mind, and therefore is expecting a 127 qubit map. If you use another backend you might encounter issues.\n",
        "\n",
        "    \n",
        "</div>"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "bb4cda57",
      "metadata": {
        "id": "bb4cda57"
      },
      "outputs": [],
      "source": [
        "# Submit your answer using following code\n",
        "\n",
        "grade_lab1_ex5(isa_circuit) # Expected result type: QuantumCircuit"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "d12f9a35",
      "metadata": {
        "id": "d12f9a35"
      },
      "source": [
        "With the newest version of Qiskit Runtime, all circuits submitted to a backend must conform to the constraints of the backend’s Target. Such circuits are considered to be written in terms of that backend’s Instruction Set Architecture ([ISA](https://www.ibm.com/quantum/blog/isa-circuits?social_post=sf187802680&sf187802680=1)) — i.e., the set of instructions the device can understand and execute. These Target constraints are defined by factors like the device’s native basis gates, its qubit connectivity, and when relevant, its pulse and other instruction timing specifications.\n",
        "To visualize our ISA circuits we can run:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "1b4dc9d7",
      "metadata": {
        "id": "1b4dc9d7"
      },
      "outputs": [],
      "source": [
        "isa_circuit.draw('mpl', idle_wires=False,)"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "3b3eaca0",
      "metadata": {
        "id": "3b3eaca0"
      },
      "source": [
        "As you can see, after transpilation, the circuit only contain the native basis gates of the backend. For more details on ISA circuits check out these resources from the IBM team:\n",
        "\n",
        "- [What are ISA circuits?](https://www.ibm.com/quantum/blog/isa-circuits)\n",
        "- [Understanding the new ISA circuits requirement](https://docs.quantum.ibm.com/announcements/news/2024-05-06-ISA-circuit-requirement#understanding-the-new-isa-circuits-requirement)\n",
        "\n",
        "You can run the next cell to define our Hamiltonian, then move on to Exercise 6."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "930c1e14",
      "metadata": {
        "id": "930c1e14"
      },
      "outputs": [],
      "source": [
        "# Define our Hamiltonian\n",
        "hamiltonian_isa = pauli_op.apply_layout(layout=isa_circuit.layout)"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "e9370742",
      "metadata": {
        "id": "e9370742"
      },
      "source": [
        "<div class=\"alert alert-block alert-info\">\n",
        "    \n",
        "<b>Tip: For the following two exercises make sure you are working with Qiskit 1.0.2! </b>\n",
        "\n",
        "You can download this version using: **%pip install qiskit==1.0.2**\n",
        "\n",
        "    \n",
        "</div>"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "2afa03b7",
      "metadata": {
        "id": "2afa03b7"
      },
      "source": [
        "<a id=\"exercise6\"></a>\n",
        "<a name=\"exercise6\"></a>\n",
        "<div class=\"alert alert-block alert-success\">\n",
        "    \n",
        "<b> Exercise 6: Defining the cost function </b>\n",
        "    \n",
        "Like many classical optimization problems, the solution to a VQE problem can be formulated as minimization of a scalar cost function. The cost function for our VQE is simple: the energy!\n",
        "\n",
        "**Your Task:** Define a cost function by using Qiskit Runtime Estimator to find the energy for a given parameterized state and our Hamiltonian.\n",
        "\n",
        "</div>"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "9f40eea6",
      "metadata": {
        "id": "9f40eea6"
      },
      "outputs": [],
      "source": [
        "def cost_func(params, ansatz, hamiltonian, estimator, callback_dict):\n",
        "    \"\"\"Return estimate of energy from estimator\n",
        "\n",
        "    Parameters:\n",
        "        params (ndarray): Array of ansatz parameters\n",
        "        ansatz (QuantumCircuit): Parameterized ansatz circuit\n",
        "        hamiltonian (SparsePauliOp): Operator representation of Hamiltonian\n",
        "        estimator (EstimatorV2): Estimator primitive instance\n",
        "\n",
        "    Returns:\n",
        "        float: Energy estimate\n",
        "    \"\"\"\n",
        "    pub = #Add your code\n",
        "    result = #Add your code\n",
        "    energy = #Add your code\n",
        "\n",
        "    callback_dict[\"iters\"] += #Add your code\n",
        "    callback_dict[\"prev_vector\"] = #Add your code\n",
        "    callback_dict[\"cost_history\"].#Add your code\n",
        "\n",
        "\n",
        "### Don't change any code past this line ###\n",
        "    print(energy)\n",
        "    return energy, result"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "14f256ca",
      "metadata": {
        "id": "14f256ca"
      },
      "outputs": [],
      "source": [
        "# Submit your answer using following code\n",
        "\n",
        "grade_lab1_ex6(cost_func) # Expected result type: Callable"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "587180d4",
      "metadata": {
        "id": "587180d4"
      },
      "source": [
        "Callback functions are a standard way for users to obtain additional information about the status of an iterative algorithm (such as VQE). However, it is possible to do much more than this. Here, we use a mutable object (dictionary), to store resulting vector at each iteration of our algorithm, in case we need to restart the routine due to failure or return the another iteration number."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "e8081f4d",
      "metadata": {
        "id": "e8081f4d"
      },
      "outputs": [],
      "source": [
        "callback_dict = {\n",
        "    \"prev_vector\": None,\n",
        "    \"iters\": 0,\n",
        "    \"cost_history\": [],\n",
        "}"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "bcb18957",
      "metadata": {
        "id": "bcb18957"
      },
      "source": [
        "### Using the Classical Optimizer"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "418ab1a1",
      "metadata": {
        "id": "418ab1a1"
      },
      "source": [
        "We can now use a classical optimizer of our choice to minimize the cost function.\n",
        "In real quantum hardware, the choice of optimizer is important, as not all optimizers handle noisy cost function landscapes equally well. Here, we can use SciPy routines.\n",
        "\n",
        "To begin the routine, we specify a random initial set of parameters:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "fc62c033",
      "metadata": {
        "id": "fc62c033"
      },
      "outputs": [],
      "source": [
        "x0 = 2 * np.pi * np.random.random(num_params)\n",
        "x0"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "d0aa5a8a",
      "metadata": {
        "id": "d0aa5a8a"
      },
      "source": [
        "<a id=\"exercise7\"></a>\n",
        "<a name=\"exercise7\"></a>\n",
        "<div class=\"alert alert-block alert-success\">\n",
        "    \n",
        "<b> Exercise 7: QiskitRuntimeService V2 Primitives, local testing mode and Sessions, a first look </b>\n",
        "    \n",
        "\n",
        "Next, we will use the new QiskitRuntimeService [V2 primitives](https://docs.quantum.ibm.com/api/migration-guides/v2-primitives): [EstimatorV2](https://docs.quantum.ibm.com/api/qiskit-ibm-runtime/qiskit_ibm_runtime.EstimatorV2) and [SamplerV2](https://docs.quantum.ibm.com/api/qiskit-ibm-runtime/qiskit_ibm_runtime.SamplerV2).\n",
        "\n",
        "The new Estimator interface lets you specify a single circuit and multiple observables and parameter value sets for that circuit, so that sweeps over parameter value sets and observables can be efficiently specified. Previously, you had to specify the same circuit multiple times to match the size of the data to be combined. Also, while you can still use optimization_level and resilience_level as the simple knobs, V2 primitives give you the flexibility to turn on or off individual error mitigation / suppression methods to customize them for your needs.\n",
        "\n",
        "SamplerV2 is simplified to focus on its core task of sampling the quantum register from the execution of quantum circuits. It returns the samples, whose type is defined by the program, without weights. The output data is also separated by the output register names defined by the program. This change enables future support for circuits with classical control flow.\n",
        "\n",
        "We will also use Qiskit's 1.0 [local testing mode](https://docs.quantum.ibm.com/verify/local-testing-mode). Local testing mode (available with qiskit-ibm-runtime 0.22.0 or later) can be used to help develop and test programs before fine-tuning them and sending them to real quantum hardware.\n",
        "\n",
        "**Your Task:** After using local testing mode to verify your program, all you need to do is change the backend name to run it on an IBM Quantum system.\n",
        "\n",
        "</div>"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "ef5a4b21",
      "metadata": {
        "id": "ef5a4b21"
      },
      "outputs": [],
      "source": [
        "### Select a Backend\n",
        "## Use FakeSherbrooke to simulate with noise that matches closer to the real experiment. This will run slower.\n",
        "## Use AerSimulator to simulate without noise to quickly iterate. This will run faster.\n",
        "\n",
        "backend = FakeSherbrooke()\n",
        "# backend = AerSimulator()\n",
        "\n",
        "# ### Don't change any code past this line ###\n",
        "\n",
        "# Here we have updated the cost function to return only the energy to be compatible with recent scipy versions (>=1.10)\n",
        "def cost_func_2(*args, **kwargs):\n",
        "    energy, result = cost_func(*args, **kwargs)\n",
        "    return energy\n",
        "\n",
        "with Session(backend=backend) as session:\n",
        "    estimator = Estimator(session=session)\n",
        "\n",
        "    res = minimize(\n",
        "        cost_func_2,\n",
        "        x0,\n",
        "        args=(isa_circuit, hamiltonian_isa, estimator, callback_dict),\n",
        "        method=\"cobyla\",\n",
        "        options={'maxiter': 30})"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "dbf51251",
      "metadata": {
        "id": "dbf51251"
      },
      "outputs": [],
      "source": [
        "# Submit your answer using following code\n",
        "\n",
        "grade_lab1_ex7(res) # Expected result type: OptimizeResult"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "ed244e79",
      "metadata": {
        "id": "ed244e79"
      },
      "source": [
        "<div class=\"alert alert-block alert-info\">\n",
        "    \n",
        "<b>Tip: Increase `maxiter` if you do not see convergence </b>\n",
        "\n",
        "If the cost is not converging, increase the `maxiter` (100 is an appropriate number) and run Ex 7 again.\n",
        "    \n",
        "</div>"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "ff0288b9",
      "metadata": {
        "id": "ff0288b9"
      },
      "source": [
        "Let's look at our results:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "83a37869",
      "metadata": {
        "id": "83a37869"
      },
      "outputs": [],
      "source": [
        "fig, ax = plt.subplots()\n",
        "plt.plot(range(callback_dict[\"iters\"]), callback_dict[\"cost_history\"])\n",
        "plt.xlabel(\"Iteration\")\n",
        "plt.ylabel(\"Cost\")\n",
        "plt.draw()"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "82dbcec9",
      "metadata": {
        "id": "82dbcec9"
      },
      "source": [
        "🎉 As expected our VQE algorithm minimized our energy across iterations, until reaching the ground state. We have now successfully implemented a VQE algorithm using brand-new Qiskit 1.0 functionalities!"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "51e406f1",
      "metadata": {
        "id": "51e406f1"
      },
      "source": [
        "Thank you for completing this lab, and good luck with the remaining ones!"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "d410b818",
      "metadata": {
        "id": "d410b818"
      },
      "source": [
        "# Additional information\n",
        "\n",
        "**Created by:** James Weaver, Maria Gragera Garces\n",
        "\n",
        "**Advised by:** Junye Huang\n",
        "\n",
        "**Version:** 1.3.0"
      ]
    }
  ],
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