{ "cells": [ { "cell_type": "markdown", "id": "miniature-tunisia", "metadata": {}, "source": [ "# Qiskit 1 - 2020/2021" ] }, { "cell_type": "markdown", "id": "super-interpretation", "metadata": {}, "source": [ " \n", "\n", "## Contents\n", "0. [Installation](#inst)\n", "\n", "1. [Introduction](#introduction)\n", "\n", " 1.1 [Overview of Qiskit](#qiskit_overview)\n", " \n", " 1.2 [The quantum bit](#quantum_bit)\n", " \n", "2. [Single-qubit states](#single_states)\n", "\n", " 2.1 [Single-qubit operations](#single_operations)\n", " \n", "3. [Multi-qubit states](#multi_qubits)\n", "\n", " 3.1 [Multi-qubit operations](#multi_op)\n", " \n", "4. [Summary](#summary)\n", "\n", "5. [Exercises](#exer)\n", "\n", " " ] }, { "cell_type": "markdown", "id": "flexible-reporter", "metadata": {}, "source": [ "## Installation " ] }, { "cell_type": "markdown", "id": "intense-popularity", "metadata": {}, "source": [ "1. Create an account in [IBM Q Experience](https://quantum-computing.ibm.com/). You need an account to use IBM Q Quantum computers. This account can be used to run your programs if the local installation fails.\n", "2. Download [Anaconda](https://www.anaconda.com/) and execute the sh file.\n", "3. Run:\n", "\n", "``conda create -n name_of_my_env python=3``\n", "\n", "``source activate name_of_my_env`` or ``conda activate ENV_NAME``\n", "\n", "``pip install qiskit``\n", "\n", "Check [Qiskit Documentation](https://qiskit.org/documentation/install.html) for more information." ] }, { "cell_type": "code", "execution_count": 1, "id": "affiliated-yukon", "metadata": {}, "outputs": [ { "data": { "text/html": [ "

Version Information

Qiskit SoftwareVersion
Qiskit0.24.0
Terra0.16.4
Aer0.7.6
Ignis0.5.2
Aqua0.8.2
IBM Q Provider0.12.1
System information
Python3.9.2 (default, Mar 3 2021, 15:03:14) [MSC v.1916 64 bit (AMD64)]
OSWindows
CPUs4
Memory (Gb)15.885398864746094
Mon Apr 26 11:33:31 2021 Hora de Verão de GMT
" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import qiskit.tools.jupyter\n", "%qiskit_version_table" ] }, { "cell_type": "markdown", "id": "expensive-richardson", "metadata": {}, "source": [ " \n", "\n", "# 1. Introduction \n", "## 1.1 Qiskit Overview\n", "\n", "\"Note: Trusted Notebook\" width=\"400 px\" align=\"center\">\n", "\n", "Qiskit is an open-source framework for working with quantum computers at the level of algorithms, quantum circuits, or even pulses. It can be installed and executed locally, but to execute your code in actual, public access quantum processors, you need to create a [IBM Quantum experience](https://quantum-computing.ibm.com) account.\n", "\n", "\n", "Its main goals are:\n", "\n", " - to build a software stack for the development of quantum software and applications;\n", " - to make it easier for students to understand and learn about quantum computation;\n", " - to facilitate research on the most important open issues facing quantum computation today.\n", "\n", "Qiskit supports the *Python* language, which is itself compatible with multiple programming paradigms.\n", "\n", "\n", "The main pillar of this toolkit (which the majority of these classes will feature) is **Qiskit Terra**, and it allows us to:\n", "\n", "- compose quantum programs at the level of circuits and pulses;\n", "- optimize them for the constraints of a particular device;\n", "- interact with the execution backends.\n", "\n", "As of version `0.12`, Qiskit is composed of other 3 main modules:\n", "\n", "**Aer** is a simulator framework for the stack - it allows us to:\n", "- simulate the execution of a quantum circuit under ideal (ie noiseless) conditions;\n", "- obtain the complete mathematical description of a given quantum state or quantum operator;\n", "- construct highly configurable models for realistic noisy simulations of the errors that occur during execution on real devices;\n", "\n", "
\n", "Note that these simulations are performed on classical computers, and so are limited by classical resources.\n", "
\n", "\n", "**Ignis** is a framework for understanding and mitigating noise in quantum circuits and systems. The experiments provided in Ignis are grouped into the topics of:\n", "- characterization of quantum system parameters such as noise (T1 and T2), and control errors in the gates;\n", "- verification of quantum operation and ciruit performance, using for example process tomography or randomized benchmarking;\n", "- error mitigation routines generated by execution of calibration circuits;\n", "\n", "**Aqua** provides higher-level functionality by use of a library of quantum algorithms upon which applications of near term quantum computing can be built. Aqua specifically identifies four domains that stand to benefit from the development of quantum computation:\n", "- Chemistry;\n", "- Artificial Intelligence (AI);\n", "- Optimization;\n", "- Finance.\n", "\n", "**Qiskit 0.25.0**\n", "This release officially deprecates the Qiskit Aqua project. Accordingly, in a future release the qiskit-aqua package will be removed from the Qiskit metapackage, which means in that future release pip install qiskit will no longer include qiskit-aqua. The application modules that are provided by qiskit-aqua have been split into several new packages: qiskit-optimization, qiskit-nature, qiskit-machine-learning, and qiskit-finance. \n", "\n", "On March 2021 Qiskit lanched **[Qiskit Metal](https://qiskit.org/metal/)** the first open source project to design super conducting quantum devices.\n", "\n", "Qiskit is still under an intense development cycle, which means that new updates and features are added several times a year." ] }, { "cell_type": "markdown", "id": "public-oriental", "metadata": {}, "source": [ " \n", "\n", "## 1.2. The quantum bit\n", "\n", " \n", "\n", "### A physical qubit\n", "\n", "Any quantum system with two orthogonal states can be used to represent a quantum bit, or *qubit* for short.\n", "\n", "\n", "\n", "Consider a simplified representation of the electron of a Hydrogen atom, orbiting around the nucleus, with two possible energy states. As this is a quantum particle, these energy states are quantized, that is, they take only discrete values. The energy state of the electron can be considered a quantum bit.\n", "\n", "How can we represent quantum states and associated operations?" ] }, { "cell_type": "markdown", "id": "cheap-vacuum", "metadata": {}, "source": [ " \n", "\n", "### Bra-ket notation\n", "\n", "In quantum mechanics, wave functions and other quantum states can be represented as vectors in an abstract vector space.\n", "\n", "The bra–ket notation is a standard notation for describing quantum states. It uses angle brackets (the $\\rangle$ and $\\langle$ symbols) with a vertical bar (the $|$ symbol) to denote labelled vectors.\n", "\n", "- A *ket* $|u\\rangle$ is typically written as a column vector, while a *bra* $\\langle v |$ is typically written as a row vector.\n", "\n", "- A *bra* and a *ket* with the same label are [Hermitian conjugates](https://en.wikipedia.org/wiki/Conjugate_transpose) of each other. \n", "\n", "This notation simplifies the representation of the scalar product of vectors, as well as the action of a linear operator on a vector and other operations over a complex vector space.\n", "\n", "
\n", " \n", "**Example 1.1 - Inner product with bra-ket**\n", "\n", "Consider the ket vector $|u\\rangle$ and $|v\\rangle$ on a two-dimensional space:\n", "\n", "$$\n", "|u\\rangle = \n", "\\begin{pmatrix}\n", "1 \\\\\n", "0\n", "\\end{pmatrix};\n", "\\;\\;\n", "|v\\rangle = \n", "\\begin{pmatrix}\n", "0 \\\\\n", "i\n", "\\end{pmatrix};\n", "$$\n", "\n", " \n", "\n", "Their respective hermitian conjugates, $\\langle u|$ and $\\langle v|$, can be represented as row vectors:\n", "\n", " \n", "\n", "$$\n", "\\langle u| = \n", "\\begin{pmatrix}\n", "1 & 0\n", "\\end{pmatrix};\n", "\\;\\;\n", "\\langle v | = \n", "\\begin{pmatrix}\n", "0 & -i\n", "\\end{pmatrix};\n", "$$\n", "\n", " \n", "\n", "The inner product between $\\langle v|$ and $|u\\rangle$ is represented as $\\langle v | u \\rangle$:\n", "\n", " \n", "\n", "$$\n", "\\langle v | u \\rangle =\n", "\\begin{pmatrix}\n", "0 & -i\n", "\\end{pmatrix}\n", "\\begin{pmatrix}\n", "1 \\\\\n", "0\n", "\\end{pmatrix} = 0 \\, ;\n", "$$\n", "\n", " \n", "\n", "A null inner product means that these vectors are orthogonal, thereby forming a basis in a two-dimensional space.\n", "
" ] }, { "cell_type": "markdown", "id": "useful-burlington", "metadata": {}, "source": [ " \n", "\n", "# 2. Single qubit states\n", "\n", " \n", "\n", "A single qubit quantum state $|\\psi\\rangle$ can be written as a complex superposition of its basis states, which by convention are generally named $|0\\rangle$ and $|1\\rangle$.\n", "\n", "$$|\\psi\\rangle = \\alpha|0\\rangle + \\beta |1\\rangle$$\n", "\n", "Here, $\\alpha$ and $\\beta$ are probability amplitudes generally described by complex numbers. When the qubit is measured, the quantum system \"collapses\" to the state $|0\\rangle$ with probability $|\\alpha|^2$, or to the state $|1\\rangle$ with probability $|\\beta|^2$.\n", "\n", "\n", "The basis states represent the quantum analogue to the classical bit states $0$ and $1$:\n", "\n", "$$\n", "|0\\rangle = \n", "\\begin{pmatrix}\n", "1 \\\\\n", "0\n", "\\end{pmatrix};\n", "\\;\\;\\;\n", "|1\\rangle = \n", "\\begin{pmatrix}\n", "0 \\\\\n", "1\n", "\\end{pmatrix};\n", "$$\n", "\n", "Which allows for the column representation of $|\\psi\\rangle$:\n", "\n", "$$\n", "|\\psi\\rangle = \n", "\\begin{pmatrix}\n", "\\alpha \\\\\n", "\\beta\n", "\\end{pmatrix}\n", "$$\n", "\n", "where $|\\alpha|^2 + |\\beta^2| = 1$." ] }, { "cell_type": "code", "execution_count": 2, "id": "minute-final", "metadata": { "ExecuteTime": { "end_time": "2018-09-29T00:04:16.313210Z", "start_time": "2018-09-29T00:04:14.460647Z" }, "hideOutput": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Modules successfully imported.\n" ] } ], "source": [ "# Comments on code cells are preceded by '#'\n", "\n", "# Relevant QISKit modules\n", "\n", "from qiskit import QuantumCircuit, ClassicalRegister, QuantumRegister, Aer, execute\n", "\n", "from qiskit.tools.visualization import plot_histogram, visualize_transition\n", "\n", "# Useful additional packages \n", "\n", "import matplotlib.pyplot as plt\n", "%matplotlib inline\n", "import numpy as np\n", "from math import pi\n", "\n", "# Output a message to confirm all modules are imported\n", "\n", "print(\"Modules successfully imported.\")" ] }, { "cell_type": "markdown", "id": "deluxe-exception", "metadata": {}, "source": [ "We need to create a space to save information about your qubit state. \n", "Those are **registers**.\n", "\n", "We will need a set of **quantum registers** to save the quantum state \n", "and a set of **classical registers** where we save information after measuring the qubits. " ] }, { "cell_type": "code", "execution_count": 3, "id": "tender-climb", "metadata": {}, "outputs": [], "source": [ "qr = QuantumRegister(1,'q')\n", "cr = ClassicalRegister(1,'c')" ] }, { "cell_type": "markdown", "id": "corporate-priority", "metadata": {}, "source": [ "The next step is to apply these registers to a **quantum circuit**." ] }, { "cell_type": "code", "execution_count": 4, "id": "sound-foundation", "metadata": {}, "outputs": [], "source": [ "circuit = QuantumCircuit(qr,cr)" ] }, { "cell_type": "markdown", "id": "individual-terrorism", "metadata": {}, "source": [ "Now we have a quantum circuit with the name circuit.\n", "\n", "It would be nice to see it!" ] }, { "cell_type": "markdown", "id": "fewer-translation", "metadata": {}, "source": [ "Allow the matplotlib to run with the following line:" ] }, { "cell_type": "code", "execution_count": 5, "id": "competitive-logistics", "metadata": {}, "outputs": [], "source": [ "%matplotlib inline" ] }, { "cell_type": "markdown", "id": "voluntary-spirituality", "metadata": {}, "source": [ "Now every time you want to see your circuit you only need to use the function **draw()**." ] }, { "cell_type": "code", "execution_count": 6, "id": "theoretical-guard", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
     \n",
       "q_0: \n",
       "     \n",
       "c: 1/\n",
       "
" ], "text/plain": [ " \n", "q_0: \n", " \n", "c: 1/\n", " " ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "circuit.draw()" ] }, { "cell_type": "markdown", "id": "stopped-cambridge", "metadata": {}, "source": [ "Or in case you are a perfectionist:" ] }, { "cell_type": "code", "execution_count": 7, "id": "liable-boost", "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "circuit.draw(output='mpl')" ] }, { "cell_type": "markdown", "id": "better-suggestion", "metadata": {}, "source": [ "By default, the initial state of the qubit is |0> also known as the *ground state*." ] }, { "cell_type": "markdown", "id": "czech-cannon", "metadata": {}, "source": [ " \n", "\n", "### Bloch sphere\n", "\n", "It is then possible to create a one-to-one correspondence between a qubit state ($\\mathbb{C}^2$) and the points on the surface of a unit sphere ($\\mathbb{R}^3$). This is called the Bloch sphere representation of a qubit state.\n", "\n", "\"\"\n", "\n", "By contrast, a representation of a classical bit over the Bloch sphere would only require the two points of the sphere intersecting the Z axis." ] }, { "cell_type": "code", "execution_count": 8, "id": "sticky-appliance", "metadata": {}, "outputs": [], "source": [ "backend_vector = Aer.get_backend(\"statevector_simulator\")" ] }, { "cell_type": "code", "execution_count": 9, "id": "latest-wisconsin", "metadata": {}, "outputs": [], "source": [ "result = execute(circuit, backend_vector).result()\n", "qstate= result.get_statevector(circuit)" ] }, { "cell_type": "code", "execution_count": 10, "id": "animated-chain", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[1.+0.j 0.+0.j]\n" ] } ], "source": [ "print(qstate)" ] }, { "cell_type": "markdown", "id": "worthy-discussion", "metadata": {}, "source": [ "Import the visualization tools:" ] }, { "cell_type": "code", "execution_count": 11, "id": "through-workshop", "metadata": {}, "outputs": [], "source": [ "from qiskit.tools.visualization import *" ] }, { "cell_type": "code", "execution_count": 12, "id": "individual-hypothesis", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "plot_bloch_multivector(qstate)" ] }, { "cell_type": "markdown", "id": "mathematical-bidding", "metadata": {}, "source": [ " \n", "\n", "## 2.1 Single-Qubit Gates\n", "\n", " \n", "\n", "Quantum gates/operations are usually represented as matrices. A gate acting on a single qubit is represented by a $2\\times 2$ unitary matrix $U$ with complex entries. The action of the quantum gate on the qubit is determined by multiplying the matrix representing the gate with the vector which represents the quantum state.\n", "\n", "$$|\\psi'\\rangle = U|\\psi\\rangle$$\n", "\n", "Some of the single-qubit gates available are:\n", "- Pauli gates\n", "- Hadamard gate\n", "- Measurement gates" ] }, { "cell_type": "markdown", "id": "noticed-landing", "metadata": {}, "source": [ "### Pauli gates\n", "\n", "#### Gate $X$: bit-flip gate \n", "\n", "The X-gate is also known as NOT gate or “bit-flip”, since it changes a state $| 0 \\rangle $ to $| 1 \\rangle $ and vice versa. **This is the quantum analogue to a classical NOT gate.**\n", "\n", "On the Bloch sphere representation, this operation corresponds to a rotation of the state around the X-axis by $\\pi$ radians.\n", "\n", "
\n", " \n", " (Source)\n", "
\n", "\n", "\n", "\n", "The $X$ gate can be represented by a $2 \\times 2$ matrix:\n", "$$\n", "X = \n", "\\begin{pmatrix}\n", "0 & 1\\\\\n", "1 & 0\n", "\\end{pmatrix}\n", "$$\n", "\n", "\n", "#### $Y$: bit-and-phase-flip gate\n", "\n", "The $Y$ gate is defined by the matrix:\n", "\n", "$$\n", "Y = \n", "\\begin{pmatrix}\n", "0 & -i\\\\\n", "i & 0\n", "\\end{pmatrix}\n", "$$\n", "\n", "It is equivalent to a rotation around Y-axis of the Bloch sphere by $\\pi$ radians.\n", "This gate maps $| 0 \\rangle $ to $i | 1 \\rangle $, and $| 1 \\rangle$ to $ - i | 0 \\rangle$\n", "\n", "#### $Z$: phase-flip gate\n", "\n", "The phase flip gate $Z$ is defined by:\n", "\n", "$$\n", "Z = \n", "\\begin{pmatrix}\n", "1 & 0\\\\\n", "0 & -1\n", "\\end{pmatrix}\n", "$$\n", "\n", "It leaves the basis state $|0 \\rangle $ unchanged, while mapping $| 1 \\rangle$ to $- | 1 \\rangle $." ] }, { "cell_type": "markdown", "id": "inside-maker", "metadata": {}, "source": [ "Now we are going to add **quantum gates** to the circuit, namely **X gate**. " ] }, { "cell_type": "code", "execution_count": 13, "id": "velvet-packaging", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# use the index of qr to define the position of the hadamard gate\n", "# here we selected qubits 0 \n", "circuit.x(qr)" ] }, { "cell_type": "code", "execution_count": 14, "id": "amazing-pixel", "metadata": { "scrolled": true }, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" } ], "source": [ "circuit.draw(output='mpl')" ] }, { "cell_type": "code", "execution_count": 15, "id": "athletic-boutique", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[0.+0.j 1.+0.j]\n" ] } ], "source": [ "result = execute(circuit, backend_vector).result()\n", "qstate= result.get_statevector(circuit)\n", "print(qstate)" ] }, { "cell_type": "code", "execution_count": 16, "id": "driving-topic", "metadata": { "scrolled": false }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "execution_count": 16, "metadata": {}, "output_type": "execute_result" } ], "source": [ "plot_bloch_multivector(qstate)" ] }, { "cell_type": "markdown", "id": "gross-voltage", "metadata": {}, "source": [ "### Hadamard gate\n", "\n", "The Hadamard gate may be used to create superposition. It maps the basis state $| 0 \\rangle$ to $| + \\rangle =\\frac{| 0 \\rangle + | 1 \\rangle }{\\sqrt{2}}$, and $| 1 \\rangle $ to $ | - \\rangle =\\frac{ |0 \\rangle - |1 \\rangle }{\\sqrt{2}}$. On the Bloch sphere, $| + \\rangle$ and $| - \\rangle $ are represented by points on the X axis. \n", "\n", "When measured, these states have equal probability of becoming $| 1\\rangle $ or $| 0 \\rangle $, since the square modulus of the probability amplitude for each of the basis states has equal value.\n", "\n", "
\n", " \n", " (Source)\n", "
\n", "\n", "In fact, $|+\\rangle $ and $| - \\rangle $ are indistinguishable when measured on the computational basis. However, the states can be identified by measuring the qubit on the superposition basis, i.e. along the X-axis. A way to achieve this is by simply applying an Hadamard gate before performing the measurement.\n", "\n", "The Hadamard gate is defined by:\n", "\n", "$$\n", "H = \\frac{1}{\\sqrt{2}}\n", "\\begin{pmatrix}\n", "1 & 1\\\\\n", "1 & -1\n", "\\end{pmatrix}\n", "$$\n", "\n", " \n", "\n", "**Note**: The Hadamard gate, along with the X, Y and Z gates, is self-inverse: $H.H = I$." ] }, { "cell_type": "markdown", "id": "electoral-participant", "metadata": {}, "source": [ "Now we are going to add another **quantum gates** to the circuit, namely **Hadamard gate**. " ] }, { "cell_type": "code", "execution_count": 17, "id": "european-pickup", "metadata": {}, "outputs": [], "source": [ "# use the index of qr to define the position of the hadamard gate\n", "# here we selected qubits 0 \n", "circuit.h(qr[0])" ] }, { "cell_type": "code", "execution_count": 18, "id": "blocked-aside", "metadata": { "scrolled": false }, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "execution_count": 18, "metadata": {}, "output_type": "execute_result" } ], "source": [ "circuit.draw(output='mpl')" ] }, { "cell_type": "markdown", "id": "muslim-masters", "metadata": {}, "source": [ "This gate creates **superposition**." ] }, { "cell_type": "code", "execution_count": 19, "id": "thermal-montana", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[ 0.70710678-8.65956056e-17j -0.70710678+8.65956056e-17j]\n" ] } ], "source": [ "result = execute(circuit, backend_vector).result()\n", "qstate= result.get_statevector(circuit)\n", "print(qstate)" ] }, { "cell_type": "code", "execution_count": 20, "id": "joined-metropolitan", "metadata": { "scrolled": false }, "outputs": [ { "data": { "image/png": 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\n", 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "visualize_transition(circuit, fpg=20, spg=1, trace=True)" ] }, { "cell_type": "markdown", "id": "turned-pillow", "metadata": {}, "source": [ " \n", "\n", "### Measurement gate\n", "\n", "A direct measurement causes the system to collapse to a deterministic state i.e. stabilise in a non-reversible way. Physically, we still don't know exactly how this collapse occurs, in what is called the [measurement problem](https://en.wikipedia.org/wiki/Measurement_problem).\n", "\n", "A repeated measurement of the collapsed quantum system will return the same results, just like repeated readings of a bit string.\n", "\n", "When we perform a measurement on a qubit, we observe either $|0\\rangle$ or $|1\\rangle$ - which is then interpreted as a binary digit, $0$ or $1$. As such, a single measurement of a quantum system yields at most 1 bit per qubit. When a quantum system is in a superposition of basis states, many more measurements are needed to accurately estimate probability amplitudes.\n", "\n", "\n", "\n", "In Qiskit measurement operations can be performed by defining the correspondence between the measured qubit and the bit where the result of the operation (0 or 1) is going to be stored. \n", "\n", "Since the measuring process physically collapses the qubit into a classical state, QISKit does not allow for subsequent quantum operations on the measured qubit.\n", "\n", "
\n", "\n", "The measurement operation `measure(qr[i], cr[j])` is called on a circuit object by specifying the quantum register `qr`and qubit `i` to be measured, and the classical register `cr` and bit `j` which is to store the measurement value. A measurement can also be called over the complete register, provided that registers `qr` and `cr` are the same size: `measure(qr, cr)`.\n", "\n", "
" ] }, { "cell_type": "code", "execution_count": 22, "id": "constant-defense", "metadata": {}, "outputs": [ { "data": { "image/png": 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" ] }, "execution_count": 22, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Create quantum register with 2 qubits\n", "qr = QuantumRegister(2)\n", "\n", "# Create a classical register with 2 bits\n", "cr = ClassicalRegister(2)\n", "\n", "# Quantum circuit\n", "qc_m = QuantumCircuit(qr, cr)\n", "\n", "#Measurement operation\n", "qc_m.measure(qr, cr)\n", "\n", "# Draw circuit (using matplotlib)\n", "qc_m.draw(output='mpl')" ] }, { "cell_type": "markdown", "id": "otherwise-project", "metadata": {}, "source": [ " \n", "\n", "# 3. Multi-qubit states\n", "\n", " \n", "\n", "Multiple quantum bits can be described with the ket notation. The tensor product is typically implicit; for a state composed of qubits $q_0$ and $q_1$:\n", "\n", " \n", "\n", "$$\n", "|q_1\\rangle \\otimes |q_0\\rangle = |q_1\\rangle |q_0\\rangle = |q_1 q_0\\rangle\n", "$$\n", "\n", " \n", "\n", "**Note**: The ordering convention adopted in Qiskit writes the first qubit of a circuit at the far-right of the ket, and adds each additional qubit on the left:\n", "\n", " \n", "\n", "$$ |q_n\\rangle \\otimes \\cdots \\otimes |q_1\\rangle \\otimes |q_0\\rangle $$\n", "\n", " \n", "\n", "Keep in mind that this ordering may be different than quantum circuits and algorithms described in scientific literature, and needs to be taken into account when analysing results of multi-qubit measurements, or the algebraic description of multi-qubit operations and states.\n", "\n", "
\n", "\n", "**Example 1.2 - Tensor product**\n", "\n", "Consider two non-entangled qubits of a quantum circuit, $q_a$ and $q_b$. Their joint-state description can be written in bra-ket notation, with the tensor product providing an algebraic description of the state.\n", "\n", " \n", "\n", "$$|q_a q_b\\rangle = |q_a\\rangle \\otimes |q_b\\rangle = \n", "\\begin{pmatrix}\n", "q_{a1} \\\\ \n", "q_{a2}\n", "\\end{pmatrix} \\otimes\n", "\\begin{pmatrix}\n", "q_{b1} \\\\ \n", "q_{b2}\n", "\\end{pmatrix} =\n", "\\begin{pmatrix}\n", "q_{a1}.q_{b1} \\\\\n", "q_{a1}.q_{b2} \\\\\n", "q_{a2}.q_{b1} \\\\\n", "q_{a2}.q_{b2}\n", "\\end{pmatrix}\n", "$$\n", "\n", " \n", "\n", "Using the tensor product, we can determine the vector of an $n$-qubit basis state. For example:\n", "\n", " \n", "\n", "$$|10\\rangle = |1\\rangle \\otimes |0\\rangle = \n", "\\begin{pmatrix}\n", "0 \\\\ \n", "1\n", "\\end{pmatrix} \\otimes\n", "\\begin{pmatrix}\n", "1 \\\\ \n", "0\n", "\\end{pmatrix} = \n", "\\begin{pmatrix}\n", "0 \\\\ \n", "0 \\\\\n", "1 \\\\\n", "0\n", "\\end{pmatrix}\n", "$$\n", "
\n", "\n", " \n", "\n", "### Entanglement and Bloch sphere for multi-qubit states\n", "\n", " \n", "\n", "Since qubits can be entangled, multi-qubit states, in general, cannot be expressed by simply representing each qubit's Bloch sphere. This is because the dimension of the vector space rises exponentially with the number of qubits, to account for correlation between qubits. One attempt to visualize multi-qubit states is made [here](https://medium.com/qiskit/visualizing-bits-and-qubits-9af287047b28). \n", "\n", "**For a quantum system, its description is more than the sum of descriptions for each individual qubit.**" ] }, { "cell_type": "markdown", "id": "appreciated-tuition", "metadata": {}, "source": [ " \n", "\n", "## 3.1 Multi-qubit operations \n", "\n", " \n", "\n", "### CNOT gate \n", "\n", "The controlled-NOT (or controlled-$X$) gate allows for the creation of entanglement between two qubits in a quantum circuit. The CNOT gate's action on basis states is to flip, i.e. apply an $X$ gate to, the target qubit (denoted as $\\oplus$ in quantum circuits) if the control qubit (denoted as $\\bullet$), is $|1\\rangle$; otherwise the target qubit goes unchanged.\n", "\n", "The matrix describing a CNOT depends on which qubit acts as control. For a state $|q_1 q_0\\rangle$, if we apply a CNOT operation with $q_1$ as control, the matrix is described as:\n", "\n", "$$\n", "C_X = \n", "\\begin{pmatrix}\n", "1 & 0 & 0 & 0\\\\\n", "0 & 1 & 0 & 0\\\\\n", "0 & 0 & 0 & 1\\\\\n", "0 & 0 & 1 & 0\n", "\\end{pmatrix}. \n", "$$" ] }, { "cell_type": "code", "execution_count": 23, "id": "appreciated-trust", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 23, "metadata": {}, "output_type": "execute_result" } ], "source": [ "circuit_aux = QuantumCircuit(qr,cr)\n", "circuit_aux.cx(qr[0],qr[1])" ] }, { "cell_type": "code", "execution_count": 24, "id": "fifth-harassment", "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "execution_count": 24, "metadata": {}, "output_type": "execute_result" } ], "source": [ "circuit_aux.draw(output='mpl')" ] }, { "cell_type": "markdown", "id": "trained-reader", "metadata": {}, "source": [ "To understand this section of the circuit you need to use the **UnitarySimulator**" ] }, { "cell_type": "code", "execution_count": 25, "id": "finished-command", "metadata": {}, "outputs": [], "source": [ "backend_unitary = Aer.get_backend('unitary_simulator')" ] }, { "cell_type": "code", "execution_count": 26, "id": "european-relationship", "metadata": { "scrolled": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[1.+0.j 0.+0.j 0.+0.j 0.+0.j]\n", " [0.+0.j 0.+0.j 0.+0.j 1.+0.j]\n", " [0.+0.j 0.+0.j 1.+0.j 0.+0.j]\n", " [0.+0.j 1.+0.j 0.+0.j 0.+0.j]]\n" ] } ], "source": [ "job = execute(circuit_aux, backend_unitary)\n", "result = job.result()\n", "unitary_matrix = result.get_unitary(circuit_aux, decimals=3)\n", "\n", "# Show the results\n", "print(unitary_matrix)" ] }, { "cell_type": "code", "execution_count": 27, "id": "speaking-retreat", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[1. 0. 0. 0.]\n", " [0. 0. 0. 1.]\n", " [0. 0. 1. 0.]\n", " [0. 1. 0. 0.]]\n" ] } ], "source": [ "# in this case you can use:\n", "print(unitary_matrix.real)" ] }, { "cell_type": "markdown", "id": "interested-notification", "metadata": {}, "source": [ "This is different from the expected matrix:\n", "\n", "$$\\begin{bmatrix}1&0&0&0\\\\0&1&0&0\\\\0&0&0&1\\\\0&0&1&0\\end{bmatrix}$$" ] }, { "cell_type": "markdown", "id": "invisible-lodge", "metadata": {}, "source": [ "In most of the literature $q_0$ is the most significant qubit:\n", "\n", "|control|target|control|target|\n", "|-|-|-|-|\n", "|input $q_0$|input $q_1$|output $q_0$|output $q_1$|\n", "|0|0|0|0|\n", "|0|1|0|1|\n", "|**1**|**0**|**1**|**1**|\n", "|**1**|**1**|**1**|**0**|\n", "\n", "In Qiskit $q_0$ is the least significant qubit:\n", "\n", "|target|control|target|control|\n", "|-|-|-|-|\n", "|input $q_1$|input $q_0$|output $q_1$|output $q_0$|\n", "|0|0|0|0|\n", "|**0**|**1**|**1**|**1**|\n", "|1|0|1|1|\n", "|**1**|**1**|**0**|**1**|\n", "\n", "Matrix change in a similar way as the truth table." ] }, { "cell_type": "markdown", "id": "bottom-calcium", "metadata": {}, "source": [ "### Merging Circuits" ] }, { "cell_type": "code", "execution_count": 28, "id": "atmospheric-professor", "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "execution_count": 28, "metadata": {}, "output_type": "execute_result" } ], "source": [ "circuit = QuantumCircuit(qr,cr)\n", "circuit.h(qr[0])\n", "circuit.draw(output='mpl')" ] }, { "cell_type": "code", "execution_count": 29, "id": "united-article", "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "execution_count": 29, "metadata": {}, "output_type": "execute_result" } ], "source": [ "circuit = circuit + circuit_aux\n", "circuit.draw(output='mpl')" ] }, { "cell_type": "code", "execution_count": 30, "id": "owned-intake", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[0.70710678+0.j 0. +0.j 0. +0.j 0.70710678+0.j]\n" ] } ], "source": [ "result = execute(circuit, backend_vector).result()\n", "qstate= result.get_statevector(circuit)\n", "print(qstate)" ] }, { "cell_type": "markdown", "id": "nominated-sampling", "metadata": {}, "source": [ "### Simulate the quantum computer" ] }, { "cell_type": "markdown", "id": "sitting-appliance", "metadata": {}, "source": [ "First, add measure gate." ] }, { "cell_type": "code", "execution_count": 31, "id": "committed-parish", "metadata": {}, "outputs": [], "source": [ "# Do you want one measure gate in every qr and creation of additional cr?\n", "all_measure_f = False\n", "\n", "if (all_measure_f):\n", " circuit.measure_all()\n", "else:\n", " # use the index of qr to define the position of the measure gate \n", " # add use the index of cr to define the position to save the value\n", " # In this example, the two option are equivalent\n", " circuit.measure(qr,cr)" ] }, { "cell_type": "code", "execution_count": 32, "id": "signed-pharmaceutical", "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "execution_count": 32, "metadata": {}, "output_type": "execute_result" } ], "source": [ "circuit.draw(output='mpl')" ] }, { "cell_type": "code", "execution_count": 33, "id": "numeric-voluntary", "metadata": {}, "outputs": [], "source": [ "backend = Aer.get_backend(\"qasm_simulator\")" ] }, { "cell_type": "code", "execution_count": 34, "id": "vital-desktop", "metadata": {}, "outputs": [], "source": [ "result = execute(circuit, backend, shots=1024).result()\n", "counts = result.get_counts(circuit)" ] }, { "cell_type": "code", "execution_count": 35, "id": "declared-parcel", "metadata": { "scrolled": true }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "execution_count": 35, "metadata": {}, "output_type": "execute_result" } ], "source": [ "plot_histogram(counts)" ] }, { "cell_type": "markdown", "id": "bigger-generic", "metadata": {}, "source": [ "# 4. Summary " ] }, { "cell_type": "markdown", "id": "artistic-matter", "metadata": {}, "source": [ "To add gates to a circuit the **syntax** is:\n", "\n", "`.([])`\n", " \n", "In control gates the sintax is:\n", "\n", "`.([],[])`\n" ] }, { "cell_type": "markdown", "id": "impossible-delaware", "metadata": {}, "source": [ "Some gates you can use:\n", "\n", "(Let qr being the quantum register and qc being the quantum circuit.)\n", "\n", "\n", "|Gate Name|Syntax |Matrix|How is it implemented| \n", "|-|-|-|-|\n", "|Identity |qc.id(qr)| $Id = \\begin{bmatrix} 1&0\\\\0&1 \\end{bmatrix}$|$u0(1)$|\n", "|Bit-flip or Pauli-X| qc.x(qr)| $ X = \\begin{bmatrix} 0&1\\\\1&0 \\end{bmatrix}$|$u3(\\pi,0,\\pi)$|\n", "|Bit and phase-flip or Pauli-Y| qc.y(qr)|$ Y = \\begin{bmatrix} 0&-i\\\\i&0 \\end{bmatrix}$|$u3(\\pi,\\pi /\\ 2,\\pi /\\ 2)$|\n", "|Phase-flip or Pauli-Z| qc.z(qr)| $Z = \\begin{bmatrix} 1&0\\\\0&-1 \\end{bmatrix}$|$u1(\\pi)$|\n", "|Hadamard|qc.h(qr)| $ H =\\frac{1}{\\sqrt{2}}\\begin{bmatrix} 1 & 1 \\\\ 1 & -1\\end{bmatrix}$|$u2(0,\\pi)$|\n", "|S or $\\sqrt{Z}$-Phase|qc.s(qr)|$ S =\\begin{bmatrix} 1 & 0 \\\\ 0 & i\\end{bmatrix}$|$u1(\\pi /\\ 2)$|\n", "|S$^\\dagger$ or conjugate $\\sqrt{Z}$-Phase|qc.sdg(qr)| $S^\\dagger =\\begin{bmatrix} 1 & 0 \\\\ 0 & -i\\end{bmatrix}$|$u1(-\\pi /\\ 2)$|\n", "|T or $\\sqrt{S}$-Phase|qc.t(qr)| $T=\\begin{bmatrix}1 & 0 \\\\ 0 & e^{i \\pi /\\ 4}\\end{bmatrix}$| $u1( \\pi /\\ 4)$|\n", "|T$^\\dagger$ or conjugate $\\sqrt{S}$-Phase|qc.tdg(qr)| $ T^\\dagger =\\begin{bmatrix}1 & 0 \\\\ 0 & e^{-i \\pi /\\ 4}\\end{bmatrix}$| $u1( -\\pi /\\ 4)$|\n", "\n" ] }, { "cell_type": "markdown", "id": "parliamentary-invention", "metadata": {}, "source": [ "Multiqubit gates:\n", "\n", "The matrix looks different from the rest of the bibliography because qiskit uses different definitions of least and most significant qubits.\n", "\n", "Let control be the the 0 qubit and the target the 1 qubit.\n", "\n", "|Gate Name|Syntax |Matrix| \n", "|-|-|-|\n", "|Controlled-X or controlled-Not|qc.cx(qr\\[control\\],qr\\[target\\])|$CX = \\begin{bmatrix}1&0&0&0\\\\0&0&0&1\\\\0&0&1&0\\\\0&1&0&0\\end{bmatrix}$ |\n", "|Controlled-Y|qc.cy(qr\\[control\\],qr\\[target\\])|$CY = \\begin{bmatrix}1&0&0&0\\\\0&0&0&-i\\\\0&0&1&0\\\\0&i&0&0\\end{bmatrix}$ |\n", "|Controlled-Z or controlled-Phase|qc.cz(qr\\[control\\],qr\\[target\\])| $CZ =\\begin{bmatrix}1&0&0&0\\\\0&1&0&0\\\\0&0&1&0\\\\0&0&0&-1\\end{bmatrix}$ |\n", "|Controlled-Hadamard|qc.ch(qr\\[control\\],qr\\[target\\])|$CH = \\begin{bmatrix}1&0&0&0\\\\0&\\frac{1}{\\sqrt{2}}&0&\\frac{1}{\\sqrt{2}}\\\\0&0&1&0\\\\0&\\frac{1}{\\sqrt{2}}&0&-\\frac{1}{\\sqrt{2}}\\end{bmatrix}$ |\n", "|SWAP|qc.swap(qr\\[control\\],qr\\[target\\])| $SAWP =\\begin{bmatrix}1&0&0&0\\\\0&0&1&0\\\\0&1&0&0\\\\0&0&0&1\\end{bmatrix}$ |" ] }, { "cell_type": "markdown", "id": "alike-clear", "metadata": {}, "source": [ "Finally, there is the measure gate.\n", "\n", "* qc.measure(qr,cr) - it adds measures to all qubits\n", "* qc.measure_all() - it adds measure to all qubits and creates the classical space to register the measures\n", "* qc.measure(qr\\[0\\],cr\\[0\\]) - it adds a measure to qubit 0 and saves value in classical register 0" ] }, { "cell_type": "markdown", "id": "objective-hughes", "metadata": {}, "source": [ "# Exercises " ] }, { "cell_type": "code", "execution_count": 3, "id": "valid-rating", "metadata": {}, "outputs": [], "source": [ "backend_state = Aer.get_backend(\"statevector_simulator\")\n", "backend_unitary = Aer.get_backend('unitary_simulator')\n", "backend = Aer.get_backend(\"qasm_simulator\")" ] }, { "cell_type": "markdown", "id": "extended-stationery", "metadata": {}, "source": [ "Create 1 quantum register and 1 classical registers (qr and cr)." ] }, { "cell_type": "code", "execution_count": 4, "id": "improved-adelaide", "metadata": {}, "outputs": [], "source": [ "qr = QuantumRegister(1,'q')\n", "cr = ClassicalRegister(1,'c')" ] }, { "cell_type": "markdown", "id": "young-biodiversity", "metadata": {}, "source": [ "# 1. " ] }, { "cell_type": "markdown", "id": "detected-thermal", "metadata": {}, "source": [ "**a)** Create a quantum circuit." ] }, { "cell_type": "code", "execution_count": null, "id": "sublime-transportation", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "smoking-arbor", "metadata": {}, "source": [ "**b)** What is the state of qubit 0?" ] }, { "cell_type": "raw", "id": "planned-therapist", "metadata": {}, "source": [] }, { "cell_type": "markdown", "id": "running-syndrome", "metadata": {}, "source": [ "**c)** Excite the state of the qubit using only one Pauli gate, i.e., send the qubit state to $|1>$." ] }, { "cell_type": "code", "execution_count": null, "id": "nearby-organizer", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "figured-convenience", "metadata": {}, "source": [ "**d)** Draw the circuit." ] }, { "cell_type": "code", "execution_count": null, "id": "tender-vacuum", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "injured-committee", "metadata": {}, "source": [ "**e)** Simulate the circuit with the `statevector_simulator`." ] }, { "cell_type": "code", "execution_count": null, "id": "major-giant", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "signed-prime", "metadata": {}, "source": [ "Optional: add representation with the Bloch sphere." ] }, { "cell_type": "code", "execution_count": null, "id": "located-feeling", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "charming-andorra", "metadata": {}, "source": [ "# 2. " ] }, { "cell_type": "markdown", "id": "junior-recovery", "metadata": {}, "source": [ "**a)** Create a quantum circuit." ] }, { "cell_type": "code", "execution_count": null, "id": "italic-thumb", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "blond-ferry", "metadata": {}, "source": [ "**b)** Make the equivalent to the identity gate using only gates X." ] }, { "cell_type": "code", "execution_count": null, "id": "previous-michigan", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "renewable-karen", "metadata": {}, "source": [ "**c)** Draw the circuit." ] }, { "cell_type": "code", "execution_count": null, "id": "inclusive-philippines", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "ongoing-seafood", "metadata": {}, "source": [ "**d)** Simulate the circuit with the `statevector_simulator`." ] }, { "cell_type": "code", "execution_count": null, "id": "deluxe-collect", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "official-bride", "metadata": {}, "source": [ "Optional: add representation with the Bloch sphere." ] }, { "cell_type": "code", "execution_count": null, "id": "adequate-bangkok", "metadata": { "scrolled": false }, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "immediate-deployment", "metadata": {}, "source": [ "**e)** What is the expected output of a circuit with 3 X-gates? " ] }, { "cell_type": "raw", "id": "inclusive-requirement", "metadata": {}, "source": [] }, { "cell_type": "markdown", "id": "satisfied-litigation", "metadata": {}, "source": [ "**f)** What is the expected output of a circuit with $N$ X-gates? *Tip: start to assume is $N$ an odd number; then consider $N$ an even number*." ] }, { "cell_type": "raw", "id": "organizational-marketing", "metadata": {}, "source": [] }, { "cell_type": "markdown", "id": "downtown-delight", "metadata": {}, "source": [ "# 3. " ] }, { "cell_type": "markdown", "id": "handmade-crowd", "metadata": {}, "source": [ "**a)** What is the result of not creating a new quantum circuit in each exercise?" ] }, { "cell_type": "raw", "id": "peripheral-apple", "metadata": {}, "source": [] }, { "cell_type": "markdown", "id": "ignored-habitat", "metadata": {}, "source": [ "# 4.\n", "\n", "Let's introduce a new gate, Hadamard, the superposition gate. Qiskit simply calls it `h`." ] }, { "cell_type": "markdown", "id": "complete-navigator", "metadata": {}, "source": [ "**a)** Create a quantum circuit." ] }, { "cell_type": "code", "execution_count": null, "id": "concrete-administrator", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "pretty-organizer", "metadata": {}, "source": [ "**b)** Create superposition in the qubit state using the hadamard gate." ] }, { "cell_type": "code", "execution_count": null, "id": "similar-apartment", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "western-retention", "metadata": {}, "source": [ "**c)** Draw the circuit." ] }, { "cell_type": "code", "execution_count": null, "id": "honest-thompson", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "applicable-violence", "metadata": {}, "source": [ "**d)** Simulate the circuit with the `statevector_simulator`." ] }, { "cell_type": "code", "execution_count": null, "id": "selective-breakfast", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "altered-synthetic", "metadata": {}, "source": [ "Optional: add representation with the Bloch sphere." ] }, { "cell_type": "code", "execution_count": null, "id": "crude-attraction", "metadata": { "scrolled": true }, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "extra-virus", "metadata": {}, "source": [ "# 5." ] }, { "cell_type": "markdown", "id": "aggregate-ballot", "metadata": {}, "source": [ "**a)** Create a new quantum circuit and apply the Hadamard gate 2 times and print its state. " ] }, { "cell_type": "code", "execution_count": null, "id": "congressional-challenge", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "material-fetish", "metadata": {}, "source": [ "**b)** Create a new quantum circuit and apply the Hadamard gate 3 times and print its state. " ] }, { "cell_type": "code", "execution_count": null, "id": "silver-services", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "american-marking", "metadata": {}, "source": [ "**c)** Create a new quantum circuit and apply the Hadamard gate 5 times and print its state. " ] }, { "cell_type": "code", "execution_count": null, "id": "utility-absolute", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "considerable-dryer", "metadata": {}, "source": [ "**d)** Create a new quantum circuit and apply the Hadamard gate 10 times and print its state. " ] }, { "cell_type": "code", "execution_count": null, "id": "environmental-opening", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "comic-elevation", "metadata": {}, "source": [ "**e)** What is the expected output of a circuit with $N$ Hadamard-gates? *Tip: start to assume is $N$ an odd number; then consider $N$ an even number*." ] }, { "cell_type": "raw", "id": "answering-stamp", "metadata": {}, "source": [] }, { "cell_type": "markdown", "id": "magnetic-fireplace", "metadata": {}, "source": [ "# 6" ] }, { "cell_type": "markdown", "id": "fuzzy-uruguay", "metadata": {}, "source": [ "**a)** Create a new quantum circuit and add 1 Hadamard gate and a measure gate. \n", "\n", "Draw circuit." ] }, { "cell_type": "code", "execution_count": null, "id": "proud-craps", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "pediatric-content", "metadata": {}, "source": [ "**b)** Run this circuit 100 times. *Tip: use the `qasm_simulator` backend.*" ] }, { "cell_type": "code", "execution_count": null, "id": "infrared-seafood", "metadata": { "scrolled": true }, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "id": "broken-virginia", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "magnetic-romance", "metadata": {}, "source": [ "**c)** What can you conclude about this circuit?" ] }, { "cell_type": "raw", "id": "subtle-vintage", "metadata": {}, "source": [] }, { "cell_type": "markdown", "id": "incoming-interview", "metadata": {}, "source": [ "# 7" ] }, { "cell_type": "markdown", "id": "speaking-player", "metadata": {}, "source": [ "**a)** Create a new quantum circuit and change the initial state to the superposition state.\n", "\n", "Draw the circuit." ] }, { "cell_type": "code", "execution_count": null, "id": "filled-leader", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "unexpected-austin", "metadata": {}, "source": [ "**b)** Add an X-gate to the previous circuit.\n", "\n", "Draw the circuit." ] }, { "cell_type": "code", "execution_count": null, "id": "removed-practice", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "foreign-acoustic", "metadata": {}, "source": [ "**c)** Simulate the circuit with the `statevector_simulator`." ] }, { "cell_type": "code", "execution_count": null, "id": "active-airline", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "organic-mounting", "metadata": {}, "source": [ "Optional: add representation with the Bloch sphere." ] }, { "cell_type": "code", "execution_count": null, "id": "ordered-satin", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "several-boundary", "metadata": {}, "source": [ "**d)** Explain the output." ] }, { "cell_type": "raw", "id": "dense-weight", "metadata": {}, "source": [] }, { "cell_type": "markdown", "id": "careful-houston", "metadata": {}, "source": [ "# 8" ] }, { "cell_type": "markdown", "id": "processed-bradley", "metadata": {}, "source": [ "**a)** Create a new quantum circuit, add one quantum Z-gate. Draw the circuit." ] }, { "cell_type": "code", "execution_count": null, "id": "quarterly-modern", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "announced-external", "metadata": {}, "source": [ "**b)** Simulate the circuit with the `statevector_simulator`." ] }, { "cell_type": "code", "execution_count": null, "id": "destroyed-devices", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "herbal-saint", "metadata": {}, "source": [ "Optional: add representation with the Bloch sphere." ] }, { "cell_type": "code", "execution_count": null, "id": "surface-seller", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "proved-efficiency", "metadata": {}, "source": [ "**c)** Add another Z gate to the previous quantum circuit. Draw the circuit." ] }, { "cell_type": "code", "execution_count": null, "id": "hazardous-taiwan", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "serious-montreal", "metadata": {}, "source": [ "**d)** Simulate the circuit with the `statevector_simulator`." ] }, { "cell_type": "code", "execution_count": null, "id": "southeast-illinois", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "thermal-naples", "metadata": {}, "source": [ "Optional: add representation with the Bloch sphere." ] }, { "cell_type": "code", "execution_count": null, "id": "married-salad", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "pointed-detection", "metadata": {}, "source": [ "**e)** Do again the exercises a), b), c), and d), but add a Hadamard gate before the first Z gate (in exercise a))." ] }, { "cell_type": "code", "execution_count": null, "id": "piano-onion", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "id": "orange-immune", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "id": "norwegian-bridges", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "id": "flying-thirty", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "id": "several-evans", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "id": "appointed-bhutan", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "consistent-enemy", "metadata": {}, "source": [ "**f)** Explain the output." ] }, { "cell_type": "raw", "id": "configured-continent", "metadata": {}, "source": [] }, { "cell_type": "markdown", "id": "individual-finder", "metadata": {}, "source": [ "# 9" ] }, { "cell_type": "markdown", "id": "negative-receipt", "metadata": {}, "source": [ "**a)** I want to get from the default state $|0>$ to state $|1>$ but I can't apply X gate. Can you find a way to get the same result with Hadamard gates and Z-gates? Draw and test your solution with the state vector simulator." ] }, { "cell_type": "code", "execution_count": null, "id": "stone-sunglasses", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "id": "surprising-folder", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "id": "canadian-cincinnati", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "israeli-thomas", "metadata": {}, "source": [ "**b)** Simulate the unitary matrix of the circuit." ] }, { "cell_type": "code", "execution_count": null, "id": "prepared-christmas", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "raising-equilibrium", "metadata": {}, "source": [ "## Multiqubit Gates" ] }, { "cell_type": "markdown", "id": "cathedral-caution", "metadata": {}, "source": [ "Create 2 quantum register and 2 classical registers (qr_m and cr_m)." ] }, { "cell_type": "code", "execution_count": null, "id": "extraordinary-narrow", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "suffering-badge", "metadata": {}, "source": [ "# 10" ] }, { "cell_type": "markdown", "id": "productive-principle", "metadata": {}, "source": [ "**a)** Create a quantum circuit and add a CX gate. Where $q_0$ is the target and $q_1$ is the control. Draw the circuit." ] }, { "cell_type": "code", "execution_count": null, "id": "characteristic-newspaper", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "brutal-proposition", "metadata": {}, "source": [ "**b)** Simulate the circuit with the `statevector_simulator`." ] }, { "cell_type": "code", "execution_count": null, "id": "ordinary-silicon", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "structural-burlington", "metadata": {}, "source": [ "**c)** Why shouldn't you use the Bloch sphere representation?" ] }, { "cell_type": "raw", "id": "balanced-liberal", "metadata": {}, "source": [] }, { "cell_type": "markdown", "id": "distant-sydney", "metadata": {}, "source": [ "**d)** Simulate the circuit with `unitary_simulator`." ] }, { "cell_type": "code", "execution_count": null, "id": "intermediate-alpha", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "bearing-missouri", "metadata": {}, "source": [ "**e)** Create a new quantum circuit with X gate in qubit 1. Draw the circuit." ] }, { "cell_type": "code", "execution_count": null, "id": "precious-joyce", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "involved-chorus", "metadata": {}, "source": [ "**f)** Merge the previous circuit to the circuit created in a) and simulate with vector simulator." ] }, { "cell_type": "code", "execution_count": null, "id": "hispanic-sociology", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "id": "numerous-moore", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "id": "sought-pastor", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "north-flash", "metadata": {}, "source": [ "# 11" ] }, { "cell_type": "markdown", "id": "exterior-nation", "metadata": {}, "source": [ "Now let's test something less trivial.\n", "\n", "**a)** Find a circuit that does the same as a control-Z. Use CX and Hadamard gates." ] }, { "cell_type": "code", "execution_count": null, "id": "editorial-miracle", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "id": "caroline-mercy", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "id": "acquired-result", "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": "3.9.2" } }, "nbformat": 4, "nbformat_minor": 5 }