{ "cells": [ { "cell_type": "markdown", "id": "986118aa-057c-45e7-933e-0a690bc4ed2a", "metadata": { "tags": [ "remove_cell" ] }, "source": [ "# Introduction to Python and Jupyter notebooks\n", "We will learn quantum computation using the QISKIT-Toolbox, which is a Phython Interface to both Quanutm Simulators but also Quantum Hardware, provided by IBM. In the very first subchapter we shall have a quick look at the way we can use python to run simple calculations.\n", "\n", "One way to code in Python is to use a Jupyter notebook. This is probably the best way to combine programming, text and images. In a notebook, everything is laid out in cells. Text cells and code cells are the most common. If you are viewing this section as a Jupyter notebook, the text you are now reading is in a text cell. A code cell can be found just below.\n", "\n", "To run the contents of a code cell, you can click on it and press Shift + Enter. Or if there is a little arrow thing on the left, you can click on that.\n" ] }, { "cell_type": "markdown", "id": "f1af9e44-edcc-4078-878d-c83b7788a007", "metadata": { "tags": [] }, "source": [ "## Simple Arthmetics" ] }, { "cell_type": "code", "execution_count": 146, "id": "e10bd3a5-c2d4-4255-b16e-ba1aa7e63da4", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "2" ] }, "execution_count": 146, "metadata": {}, "output_type": "execute_result" } ], "source": [ "1 + 1" ] }, { "cell_type": "markdown", "id": "a8a35e1d-8065-4f36-8a61-6d88caae4555", "metadata": {}, "source": [ "There is of course much more you can do, than just adding 1+1. The notebook gives you full accesibility to the entirety of Python's galore. Here are just a few examples." ] }, { "cell_type": "markdown", "id": "b1b0d118-be82-4986-b49e-82275d37ea5f", "metadata": { "tags": [] }, "source": [ "## Creating and manipulating variables" ] }, { "cell_type": "code", "execution_count": 147, "id": "5fe5e5af-fdc7-4cca-b75e-2a6c6cf36964", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "42\n", "0.21000000000000002\n", "just enclose text between two 's, or two \"s, or do what we did for this string\n", "None\n" ] }, { "data": { "text/plain": [ "0.21000000000000002" ] }, "execution_count": 147, "metadata": {}, "output_type": "execute_result" } ], "source": [ "an_integer = 42 # Just an integer\n", "an_integer #intermediate results are not displayed implicitly\n", "print(an_integer) #use print to display instead\n", "\n", "\n", "a_float = 0.1 # A non-integer number, up to a fixed precision\n", "a_float = a_float * 2.1 #Multiply by 2.1\n", "print(a_float)\n", "\n", "a_boolean = True # A value that can be True or False\n", "a_string = '''just enclose text between two 's, or two \"s, or do what we did for this string''' # Text\n", "print(a_string)\n", "\n", "none_of_the_above = None # The absence of any actual value or variable type\n", "print(none_of_the_above)\n", "\n", "a_float #last result is displayed implicity" ] }, { "cell_type": "markdown", "id": "39d418d4-7aa1-49ba-b309-da386a400c99", "metadata": { "tags": [] }, "source": [ "## Creating and manipulating lists and dictionaries" ] }, { "cell_type": "code", "execution_count": 148, "id": "98d31739-95d5-4bd6-a7bf-bf154a666fb0", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[42, 0.5, True, [0, 1], None, 'Banana']\n", "42\n", "[42, 0.5, True, [0, 1], None, 'apple']\n", "[42, 0.5, True, [0, 1], None, 'apple', 3.14]\n" ] } ], "source": [ "a_list = [0,1,2,3] #A very simple list of identical items\n", "a_list = [ 42, 0.5, True, [0,1], None, 'Banana' ] #Lists can be of different types, too\n", "print(a_list) #show list\n", "\n", "print(a_list[0]) #access an individual list item\n", "\n", "a_list[5] = 'apple' #change list item\n", "print(a_list)\n", "\n", "a_list.append( 3.14 ) #append items to list\n", "print(a_list)\n", "\n" ] }, { "cell_type": "markdown", "id": "b544d718-fd41-4baa-9066-30c25163d29a", "metadata": {}, "source": [ "Dictioraries are similar to lists, the difference being that were list have 0 to n-1 indicicies, dictionaries have well-defined key:value pairs. Key must be unique, obvisouly." ] }, { "cell_type": "code", "execution_count": 6, "id": "9939d208-01d4-4d0a-9ee3-b1087eea5018", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "{1: 'This is the value, for the key 1', 'This is the key for a value 1': 1, False: ':)', (0, 1): 256}\n", "1\n", "{1: 'New Key', 'This is the key for a value 1': 1, False: ':)', (0, 1): 256, 'new key': 'new_value'}\n" ] } ], "source": [ "a_dict = { 1:'This is the value, for the key 1', 'This is the key for a value 1':1, False:':)', (0,1):256 }\n", "print(a_dict)\n", "print(a_dict['This is the key for a value 1']) #you can acces any list items by it's unique key, whateever that may be\n", "a_dict['new key'] = 'new_value' #add a new key:value pair\n", "a_dict[1] = 'New Key' #Change the value for an existing key\n", "print(a_dict)\n" ] }, { "cell_type": "markdown", "id": "29a65cd4-607f-4ef5-ad53-2d076dc5b34e", "metadata": { "tags": [] }, "source": [ "## Looping lists and dictionaries\n", "\n", "We start by simply looping over a range of numbers using the range(n) command to create a list running from 0 to n" ] }, { "cell_type": "code", "execution_count": 7, "id": "ebc2c2d3-efb1-479b-b3c3-2f015603b64b", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0\n", "1\n", "2\n", "3\n", "4\n" ] } ], "source": [ "for j in range(5):\n", " print(j)" ] }, { "cell_type": "markdown", "id": "64869b99-da91-4b15-87a0-f06903573ead", "metadata": {}, "source": [ "You can also loop over any 'iterable' object, such as lists" ] }, { "cell_type": "code", "execution_count": 8, "id": "88b9bb4f-1abb-4321-8c62-7848841eb064", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "42\n", "0.5\n", "True\n", "[0, 1]\n", "None\n", "apple\n", "3.14\n" ] } ], "source": [ "for j in a_list:\n", " print(j)" ] }, { "cell_type": "markdown", "id": "c3a40b3b-048f-49aa-8369-bf810a81c3ba", "metadata": {}, "source": [ "or dictionaries, where you automatically get access to key/value pairs" ] }, { "cell_type": "code", "execution_count": 9, "id": "ee13012b-4434-441b-aa60-587e73b07f2c", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "key = 1\n", "value = New Key\n", "\n", "key = This is the key for a value 1\n", "value = 1\n", "\n", "key = False\n", "value = :)\n", "\n", "key = (0, 1)\n", "value = 256\n", "\n", "key = new key\n", "value = new_value\n", "\n" ] } ], "source": [ "for key in a_dict:\n", " value = a_dict[key]\n", " print('key =',key)\n", " print('value =',value)\n", " print() \n" ] }, { "cell_type": "markdown", "id": "74ab0f85-05f9-4bbc-8235-71a8ebb0e684", "metadata": {}, "source": [ "You can also use a slightly different notation" ] }, { "cell_type": "code", "execution_count": 10, "id": "6250ff60-b406-43bf-8c49-2b742972eead", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "key = 1\n", "value = New Key\n", "\n", "key = This is the key for a value 1\n", "value = 1\n", "\n", "key = False\n", "value = :)\n", "\n", "key = (0, 1)\n", "value = 256\n", "\n", "key = new key\n", "value = new_value\n", "\n" ] } ], "source": [ "for key, value in a_dict.items():\n", " print('key =',key)\n", " print('value =',value)\n", " print()" ] }, { "cell_type": "markdown", "id": "27fe7658-6b70-4032-9f46-aa0445928b98", "metadata": { "tags": [] }, "source": [ "## If-Then Statements" ] }, { "cell_type": "code", "execution_count": 11, "id": "adcdcc74-6a41-4aa5-8c8d-aec65ed0d968", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "We have an apple!\n" ] } ], "source": [ "if 'strawberry' in a_list:\n", " print('We have a strawberry!')\n", "elif a_list[5]=='apple':\n", " print('We have an apple!')\n", "else:\n", " print('Not much fruit here!')" ] }, { "cell_type": "markdown", "id": "ec7b333c-2449-4b92-8ff8-d3243bf35826", "metadata": { "tags": [] }, "source": [ "## Import Libraries, Math and Plotting" ] }, { "cell_type": "code", "execution_count": 13, "id": "bd57a6b3-8b6f-4595-9906-76e6fc61390e", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "1.0\n", "[0.00000000e+00 3.17279335e-02 6.34239197e-02 9.50560433e-02\n", " 1.26592454e-01 1.58001396e-01 1.89251244e-01 2.20310533e-01\n", " 2.51147987e-01 2.81732557e-01 3.12033446e-01 3.42020143e-01\n", " 3.71662456e-01 4.00930535e-01 4.29794912e-01 4.58226522e-01\n", " 4.86196736e-01 5.13677392e-01 5.40640817e-01 5.67059864e-01\n", " 5.92907929e-01 6.18158986e-01 6.42787610e-01 6.66769001e-01\n", " 6.90079011e-01 7.12694171e-01 7.34591709e-01 7.55749574e-01\n", " 7.76146464e-01 7.95761841e-01 8.14575952e-01 8.32569855e-01\n", " 8.49725430e-01 8.66025404e-01 8.81453363e-01 8.95993774e-01\n", " 9.09631995e-01 9.22354294e-01 9.34147860e-01 9.45000819e-01\n", " 9.54902241e-01 9.63842159e-01 9.71811568e-01 9.78802446e-01\n", " 9.84807753e-01 9.89821442e-01 9.93838464e-01 9.96854776e-01\n", " 9.98867339e-01 9.99874128e-01 9.99874128e-01 9.98867339e-01\n", " 9.96854776e-01 9.93838464e-01 9.89821442e-01 9.84807753e-01\n", " 9.78802446e-01 9.71811568e-01 9.63842159e-01 9.54902241e-01\n", " 9.45000819e-01 9.34147860e-01 9.22354294e-01 9.09631995e-01\n", " 8.95993774e-01 8.81453363e-01 8.66025404e-01 8.49725430e-01\n", " 8.32569855e-01 8.14575952e-01 7.95761841e-01 7.76146464e-01\n", " 7.55749574e-01 7.34591709e-01 7.12694171e-01 6.90079011e-01\n", " 6.66769001e-01 6.42787610e-01 6.18158986e-01 5.92907929e-01\n", " 5.67059864e-01 5.40640817e-01 5.13677392e-01 4.86196736e-01\n", " 4.58226522e-01 4.29794912e-01 4.00930535e-01 3.71662456e-01\n", " 3.42020143e-01 3.12033446e-01 2.81732557e-01 2.51147987e-01\n", " 2.20310533e-01 1.89251244e-01 1.58001396e-01 1.26592454e-01\n", " 9.50560433e-02 6.34239197e-02 3.17279335e-02 1.22464680e-16]\n" ] } ], "source": [ "import numpy as np\n", "print(np.sin( np.pi/2 ))\n", "x = np.linspace(0,np.pi,100)\n", "print(np.sin(x))\n" ] }, { "cell_type": "code", "execution_count": 19, "id": "6cd2d2a8-38f4-40be-8199-bfeade22cc16", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import matplotlib.pylab as plt\n", "plt.figure(figsize=(12,8), facecolor='white')\n", "plt.rcParams.update({'font.size': 22})\n", "plt.plot(x, np.sin(x))\n", "plt.xlabel('Angle [rad]')\n", "plt.ylabel('sin(x)')\n", "plt.grid(which='major',axis='both')\n", "\n" ] }, { "cell_type": "markdown", "id": "a1f804a8-ce72-450d-9d46-98b674259d3a", "metadata": { "tags": [] }, "source": [ "## Defining Functions" ] }, { "cell_type": "code", "execution_count": 21, "id": "6a17106b-0e58-4298-b806-80719f8a1ee2", "metadata": {}, "outputs": [], "source": [ "def add_sausages ( input_list ):\n", " if 'sausages' not in input_list:\n", " input_list.append('sausages')" ] }, { "cell_type": "code", "execution_count": 22, "id": "07fe630a-1153-4805-a3fc-d03996c63009", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "List before the function\n", "[42, 0.5, True, [0, 1], None, 'apple', 3.14]\n", "\n", "List after the function\n", "[42, 0.5, True, [0, 1], None, 'apple', 3.14, 'sausages']\n" ] } ], "source": [ "print('List before the function')\n", "print(a_list)\n", "\n", "add_sausages(a_list) # function called without an output\n", "\n", "print('\\nList after the function')\n", "print(a_list)\n" ] }, { "cell_type": "markdown", "id": "4ec64845-13db-4f6d-a28a-1aefa71b2cd1", "metadata": { "tags": [] }, "source": [ "# Your first Quantum Circuits" ] }, { "cell_type": "markdown", "id": "b2713fb4-0e6e-4910-91dd-0701a3212586", "metadata": { "tags": [] }, "source": [ "## Libraries\n", "So far we have only looked into Pyhton/Juypiter in general. Next we start with the proper quantum. Do to so, we must import a few important libraries/classes/functions." ] }, { "cell_type": "code", "execution_count": 5, "id": "42077c29-9059-4f36-a8fa-f70c81e0110f", "metadata": {}, "outputs": [], "source": [ "from qiskit import QuantumCircuit, assemble, Aer\n", "from qiskit.visualization import plot_histogram" ] }, { "cell_type": "markdown", "id": "b7638fe8-b53c-408e-9415-7893b7504c19", "metadata": {}, "source": [ "In a circuit, we typically need to do three jobs: First, encode the input, then do some actual computation, and finally extract an output. For your first quantum circuit, we'll focus on the last of these jobs. We start by creating a circuit with eight qubits and eight outputs." ] }, { "cell_type": "code", "execution_count": 23, "id": "4a0838e9-50ed-484f-90d4-7755afd77903", "metadata": {}, "outputs": [], "source": [ "n=4\n", "qc_output = QuantumCircuit(n)" ] }, { "cell_type": "markdown", "id": "c0c5391f-61fb-4c2e-a1cc-5c15358f7585", "metadata": {}, "source": [ "This circuit, which we have called `qc_output`, is created by Qiskit using `QuantumCircuit`. The `QuantumCircuit` takes the number of qubits in the quantum circuit as an argument. \n", "\n", "The extraction of outputs in a quantum circuit is done using an operation called `measure_all()`. Each measurement tells a specific qubit to give an output to a specific output bit. The command `qc_output.measure_all()` adds a measurement to each qubit in the circuit `qc_output`, and also adds some classical bits to write the output to." ] }, { "cell_type": "code", "execution_count": 24, "id": "dcd75f47-5c96-477a-aa9f-935ee17a43a3", "metadata": {}, "outputs": [], "source": [ "qc_output.measure_all()" ] }, { "cell_type": "markdown", "id": "426d7411-aea2-426e-b7a2-bd3ec68b6d10", "metadata": {}, "source": [ "Qubits are always initialized to give the output ```0```. Since we don't do anything to our qubits in the circuit above, this is exactly the result we'll get when we measure them. We can see this by running the circuit many times and plotting the results in a histogram. We will find that the result is always ```00000000```: a ```0``` from each qubit." ] }, { "cell_type": "markdown", "id": "c6b05287-4b4c-41b2-b2b3-dee7e5040f97", "metadata": {}, "source": [ "sim = Aer.get_backend('aer_simulator') \n", "result = sim.run(qc_output).result()\n", "counts = result.get_counts()\n", "plot_histogram(counts)" ] }, { "cell_type": "markdown", "id": "318dd443-f661-4845-bcee-959ef7883cc2", "metadata": { "tags": [] }, "source": [ "## Initialization of QuBits\n", "We first import a few helpful classes into visualize the state of QuBits" ] }, { "cell_type": "code", "execution_count": null, "id": "fff92ad2-8c63-4783-af84-71d32aa933ef", "metadata": {}, "outputs": [], "source": [ "from qiskit.visualization import plot_histogram, plot_bloch_vector\n", "from math import sqrt, pi" ] }, { "cell_type": "markdown", "id": "6c293ddb-73fc-47cc-bec0-d3ddfe7c4cfc", "metadata": {}, "source": [ "We then create a single quibt circuit" ] }, { "cell_type": "code", "execution_count": 6, "id": "83953b6b-11d9-4925-9311-a3cebd6db112", "metadata": {}, "outputs": [ { "data": { "image/png": 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"text/plain": [ "
" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "qc = QuantumCircuit(3) # Create a quantum circuit with two qubits\n", "initial_stateV = [0,1] # Definean initial_state as |1>\n", "initial_stateU = [1/sqrt(2),1/sqrt(2)] # Definean initial_state as |1>\n", "qc.initialize(initial_stateV, 1) # Apply initialisation operation to the 1sr qubit\n", "qc.initialize(initial_stateU, 2) # Apply initialisation operation to the 1sr qubit\n", "qc.draw() # Let's view our circuit" ] }, { "cell_type": "markdown", "id": "1c6c25ef-230a-484e-8b27-9adbb4bbc38f", "metadata": { "tags": [] }, "source": [ "### Task1: Create a balanced single-bit quantum random number generator, draw it, run it, and display the results" ] }, { "cell_type": "markdown", "id": "c00441ee-b3ec-4f67-aa2b-91fcef9a4c88", "metadata": {}, "source": [ "We first create the Quantum Circuit by inititalizing the QuBit into a 45° linear polarization state" ] }, { "cell_type": "code", "execution_count": 7, "id": "d6d7eea2-c2a2-4ee3-8745-a7ea06a4e80c", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "#Deleted code. Students need to complete this." ] }, { "cell_type": "markdown", "id": "009437ad-f755-472a-8a12-2e09b81e08df", "metadata": {}, "source": [ "Then we run the circuit on a simulator" ] }, { "cell_type": "code", "execution_count": 8, "id": "e6c23fb4-a66f-4d76-9474-471e577b1136", "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ ":219: RuntimeWarning: scipy._lib.messagestream.MessageStream size changed, may indicate binary incompatibility. Expected 56 from C header, got 64 from PyObject\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "#Deleted code. Students need to complete this." ] }, { "cell_type": "markdown", "id": "8a9a4524-b269-4dd6-88f7-9434c9dc5d31", "metadata": {}, "source": [ "This is close to the expected 50/50-result. However, this never exactly hits 50/50 because we are merely doing a sample over N=1000 runs, which means we get a probability distribution for the average of 0.5(1 +/- 1/sqrt(N)) = 0.5*(1 +/- 0.03). The simplified version of think about this is: we estmiate the probabilities." ] }, { "cell_type": "markdown", "id": "7726facc-7833-4e26-89ce-b6217f616841", "metadata": { "tags": [] }, "source": [ "## Single Qubit Gates\n", "This is however not the preferred way of creating quanutm circuits, instead we typicall start with a |0> state and use a Hadamard-Gate (a 22.5° HWP) to create the superposition state. This time we would also like to visualize the state vector." ] }, { "cell_type": "code", "execution_count": 71, "id": "2563da09-adba-4cbc-a7c7-65a43ab32a20", "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "execution_count": 71, "metadata": {}, "output_type": "execute_result" } ], "source": [ "qc = QuantumCircuit(1)\n", "qc.h(0) #Add a Hadamard Gate to the 0th Qubit\n", "qc.save_statevector()\n", "qc.draw() # Let's view our circuit\n" ] }, { "cell_type": "code", "execution_count": 73, "id": "be29ddd7-e151-4737-8f11-f7462ad62883", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "State of Measured Qubit = Statevector([0.70710678+0.j, 0.70710678+0.j],\n", " dims=(2,))\n" ] }, { "data": { "image/png": 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\n", 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" ] }, "execution_count": 73, "metadata": {}, "output_type": "execute_result" } ], "source": [ "sim = Aer.get_backend('aer_simulator') \n", "\n", "\n", "result = sim.run(qc).result(); \n", "state = result.get_statevector()\n", "print(\"State of Measured Qubit = \" + str(state))\n", "\n", "counts = result.get_counts()\n", "plot_histogram(counts)\n" ] }, { "cell_type": "markdown", "id": "2f543801-932e-4c43-8a85-9dba603cc3ed", "metadata": {}, "source": [ "You see two things. First you see that the state-vector is kind of hard to visulaize and second you see that the omission of a specific measurement leads to the replacement of samples with properties. We can easily visulize teh state-vectors unsing built-in fucntions." ] }, { "cell_type": "code", "execution_count": 75, "id": "4ceb6faf-67f9-4878-aadb-6963083d92a6", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "execution_count": 75, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from qiskit.visualization import plot_bloch_multivector\n", "plot_bloch_multivector(state)" ] }, { "cell_type": "code", "execution_count": null, "id": "8d69f37e-048b-4135-a85c-37aeddabe76b", "metadata": {}, "outputs": [], "source": [ "We can nicely us this function to visualize the action of different gates" ] }, { "cell_type": "code", "execution_count": null, "id": "5de9e051-6878-48c2-b3bc-0a1d91fdbb95", "metadata": {}, "outputs": [], "source": [ "qc = QuantumCircuit(4)\n", "qc.h(1) #Add a Hadamard Gate to the 1st Qubit --> diagonal polarization\n", "qc.h(2) #Add a Hadamard Gate to the 2nd Qubit --> diagonal polarization\n", "qc.p(np.pi/2,2) #Add a 90 Deg Phase to the |1> part of the 2nd Quabit --> Circular Pol\n", "qc.h(3) #Add a Hadamard Gate to the 3rd Qubit --> diagonal polarization\n", "qc.z(3) #Add a Z- Gate to the 3rd Qubit --> inverse diagonal pol\n", "qc.save_statevector()\n", "qc.draw() # Let's view our circuit" ] }, { "cell_type": "code", "execution_count": 87, "id": "cc7afe1d-4458-4b3f-916e-eed45e539015", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "execution_count": 87, "metadata": {}, "output_type": "execute_result" } ], "source": [ "sim = Aer.get_backend('aer_simulator') \n", "\n", "\n", "result = sim.run(qc).result(); \n", "state = result.get_statevector()\n", "plot_bloch_multivector(state)" ] }, { "cell_type": "markdown", "id": "992b8d11-bb72-4c73-838b-90fb0ec18220", "metadata": { "tags": [] }, "source": [ "## A Real Quantum Computer Experimnent\n", "So far we have only looked at very simple simulated exampled. Now we want to execute the quanum random number generator example for real. We first must load into the networks of QCs properly." ] }, { "cell_type": "code", "execution_count": 90, "id": "280a6034-5711-43b8-aba7-75c12f855d26", "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "ibmqfactory.load_account:WARNING:2022-04-19 11:06:15,106: Credentials are already in use. The existing account in the session will be replaced.\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Running on current least busy device: ibmq_belem\n" ] } ], "source": [ "from qiskit import IBMQ, Aer, assemble, transpile\n", "from qiskit import QuantumCircuit, ClassicalRegister, QuantumRegister\n", "from qiskit.providers.ibmq import least_busy\n", "\n", "IBMQ.load_account()\n", "provider = IBMQ.load_account()\n", "provider = IBMQ.get_provider(\"ibm-q\")\n", "device = least_busy(provider.backends(filters=lambda x: x.configuration().n_qubits >= 3 and \n", " not x.configuration().simulator and x.status().operational==True))\n", "print(\"Running on current least busy device: \", device)" ] }, { "cell_type": "code", "execution_count": 88, "id": "04f9a2d1-dbc0-42b7-a0e4-dee146989f52", "metadata": {}, "outputs": [ { "data": { "image/png": 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"text/plain": [ "
" ] }, "execution_count": 88, "metadata": {}, "output_type": "execute_result" } ], "source": [ "qc = QuantumCircuit(1)\n", "qc.h(0) #Add a Hadamard Gate to the 0th Qubit\n", "qc.measure_all()\n", "qc.draw() # Let's view our circuit" ] }, { "cell_type": "code", "execution_count": 91, "id": "bfc52a00-827d-4028-9397-c9bcf0a6a3e8", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Job Status: job has successfully run\n" ] } ], "source": [ "from qiskit.tools.monitor import job_monitor\n", "qc_transpiled = transpile(qc, device, optimization_level=3)\n", "job = device.run(qc_transpiled)\n", "job_monitor(job, interval=2)" ] }, { "cell_type": "code", "execution_count": 95, "id": "83820209-a47e-43d8-a8d4-3f5d3ded818c", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "execution_count": 95, "metadata": {}, "output_type": "execute_result" } ], "source": [ "results = job.result()\n", "answer = results.get_counts()\n", "plot_histogram(answer)" ] }, { "cell_type": "markdown", "id": "72f17847-964a-416d-8723-0f9b67377bc5", "metadata": { "tags": [] }, "source": [ "## Multi-Qubit-Circuits and Entanglement\n", "So far we have only looked into single-qubit states and hence have totally ignored the key-resource of quantum computation, that is Entanglement. We'll start out with an extremely simple example to visualize the computational power sclaing of a quanutm computer. A 4 q-bit Random number generator." ] }, { "cell_type": "code", "execution_count": 134, "id": "0caad90d-01ae-4dfe-8ed0-2a7acdcb18a0", "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "execution_count": 134, "metadata": {}, "output_type": "execute_result" } ], "source": [ "qc = QuantumCircuit(4)\n", "qc.h(0) #Add a Hadamard Gate to the 0th Qubit\n", "qc.h(1) #Add a Hadamard Gate to the 0th Qubit\n", "qc.h(2) #Add a Hadamard Gate to the 0th Qubit\n", "qc.h(3) #Add a Hadamard Gate to the 0th Qubit\n", "qc.save_statevector()\n", "qc.draw() # Let's view our circuit" ] }, { "cell_type": "markdown", "id": "ffe111a6-2032-42aa-8c4d-d33acf800b73", "metadata": {}, "source": [ "Let's first display the state vector, which is 2^4=16 Dimensional:" ] }, { "cell_type": "code", "execution_count": 135, "id": "509dde81-6c35-45f2-844e-da2d8d56e2cf", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Statevector([0.25+0.j, 0.25+0.j, 0.25+0.j, 0.25+0.j, 0.25+0.j, 0.25+0.j,\n", " 0.25+0.j, 0.25+0.j, 0.25+0.j, 0.25+0.j, 0.25+0.j, 0.25+0.j,\n", " 0.25+0.j, 0.25+0.j, 0.25+0.j, 0.25+0.j],\n", " dims=(2, 2, 2, 2))\n" ] } ], "source": [ "sim = Aer.get_backend('aer_simulator') \n", "\n", "\n", "result = sim.run(qc).result(); \n", "state = result.get_statevector()\n", "state" ] }, { "cell_type": "markdown", "id": "3dc446a9-2588-4342-b857-1620b72e5733", "metadata": {}, "source": [ "This 16-Dimensional State-Vector then collapses into a 4-bit number (ranging from 0 to 15) with qual probability. So each run of the circuit generates exactly one 4-bit number; their probability is: " ] }, { "cell_type": "code", "execution_count": 149, "id": "79f5cd33-49e3-49b8-b184-20b5337c3f81", "metadata": {}, "outputs": [ { "data": { "image/png": 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SSSfRsWNH3nnnHSoqKmjXrh333nsvgwYNiss+2xKFpohIAk2fPp3CwkIeeOAB5s2bR3V1NcOGDeOCCy5gypQpBx1lHi7jx4+nvLyce+65h1dffZW5c+dy4MABMjIy+Na3vsXVV1/NySeffNjraI0seArKkSkvL89LS0ubvZ2L721+LdLyzLgm2RWISDKY2UJ3z6tvma5pioiIhKTQFBERCUmhKSIiEpJCU0REJCSFpoiISEgKTRERkZAUmiIiIiEpNEVEREJSaIqIiISk0BQREQlJoSkiIhKSQlNERCQkhaaIiEhIejSYiBxx9GSitikRTybSkaaIiEhICk0REZGQFJoiIiIhKTRFRERCUmiKiIiEpNAUEREJSaEpIiISkkJTREQkJIWmiIhISApNERGRkBIemmZ2mZlVmNleM1toZqeFXK/QzKrMbHGd9u+ZmdfzOurwfAciInKkSmhomtl5wDTgDmAU8AbwdzPre4j1ugGPAXMa6LIbODb65e5741W3iIgIJP5I8zrgEXef4e7vu/uVwAZgyiHWexh4FChuYLm7+8boVxxrFhERARIYmmbWARgNvFRn0UvAKY2sdxmQAdzeyOY7mtkaM1tnZi+Y2ahmFywiIlJHIh8N1hNIATbVad8EnF7fCmb2ReAW4GR3rzaz+rotAy4AyoF04GrgdTPLcfcV9WzzEuASgKysLObOnQvAwIEDSU9Pp7y8HIAePXowYsQI5s+fD0BqaiqFhYWUlZWxY8cOAPLy8ti0aRMwKOx/A2lFSktL2bVrFwD5+fmsW7eO9evXAzB06FBSUlJYunQpAJmZmQwYMIDi4uBkSMeOHcnPz6ekpIQ9e/YAUFBQQEVFBRs3BidChg8fTnV1NcuWLQMgOzub3r17U1JSAkDnzp3Jy8ujuLiYyspKAAoLC1m+fDmbN28GYOTIkVRWVrJiRfCr3qdPHzIyMigtLQWgS5cu5ObmsmDBAqqqqgAYM2YMS5YsYevWrQDk5OSwc+dOVq1aBUD//v3p3r07ZWVlAHTr1o2cnBzmzZuHu2NmFBUVUV5ezvbt2wHIzc1l27ZtrF69Gmje52nt2rUADB48mLS0NBYvDoYx9OrViyFDhrBgwQIA0tLSKCgoaNLPCdJi/G2Q1mDDhg1x+Tw1xtz9MH4LUTsyywLWA0XuPj+q/WbgO+4+tE7/NGARcKe7z4y03Qp8091HNrKfFOAd4DV3v6qxmvLy8rzmfy7NoWfztU2JeDafJIc+s21TvD6zZrbQ3fPqW5bII80tQDXBqdZoGUB91yCPBY4H/mhmf4y0tQPMzKqAM9y97qleIkekpcDguFUuIiJCAq9puvs+YCEwvs6i8QSjaOtaD3wRODHq9RCwMvK+vnWw4BzuCQQDjEREROImkUeaAPcAM83sLeB14FIgiyAMMbPHANz9fHffD9S9J3MzUOnui6PabgHeBFYAXYCrCELzUCNyRUREYpLQ0HT3p8ysB3ATwenXxQSnWddEujR6v2YDugK/BzKBTwmug45x97eaX7GIiMi/JPpIE3efDkxvYNnYQ6x7K3BrnbZrgWvjU52IiEjDNPesiIhISApNERGRkBSaIiIiISk0RUREQlJoioiIhKTQFBERCUmhKSIiEpJCU0REJCSFpoiISEgKTRERkZAUmiIiIiEpNEVEREJSaIqIiISk0BQREQlJoSkiIhJSTKFpZu3MrF3U15lmdpGZnRr/0kRERFqWWI80/wZcCWBmnYFS4NfAXDM7P861iYiItCixhmYe8Grk/TeAHUAv4GLg+jjWJSIi0uLEGpqdgU8i7ycAs919P0GQDopjXSIiIi1OrKH5IXCqmR0NfAV4OdLeHdgdz8JERERamtQY+98DzAR2AWuA+ZH2McB7caxLRESkxYkpNN39d2a2EOgDvOzuByKLPgB+Gu/iREREWpJYjzRx91KCUbPRbX+LW0UiIiItVMyTG5jZZWa2xMx2m9nASNsNZvYf8S9PRESk5Yh1coNrgJuA3wMWtegj4Ir4lSUiItLyxHqkeSlwsbtPA6qi2suAEXGrSkREpAWKNTT7AYvrad8PdGx+OSIiIi1XrKG5Csitp/0MYGnzyxEREWm5Yh09+1/A/WbWieCaZoGZfRf4EXBBvIsTERFpSWK9T/OPZpYK3AF0Ipjo4CPgKnd/6jDUJyIi0mI05T7NGcAMM+sJtHP3zfEvS0REpOWJOTRruPuWeBYiIiLS0h0yNM3sXaDI3beb2XuAN9TX3U+IZ3EiIiItSZgjzWeAyqj3DYamiIhIW3bI0HT3n0W9v/WwViMiItKCxTqN3qtm1rWe9i5m9mrcqhIREWmBYp3cYCzQoZ72o4DTml2NiIhICxZq9KyZRc8CdIKZbYv6OgX4CrA+noWJiIi0NGFvOSklGADkwEv1LN8DXBmvokRERFqisKE5gGDavFXAvwEfRy3bB2x29+o41yYiItKihApNd18TeRvzQ6tFRETaijCTG3wDeN7d90feN8jdn41bZSIiIi1MmCPNWUAmsDnyviFOMChIRESkTQozuUG7+t6LiIgcaRSCIiIiIYW9phmKrmmKiEhbFvaaZhi6pikiIm1aTNc0RUREjmQKRBERkZB0n6aIiEhIuk9TREQkJN2nKSIiEpJCUEREJKSYQ9PMcs3sMTMrjbxm1nnepoiISJsUU2ia2XeAt4FjgRcjrwzgLTObHP/yREREWo5YjzR/AfzU3ce7+82R1wTgp8DtYTZgZpeZWYWZ7TWzhWZ2WiN9i8zsDTPbamZ7zOyfZnZ9Pf0mmdlSM6uM/HtOjN+XiIjIIcUaml8A/lJP+9NAr0OtbGbnAdOAO4BRwBvA382sbwOr7AJ+C4wBhhME88/M7LKobRYATwFPACdG/n3azPLDfUsiIiLhxBqarwFj62kfC8wLsf51wCPuPsPd33f3K4ENwJT6Orv7Qnf/s7svcfcKd38c+AcQfXR6DfCau/8iss1fAHMj7SIiInET64TtfwfuNLM84M1I28nAN4BbD7GdDsBo4L/qLHoJOCVMsWY2KtI3el8FwH11uv4DuCLMNkVERMJq6oTtl0Re0e4DpjeynZ4Ekx9sqtO+CTi9sQLMbB3BqeFU4Gfu/lDU4swGtpnZwLZqa8/KymLu3LkADBw4kPT0dMrLywHo0aMHI0aMYP78+QCkpqZSWFhIWVkZO3bsACAvL49NmzYBgxorX1qp0tJSdu3aBUB+fj7r1q1j/fr1AAwdOpSUlBSWLl0KQGZmJgMGDKC4uBiAjh07kp+fT0lJCXv27AGgoKCAiooKNm7cCMDw4cOprq5m2bJlAGRnZ9O7d29KSkoA6Ny5M3l5eRQXF1NZWQlAYWEhy5cvZ/PmzQCMHDmSyspKVqxYAUCfPn3IyMigtLQUgC5dupCbm8uCBQuoqqoCYMyYMSxZsoStW7cCkJOTw86dO1m1ahUA/fv3p3v37pSVlQHQrVs3cnJymDdvHu6OmVFUVER5eTnbt28HIDc3l23btrF69WqgeZ+ntWvXAjB48GDS0tJYvHgxAL169WLIkCEsWLAAgLS0NAoKCpr0c4K0GH8bpDXYsGFDXD5PjTF3P4zfQtSOzLKA9UCRu8+Par8Z+I67D21k3QFAZ4Kj2l8CV7v7zMiyfcBF7v5YVP/zgRnu3ugnIy8vz2v+59IcF9/b7E1ICzTjmmRXIIeLPrNtU7w+s2a20N3z6lsW5kgzXrYA1QS3qETLADY2tqK7V0TevmdmGQSnZ2dG2jY2ZZsiIiKxijk0zawb8DWgL9Ahepm7/7yh9dx9n5ktBMYTjLatMR54JoYS2nHwuZXiyDZ+XWebb8SwTRERkUOKKTTN7GTgb0AlwTXG9QQTHVQCq4EGQzPiHmCmmb0FvA5cCmQBD0W2/xiAu58f+fpKoAJYFll/DHA9B187nQbMN7OpwHPAOcA4oDCW701ERORQYj3S/DXBfZBXAzuALwGfAX8CHj7Uyu7+lJn1AG4iCNvFwBnuvibSpe79mikE1zD7A1XAB8BUIiEb2eYbZvYtgns4fx7pc567l8T4vYmIiDQq1tA8AbjQ3d3MqoE0d19lZjcATxIEaqPcfToNjLJ197F1vr4XuDfENmfR+GPLREREmi3WyQ32Rb3fBPSLvN9FcJpVRESkzYr1SLMMOAlYTjDrzu2R0ayTgXfjW5qIiEjLEuuR5k+AjyLvbwI+JpjUoBufn+xARESkTYnpSNPdS6Pef0xw64mIiMgRoUmTG5jZIOD4yJdL3X1V/EoSERFpmWK9T7MHwa0lZwMH/tVsLwAXuPvWONcnIiLSYsR6TfO/geMIHs11VOQ1BhgAzIhvaSIiIi1LrKdnvwJ82d2Lo9peN7PvA6/ErywREZGWJ9YjzY8JZgCqazegU7MiItKmxRqaPwfuNbPsmobI+7s59LyzIiIirdohT8+a2XtA9EM3BwCrzWx95OtsYC/Qi+Cap4iISJsU5pqm5nQVEREhRGi6+88SUYiIiEhL19TJDb4EDCc4bbvE3efGsygREZGWKNbJDbKB2cBo/jUHbZaZlQLnuPtHDa4sIiLSysU6eva3QDVwnLv3cfc+wOBI22/jXZyIiEhLEuvp2fHAWHevqGmIPIT6KmBOXCsTERFpYWI90oSDbz9prE1ERKRNiTU05wD3mVmfmgYz6wvci440RUSkjYs1NK8CjgZWmdkaM1sDfBBpuyrexYmIiLQksV7T3Ar8GzAWGBZpe9/dNVm7iIi0eaFD08xSgE+BHHd/GXj5sFUlIiLSAoU+Pevu1cAaoMPhK0dERKTlivWa5m3AXWbW83AUIyIi0pLFek3zeoKnnKw3s3XUebamu58Qr8JERERamlhDcxbBPZl2GGoRERFp0UKFppl1An4NTATaE9yTeaW7bzl8pYmIiLQsYa9p/gz4HvA34E/A6cCDh6kmERGRFins6dlvABe6+58BzOwJ4HUzS4mMqhUREWnzwh5p9gH+t+YLd38LqAKyDkdRIiIiLVHY0EwB9tVpq6KJD7EWERFpjcKGngGPm1llVNtRwAwz213T4O5nx7M4ERGRliRsaD5aT9vj8SxERESkpQsVmu7+n4e7EBERkZauKQ+hFhEROSIpNEVEREJSaIqIiISk0BQREQlJoSkiIhKSQlNERCQkhaaIiEhICk0REZGQFJoiIiIhKTRFRERCUmiKiIiEpNAUEREJSaEpIiISkkJTREQkJIWmiIhISApNERGRkBSaIiIiISk0RUREQlJoioiIhKTQFBERCUmhKSIiElLCQ9PMLjOzCjPba2YLzey0Rvoea2ZPmtk/zazazB6pp8/3zMzreR11WL8RERE54iQ0NM3sPGAacAcwCngD+LuZ9W1glTRgC3AXUNLIpncDx0a/3H1vvOoWERGBxB9pXgc84u4z3P19d78S2ABMqa+zu69296vc/RFgWyPbdXffGP2Kf+kiInKkS1homlkHYDTwUp1FLwGnNHPzHc1sjZmtM7MXzGxUM7cnIiLyOakJ3FdPIAXYVKd9E3B6M7a7DLgAKAfSgauB180sx91X1O1sZpcAlwBkZWUxd+5cAAYOHEh6ejrl5eUA9OjRgxEjRjB//nwAUlNTKSwspKysjB07dgCQl5fHpk2bgEHNKF9aqtLSUnbt2gVAfn4+69atY/369QAMHTqUlJQUli5dCkBmZiYDBgyguLgYgI4dO5Kfn09JSQl79uwBoKCggIqKCjZuDE6EDB8+nOrqapYtWwZAdnY2vXv3pqQkuBLRuXNn8vLyKC4uprKyEoDCwkKWL1/O5s2bARg5ciSVlZWsWBH8qvfp04eMjAxKS0sB6NKlC7m5uSxYsICqqioAxowZw5IlS9i6dSsAOTk57Ny5k1WrVgHQv39/unfvTllZGQDdunUjJyeHefPm4e6YGUVFRZSXl7N9+3YAcnNz2bZtG6tXrwaa93lau3YtAIMHDyYtLY3FixcD0KtXL4YMGcKCBQsASEtLo6CgoEk/p+DKj7Q1GzZsiMvnqTHm7ofxW4jakVkWsB4ocvf5Ue03A99x96GHWP8FYIu7f+8Q/VKAd4DX3P2qxvrm5eV5zf9cmuPie5u9CWmBZlyT7ArkcNFntm2K12fWzBa6e159yxJ5TXMLUA1k1GnPAOJ2DdLdq4FSYHC8tikiIgIJDE133wcsBMbXWTSeYBRtXJiZAScQDDASERGJm0Re0wS4B5hpZm8BrwOXAlnAQwBm9hiAu59fs4KZnRh52wU4EPl6n7svjSy/BXgTWBHpcxVBaNY7IldERKSpEhqa7v6UmfUAbiK4n3IxcIa7r4l0qe9+zUV1vv53YA3QP/J1V+D3QCbwaaT/GHd/K67Fi4jIES/RR5q4+3RgegPLxtbTZofY3rXAtXEpTkREpBGae1ZERCQkhaaIiEhICk0REZGQFJoiIiIhKTRFRERCUmiKiIiEpNAUEREJSaEpIiISkkJTREQkJIWmiIhISApNERGRkBSaIiIiISk0RUREQlJoioiIhKTQFBERCUmhKSIiEpJCU0REJCSFpoiISEgKTRERkZAUmiIiIiEpNEVEREJSaIqIiISk0BQREQlJoSkiIhKSQlNERCQkhaaIiEhICk0REZGQFJoiIiIhKTRFRERCUmiKiIiEpNAUEREJSaEpIiISkkJTREQkJIWmiIhISApNERGRkBSaIiIiISk0RUREQlJoioiIhKTQFBERCUmhKSIiEpJCU0REJCSFpoiISEgKTRERkZAUmiIiIiEpNEVEREJSaIqIiISk0BQREQlJoSkiIhKSQlNERCQkhaaIiEhICk0REZGQFJoiIiIhKTRFRERCUmiKiIiElPDQNLPLzKzCzPaa2UIzO+0Q/Ysi/faa2Sozu7S52xQREWmKhIammZ0HTAPuAEYBbwB/N7O+DfQfALwY6TcKuBO4z8wmNXWbIiIiTZXoI83rgEfcfYa7v+/uVwIbgCkN9L8U+Mjdr4z0nwE8ClzfjG2KiIg0ScJC08w6AKOBl+osegk4pYHVCurp/w8gz8zaN3GbIiIiTZKawH31BFKATXXaNwGnN7BOJvBKPf1TI9uzWLdpZpcAl0S+3GVmy8IUL7V6AluSXUQi/Pe1ya5AJC70mY1dv4YWJDI0WwR3/z3w+2TX0VqZWam75yW7DhEJR5/Z+EpkaG4BqoGMOu0ZwMYG1tnYQP+qyPasCdsUERFpkoRd03T3fcBCYHydReMJRrzWp7iB/qXuvr+J2xQREWmSRJ+evQeYaWZvAa8TjI7NAh4CMLPHANz9/Ej/h4ArzOxe4HfAqcD3gG+H3abEnU5ti7Qu+szGkbl7YndodhnwI+BYYDFwrbvPjyybC+DuY6P6FwG/AUYAHwG/dPeHwm5TREQkXhIemiIiIq2V5p4VEREJSaEpIiISkkJTYmZmluwaRESSQaEpMTGzdu7uZtbdzI5Odj0iEo7+2I0PDQSS0MzsROBKgikKK4CVwFJgLvCOux8wM3P9Uom0CGbWD9jk7nuj2gxAn9OmUWhKKGbWFXgbWA38FRgGDAV6ANuAJ939D8mqT0QOZmbpwN8IJokpAd4BKqLDMhKgg9x9ZVKKbIWOuLlnpckuJQjHr7v7bghO1QJjgf8EZpjZF4EfuPuBpFUpIjX+L1AIHAN8HVgOvGlmbwPvufvGyLK/mdlEd38/eaW2HjrSlFDM7EGgi7t/J/LXafvINIY1y78L3AyMd/fVSSpTRCLMbCbBH7q/IAjP84ATgb0Ek8C8DhwHfNfdv5CkMlsdDQSSsJ4HJpjZBA/sM7MUM0uLLP8bsA8Yk7wSRQTAzNoTzL+9xd03u/uz7n4ewZmhGcAXgKuAa9CUozHRkaaEYmbHAI8AXwMeAO5197WRZSlAf2AJcLy7VySpTBGJMLMuQEd33xQJ0ao61zP/nWB8Qr+az7IcmkJTDil6RKyZXU0wgnYAwSmeV4CuBJPpv+fu5yarThFpXOTSSjt3rzaz24BL3L3uoxWlEQpNCS1yj+YBM+tO8Pi1LwP5wFbgCeBFd9+QzBpFpPbsjzc2KC8yDmGfuz+VuMpaP4WmNMrMuhE8ju04oAuwHpjt7iVRfVLdvSo5FYpIYyKj3F33ZcaHQlMaZWavAtnARuBjIIPg+uUKggEFs919b81RaNIKFREAIs8fXgj8b/RI9sipWdPntHl0n6Y0yMzOJwjIL7t7ReRm6f7AaOCrwI+B3cBf9UEUST4zO5dgVGwJ8H/M7F1gAfCGu28F3Mw6Ewzq+6EG7cVOR5rSIDP7HZDq7hfWs6wncBdwFnBi5EZpEUkiM/sDwWWUFwkG5w0jODhaT3D0+RrQF3jc3XXQ1AS6T1Ma8wYw0czG1l3g7luAG4ANBPd+iUgSRW4rqQbWuvsfIn/sXkgwSO8AcDZwB/B74PGkFdrK6UhTGhSZb/ZRIB24j2Bi9k+ibj/pRjBx+wR3fytJZYpIhJllAb3c/Z26D08ws5OBScAPgDx3L0tWna2ZQlPqVfOBizzZ5FcETzZZDPwP8B4wGDgJ6Ovuo5JWqIg0KPq+zMjXFwK3u/uxya2s9VJoSihmNpLgVM85QBqwieAayTR3fzeZtYnIoZlZKsGp2u3ufmmy62mtFJrSqPpukjazPsABd1+fvMpEpCnMrL277092Ha2VQlNC003SIq2XHhAfHwpNaZQ+aCIi/6JbTuQgkaPJWlEjZfW7IiJHPB1pyueY2SjAgI7AOndfk+SSRERaBIWm1IqE5VXAfwDtgfeBdcA7BA+ZLiEYAKRfGpEWIHIvdTt335bsWo4UCk2pFZmcfTdwD8GE7BOAIuCLQCXwa3d/JnkVikg0M3sKyCK4lWQO8KG7V9bp0xfo7O5Lk1Bim6PQFKD2L9a1wMi6p2PN7HiCWUS+B5zj7s8nvEAROUjkM7sReBs4gWCMykvAn4FiYEPkYdOPAivc/fZk1dqWaHCH1OhNcCp2HAT3cplZBwB3f9/dLyKYDeisyByXIpJchUAZwaQj3YGLga7Ak8BbwH1mdh7wXYKJ2iUOFJpSc1vJYuB14HIzG+zu+919X83ySNdXgX/TjdEiLcJ2ImHo7tXu/md3/zLBH8D/BRQAfwJWuvvrySuzbVFoClEDe+4j+J1Yamazop5ukmpmBQQDhOYkvkIRqSsShA+4+3II/riN/AG8yd3vicwJvZTgyFPiRNc05XPM7BLgPwkeNl0JrCQYbFACXOjuHyexPBE5hMjZoWHAEuA4d1+V5JLaDIWm1DKzYcBWd/84MudsDjAcGEJw7eTvdUfmiUhy1Fw2aegWMDMbCnzN3e9NZF1tnULzCGdmvQgGClwLfAxUEQwI+jPwP+6+J4nliUgdkYF47u5VIfp2qBmbIPGh0DzCmdkjwAjgeWAbwSi8XOB44EPgbnf/f0krUEQOYmZTgM4Eg4BW1TexgZl1cvfdCS/uCKDQPIJFTu/sBM5w9/lRbb2BkwmGsPcDznP3d5JVp4gEIp/PaoIzQpuB+cCLBJdP1rr7zki/G4BKnZqNv9RkFyBJNRyoAGpP30Suj6wF1prZX4E3gPMIptITkeSaALwLXAKMBC4Cfk/wmX3JzF4iuLzyE4LJSCTOdMvJkW0VwV+rvzGzwfU84WQf8CjwtWQUJyKf0wFYDOxw9z+4+ynAYOBxYDzB7SXPEcwR/WzSqmzDdHr2CGdmJwMPAXuA3xHch7nd3XeZWSfgMWCvu09OYpkiAphZD2Ao8La77zezFHevjlp+IvAK8Cd3vzJJZbZpCk3BzEYCPwXOBj4jmLfyY+B0YANwkbu/l7wKRaQhkeucKe5eZWbdgK3Aqe5enOTS2iSFptSK3H5yJjAR2EtwGuhpd/9nMusSkXAiZ45+5u5fSXYtbZVCU+plZu3c/UCy6xCR8CL3cB7t7p8ku5a2SqEpIiISkkbPioiIhKTQFBERCUmhKSIiEpJCU0REJCSFpoiISEgKTRERkZAUmiIiIiH9f9trfJE+G5E/AAAAAElFTkSuQmCC\n", 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" ] }, "execution_count": 149, "metadata": {}, "output_type": "execute_result" } ], "source": [ "qc.measure_all()\n", "\n", "sim = Aer.get_backend('aer_simulator') \n", "result = sim.run(qc).result()\n", "plot_histogram(result.get_counts())" ] }, { "cell_type": "markdown", "id": "c8a091e0-6eb1-4276-b1be-b1385ce39b06", "metadata": {}, "source": [ "Let's now move to entanglement and true-multi-qubit gates. The most important one is the controlled-NOT gate. It is the quantum version of the q1=q1 XOR q0 gate and it can be used to create an entangled pair, in this case a $\\phi$ state" ] }, { "cell_type": "code", "execution_count": 141, "id": "61e601b1-730f-4d0c-b0ef-1d778470c9cb", "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "execution_count": 141, "metadata": {}, "output_type": "execute_result" } ], "source": [ "qc = QuantumCircuit(2)\n", "qc.h(0) #Add a Hadamard Gate to the 0th Qubit\n", "qc.cx(0,1) #Add a Hadamard Gate to the 0th Qubit\n", "qc.save_statevector()\n", "qc.draw() # Let's view our circuit\n" ] }, { "cell_type": "code", "execution_count": 142, "id": "95d03e2b-b5b9-45c1-b1cb-bd338132fa61", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Statevector([0.70710678+0.j, 0. +0.j, 0. +0.j,\n", " 0.70710678+0.j],\n", " dims=(2, 2))\n" ] } ], "source": [ "sim = Aer.get_backend('aer_simulator') \n", "\n", "\n", "result = sim.run(qc).result(); \n", "state = result.get_statevector()\n", "state" ] }, { "cell_type": "markdown", "id": "11bcf460-173e-4793-8305-4fb9e2eeeb4d", "metadata": {}, "source": [ "In reality, we rather want to measure the probabilities of different results occuring:" ] }, { "cell_type": "code", "execution_count": 143, "id": "94926884-453d-47fc-8ae5-0c6102373f69", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "execution_count": 143, "metadata": {}, "output_type": "execute_result" } ], "source": [ "qc.measure_all()\n", "sim = Aer.get_backend('aer_simulator') \n", "result = sim.run(qc).result()\n", "plot_histogram(result.get_counts())" ] }, { "cell_type": "markdown", "id": "9573896f-9e86-48e8-a85d-4e4025b6f476", "metadata": {}, "source": [ "As expecte we find that the results are prefectly correlated. Either both systems meansure 0 (00) or 1 (11) but never 01 (Qubit 0 in 0 and Qubit 1 in 1) or 10." ] }, { "cell_type": "markdown", "id": "05e74a66-324f-4e76-977c-9503098832d9", "metadata": { "tags": [] }, "source": [ "### Task 2: Repeat the experiment from above but measure in the +/--Basis\n", "Hint: Use the H-operator for 0/1 to +/- conversion" ] }, { "cell_type": "code", "execution_count": 144, "id": "50c97554-e334-45a4-b516-131b36a1244d", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "execution_count": 144, "metadata": {}, "output_type": "execute_result" } ], "source": [ "#Deleted code. Students need to complete this." ] }, { "cell_type": "code", "execution_count": 111, "id": "38c51383-3aa4-4d9b-8d6a-573f9e362489", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "execution_count": 111, "metadata": {}, "output_type": "execute_result" } ], "source": [ "#Deleted code. Students need to complete this." ] }, { "cell_type": "markdown", "id": "41a13cb7-3a75-4d20-a9d7-3dab1adbd320", "metadata": {}, "source": [ "As expected, again we find that the results are indeed perfectly correlated." ] }, { "cell_type": "markdown", "id": "cedff854-7a81-455b-b6da-9625a0a50df3", "metadata": { "tags": [] }, "source": [ "### Task 3: Repeat the experiment from above but measure in the L/R-Basis\n", "Hint: Use the H- and P-operator for 0/1 to L/R conversion" ] }, { "cell_type": "code", "execution_count": 112, "id": "7e258c2b-a3ef-465f-b2e2-decfd655b0d9", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "execution_count": 112, "metadata": {}, "output_type": "execute_result" } ], "source": [ "#Deleted code. Students need to complete this." ] }, { "cell_type": "code", "execution_count": 113, "id": "27dc346e-90b0-49d2-afa5-23bba105db80", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "execution_count": 113, "metadata": {}, "output_type": "execute_result" } ], "source": [ "#Deleted code. Students need to complete this." ] } ], "metadata": { "kernelspec": { "display_name": "Qiskit v0.35.0 (ipykernel)", "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": "3.8.13" }, "widgets": { "application/vnd.jupyter.widget-state+json": { "state": {}, "version_major": 2, "version_minor": 0 } } }, "nbformat": 4, "nbformat_minor": 5 }