├── .gitignore ├── Bhatti_Brandhofer_Mackeprang_solution.zip ├── CODE_OF_CONDUCT.md ├── LICENSE ├── Niu_Suau_Todri-Sanial_solution.zip ├── README.md ├── Ye_Zhu_solution.zip ├── dependencies ├── open-science-prize.png └── requirements.txt ├── galda_solution.zip ├── ibmquantum-graph-states-challenge.ipynb └── ibmquantum-swap-gate-challenge.ipynb /.gitignore: -------------------------------------------------------------------------------- 1 | # Byte-compiled / optimized / DLL files 2 | __pycache__/ 3 | *.py[cod] 4 | *$py.class 5 | 6 | # C extensions 7 | *.so 8 | 9 | # Distribution / packaging 10 | .Python 11 | build/ 12 | develop-eggs/ 13 | dist/ 14 | downloads/ 15 | eggs/ 16 | .eggs/ 17 | lib/ 18 | lib64/ 19 | parts/ 20 | sdist/ 21 | var/ 22 | wheels/ 23 | pip-wheel-metadata/ 24 | share/python-wheels/ 25 | *.egg-info/ 26 | .installed.cfg 27 | *.egg 28 | MANIFEST 29 | 30 | # PyInstaller 31 | # Usually these files are written by a python script from a template 32 | # before PyInstaller builds the exe, so as to inject date/other infos into it. 33 | *.manifest 34 | *.spec 35 | 36 | # Installer logs 37 | pip-log.txt 38 | pip-delete-this-directory.txt 39 | 40 | # Unit test / coverage reports 41 | htmlcov/ 42 | .tox/ 43 | .nox/ 44 | .coverage 45 | .coverage.* 46 | .cache 47 | nosetests.xml 48 | coverage.xml 49 | *.cover 50 | *.py,cover 51 | .hypothesis/ 52 | .pytest_cache/ 53 | 54 | # Translations 55 | *.mo 56 | *.pot 57 | 58 | # Django stuff: 59 | *.log 60 | local_settings.py 61 | db.sqlite3 62 | db.sqlite3-journal 63 | 64 | # Flask stuff: 65 | instance/ 66 | .webassets-cache 67 | 68 | # Scrapy stuff: 69 | .scrapy 70 | 71 | # Sphinx documentation 72 | docs/_build/ 73 | 74 | # PyBuilder 75 | target/ 76 | 77 | # Jupyter Notebook 78 | .ipynb_checkpoints 79 | 80 | # IPython 81 | profile_default/ 82 | ipython_config.py 83 | 84 | # pyenv 85 | .python-version 86 | 87 | # pipenv 88 | # According to pypa/pipenv#598, it is recommended to include Pipfile.lock in version control. 89 | # However, in case of collaboration, if having platform-specific dependencies or dependencies 90 | # having no cross-platform support, pipenv may install dependencies that don't work, or not 91 | # install all needed dependencies. 92 | #Pipfile.lock 93 | 94 | # PEP 582; used by e.g. github.com/David-OConnor/pyflow 95 | __pypackages__/ 96 | 97 | # Celery stuff 98 | celerybeat-schedule 99 | celerybeat.pid 100 | 101 | # SageMath parsed files 102 | *.sage.py 103 | 104 | # Environments 105 | .env 106 | .venv 107 | env/ 108 | venv/ 109 | ENV/ 110 | env.bak/ 111 | venv.bak/ 112 | 113 | # Spyder project settings 114 | .spyderproject 115 | .spyproject 116 | 117 | # Rope project settings 118 | .ropeproject 119 | 120 | # mkdocs documentation 121 | /site 122 | 123 | # mypy 124 | .mypy_cache/ 125 | .dmypy.json 126 | dmypy.json 127 | 128 | # Pyre type checker 129 | .pyre/ 130 | -------------------------------------------------------------------------------- /Bhatti_Brandhofer_Mackeprang_solution.zip: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/qiskit-community/open-science-prize/fb791bd179ad16be0c961bbed39ff5f8fd2e112a/Bhatti_Brandhofer_Mackeprang_solution.zip -------------------------------------------------------------------------------- /CODE_OF_CONDUCT.md: -------------------------------------------------------------------------------- 1 | 2 | 3 | # Code of Conduct 4 | All members of this project agree to adhere to the Qiskit Code of Conduct listed at [https://github.com/Qiskit/qiskit/blob/master/CODE_OF_CONDUCT.md](https://github.com/Qiskit/qiskit/blob/master/CODE_OF_CONDUCT.md) 5 | 6 | ---- 7 | 8 | License: [CC BY 4.0](https://creativecommons.org/licenses/by/4.0/), 9 | Copyright Contributors to Qiskit. 10 | -------------------------------------------------------------------------------- /LICENSE: -------------------------------------------------------------------------------- 1 | Apache License 2 | Version 2.0, January 2004 3 | http://www.apache.org/licenses/ 4 | 5 | TERMS AND CONDITIONS FOR USE, REPRODUCTION, AND DISTRIBUTION 6 | 7 | 1. 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You can read more about it and register [here](https://www.ibmquantumawards.com/), and read the IBM Quantum announcement [here](https://www.ibm.com/blogs/research/2020/11/open-science-prize/). 4 | 5 | # Objective 6 | 7 | The IBM Quantum Awards: Open Science Prize aims to solve two problems at the forefront of quantum computation based on superconducting qubits: 8 | 9 | 1. **Creating better SWAP gates** Typically, [SWAP](https://qiskit.org/textbook/ch-gates/more-circuit-identities.html#2.-Swapping-Qubits-) gates are implemented using three controlled-NOT (CNOT or CX) gates. This can be expensive, as the limiting gate error comes from the 2-qubit gates. The goal here is to create the best SWAP gate with a reduction in the infidelity of at least 50% compared with a traditional SWAP implemented using three standard CNOT gates, as estimated using randomized benchmarking techniques outlined in [this Jupyter notebook](ibmquantum-swap-gate-challenge.ipynb). **Award: $50,000** 10 | 11 | 2. **Creating larger graph states with better fidelity** Graph states entangle all involved qubits, and these entangled quantum states could be important for various applications, particularly those related to error correction, in the near future. The goal here is to create the largest graph states using the same benchmarking and error mitigation techniques that are also used to improve the individual quantum gates, ultimately looking for the best fidelity graph state with at least a 50% reduction in the infidelity as estimated by stabilizer measurements outlined in [this Jupyter notebook](ibmquantum-graph-states-challenge.ipynb). **Award: $50,000** 12 | 13 | # Open Science 14 | 15 | The goal of the Prize is to make significant progress on challenges at the forefront of quantum computation by doing science in the open. The resulting solutions will be open-sourced for the benefit of the entire quantum computing community. -------------------------------------------------------------------------------- /Ye_Zhu_solution.zip: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/qiskit-community/open-science-prize/fb791bd179ad16be0c961bbed39ff5f8fd2e112a/Ye_Zhu_solution.zip -------------------------------------------------------------------------------- /dependencies/open-science-prize.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/qiskit-community/open-science-prize/fb791bd179ad16be0c961bbed39ff5f8fd2e112a/dependencies/open-science-prize.png -------------------------------------------------------------------------------- /dependencies/requirements.txt: -------------------------------------------------------------------------------- 1 | qiskit>=0.23.1 -------------------------------------------------------------------------------- /galda_solution.zip: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/qiskit-community/open-science-prize/fb791bd179ad16be0c961bbed39ff5f8fd2e112a/galda_solution.zip -------------------------------------------------------------------------------- /ibmquantum-graph-states-challenge.ipynb: -------------------------------------------------------------------------------- 1 | { 2 | "cells": [ 3 | { 4 | "cell_type": "markdown", 5 | "metadata": {}, 6 | "source": [ 7 | "![image](dependencies/open-science-prize.png)" 8 | ] 9 | }, 10 | { 11 | "cell_type": "markdown", 12 | "metadata": {}, 13 | "source": [ 14 | "## Higher Fidelity Graph States\n", 15 | "In this notebook, we will prepare quantum circuits for a 7-qubit graph state and estimate the fidelity through stabilizer measurements using Qiskit. In this example, we use the CTMP method of error mitigation [1] and repeat the graph state measurement 16 times to find statistical error bars.\n", 16 | "\n", 17 | "**To Do:\n", 18 | "Modify the graph state preparation circuit or use your own methods of error mitigation to improve the graph state fidelity.**\n", 19 | "\n", 20 | "\n", 21 | "[1] S. Bravyi, S. Sheldon, A. Kandala, D.C. McKay, J.M. Gambetta, Mitigating measurement errors in multi-qubit experiments, [arXiv:2006.14044](https://arxiv.org/abs/2006.14044) (2020)." 22 | ] 23 | }, 24 | { 25 | "cell_type": "markdown", 26 | "metadata": {}, 27 | "source": [ 28 | "## Imports\n", 29 | "\n", 30 | "Begin by importing the necessary packages and defining the functions we will need for the stabilizer measurements." 31 | ] 32 | }, 33 | { 34 | "cell_type": "code", 35 | "execution_count": 1, 36 | "metadata": { 37 | "scrolled": false 38 | }, 39 | "outputs": [], 40 | "source": [ 41 | "### install Qiskit and other modules if you don't have them already\n", 42 | "!pip install -r dependencies/requirements.txt --quiet" 43 | ] 44 | }, 45 | { 46 | "cell_type": "code", 47 | "execution_count": 2, 48 | "metadata": {}, 49 | "outputs": [], 50 | "source": [ 51 | "# Qiskit module\n", 52 | "from qiskit import QuantumCircuit\n", 53 | "import qiskit.circuit.library as circuit_library\n", 54 | "import qiskit.quantum_info as qi\n", 55 | "import qiskit.ignis.mitigation as mit\n", 56 | "\n", 57 | "# Qiskit tools for noisy simulation\n", 58 | "from qiskit.providers.aer import QasmSimulator\n", 59 | "from qiskit.providers.aer.noise import NoiseModel\n", 60 | "from qiskit.providers.aer.utils import insert_noise\n", 61 | "\n", 62 | "# Qiskit tools for running and monitoring jobs\n", 63 | "from qiskit import execute\n", 64 | "from qiskit.tools.monitor import job_monitor\n", 65 | "\n", 66 | "# Other imports\n", 67 | "import numpy as np\n", 68 | "\n", 69 | "# Suppress warnings\n", 70 | "import warnings\n", 71 | "warnings.filterwarnings('ignore')" 72 | ] 73 | }, 74 | { 75 | "cell_type": "markdown", 76 | "metadata": {}, 77 | "source": [ 78 | "In order to run the circuits, first load the backend `ibmq_casablanca` from your account using the `IBMQ` provider. You will receive access to `ibm-q-community/ibmquantumawards/open-science` after registering for the Open Science Prize." 79 | ] 80 | }, 81 | { 82 | "cell_type": "code", 83 | "execution_count": 3, 84 | "metadata": {}, 85 | "outputs": [], 86 | "source": [ 87 | "# Load IBMQ Account data\n", 88 | "from qiskit import IBMQ\n", 89 | "IBMQ.load_account()\n", 90 | "\n", 91 | "# Get backend for experiment\n", 92 | "provider = IBMQ.get_provider(hub='ibm-q-community', group='ibmquantumawards', project='open-science')\n", 93 | "backend = provider.get_backend('ibmq_casablanca')\n", 94 | "properties = backend.properties()" 95 | ] 96 | }, 97 | { 98 | "cell_type": "markdown", 99 | "metadata": {}, 100 | "source": [ 101 | "## Preparing graph states" 102 | ] 103 | }, 104 | { 105 | "cell_type": "markdown", 106 | "metadata": {}, 107 | "source": [ 108 | "Here, we prepare the graph state circuit for 7-qubits using the `GraphState` function in Qiskit's circuit library. We define a graph that uses the connectivity map of the quantum system `ibmq_casablanca`." 109 | ] 110 | }, 111 | { 112 | "cell_type": "code", 113 | "execution_count": 4, 114 | "metadata": {}, 115 | "outputs": [], 116 | "source": [ 117 | "num_qubits = 7\n", 118 | "\n", 119 | "# adjacency matrix for `ibmq_casablanca`\n", 120 | "adjmat = [\n", 121 | " [0, 1, 0, 0, 0, 0, 0], \n", 122 | " [1, 0, 1, 1, 0, 0, 0], \n", 123 | " [0, 1, 0, 0, 0, 0, 0], \n", 124 | " [0, 1, 0, 0, 0, 1, 0], \n", 125 | " [0, 0, 0, 0, 0, 1, 0], \n", 126 | " [0, 0, 0, 1, 1, 0, 1], \n", 127 | " [0, 0, 0, 0, 0, 1, 0]]" 128 | ] 129 | }, 130 | { 131 | "cell_type": "markdown", 132 | "metadata": {}, 133 | "source": [ 134 | "### Your code goes here\n", 135 | "\n", 136 | "How would you prepare a graph state with high fidelity? In the example below, we create it using Qiskit's circuit library at the gate level. You may explore other methods for creating the graph states, including by using pulse-level techniques or accounting for the errors in the quantum system." 137 | ] 138 | }, 139 | { 140 | "cell_type": "code", 141 | "execution_count": 5, 142 | "metadata": {}, 143 | "outputs": [], 144 | "source": [ 145 | "def create_graph_state():\n", 146 | " \n", 147 | " ### YOUR CODE GOES HERE -- START\n", 148 | " \n", 149 | " graph_state_circuit = circuit_library.GraphState(adjmat)\n", 150 | " \n", 151 | " ### YOUR CODE GOES HERE -- END\n", 152 | " \n", 153 | " return graph_state_circuit" 154 | ] 155 | }, 156 | { 157 | "cell_type": "code", 158 | "execution_count": 6, 159 | "metadata": {}, 160 | "outputs": [ 161 | { 162 | "data": { 163 | "image/png": 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\n", 164 | "text/plain": [ 165 | "
" 166 | ] 167 | }, 168 | "execution_count": 6, 169 | "metadata": {}, 170 | "output_type": "execute_result" 171 | } 172 | ], 173 | "source": [ 174 | "# the graph state can be created using Qiskit's circuit library\n", 175 | "state_circuit = create_graph_state()\n", 176 | "state_circuit.draw()" 177 | ] 178 | }, 179 | { 180 | "cell_type": "markdown", 181 | "metadata": {}, 182 | "source": [ 183 | "## Creating and measuring stabilizers" 184 | ] 185 | }, 186 | { 187 | "cell_type": "markdown", 188 | "metadata": {}, 189 | "source": [ 190 | "We begin by defining functions to create stabilizer measurement circuits, and then appending them onto the circuit used to create the graph states." 191 | ] 192 | }, 193 | { 194 | "cell_type": "code", 195 | "execution_count": 7, 196 | "metadata": {}, 197 | "outputs": [], 198 | "source": [ 199 | "def compute_stabilizer_group(circuit):\n", 200 | " \"\"\"Compute the stabilizer group for stabilizer circuit.\"\"\"\n", 201 | " state = qi.Statevector.from_instruction(circuit)\n", 202 | " labels = []\n", 203 | " for i in qi.pauli_basis(state.num_qubits):\n", 204 | " val = round(qi.state_fidelity(i.to_matrix()[0], state, validate=False))\n", 205 | " if val != 0:\n", 206 | " label = i.to_labels()[0]\n", 207 | " if val == 1:\n", 208 | " label = '+' + label\n", 209 | " else:\n", 210 | " label = '-' + label\n", 211 | " labels.append(label)\n", 212 | " return labels\n", 213 | "\n", 214 | "def stabilizer_coeff_pauli(stabilizer):\n", 215 | " \"\"\"Return the 1 or -1 coeff and Pauli label.\"\"\"\n", 216 | " coeff = 1\n", 217 | " pauli = coeff\n", 218 | " if stabilizer[0] == '-':\n", 219 | " coeff = -1\n", 220 | " if stabilizer[0] in ['+', '-']:\n", 221 | " pauli = stabilizer[1:]\n", 222 | " else:\n", 223 | " pauli = stabilizer\n", 224 | " return coeff, pauli\n", 225 | "\n", 226 | "def stabilizer_measure_circuit(stabilizer, initial_circuit=None):\n", 227 | " \"\"\"Return a stabilizer measurement circuits.\n", 228 | " \n", 229 | " Args:\n", 230 | " stabilizer (str): a stabilizer string\n", 231 | " initial_circuit (QuantumCircuit): Optional, the initial circuit.\n", 232 | " \n", 233 | " Returns:\n", 234 | " QuantumCircuit: the circuit with stabilizer measurements.\n", 235 | " \"\"\"\n", 236 | " _, pauli = stabilizer_coeff_pauli(stabilizer)\n", 237 | " if initial_circuit is None:\n", 238 | " circ = QuantumCircuit(len(pauli))\n", 239 | " else:\n", 240 | " circ = initial_circuit.copy()\n", 241 | " for i, s in enumerate(reversed(pauli)):\n", 242 | " if s == 'X':\n", 243 | " circ.h(i)\n", 244 | " if s == 'Y':\n", 245 | " circ.sdg(i)\n", 246 | " circ.h(i)\n", 247 | " circ.measure_all()\n", 248 | " return circ" 249 | ] 250 | }, 251 | { 252 | "cell_type": "code", 253 | "execution_count": 8, 254 | "metadata": {}, 255 | "outputs": [ 256 | { 257 | "name": "stdout", 258 | "output_type": "stream", 259 | "text": [ 260 | "Stabilizers: ['+IIIIIII', '+IIIIIZX', '+IIIIXIX', '+IIIIXZI', '-IIIZYXY', '+IIIZYYZ', '+IIIZZXZ', '+IIIZZYY', '+IIXXIIX', '+IIXXIZI', '+IIXXXII', '+IIXXXZX', '-IIXYYXZ', '-IIXYYYY', '-IIXYZXY', '+IIXYZYZ', '+IZIXIIX', '+IZIXIZI', '+IZIXXII', '+IZIXXZX', '-IZIYYXZ', '-IZIYYYY', '-IZIYZXY', '+IZIYZYZ', '+IZXIIII', '+IZXIIZX', '+IZXIXIX', '+IZXIXZI', '-IZXZYXY', '+IZXZYYZ', '+IZXZZXZ', '+IZXZZYY', '+XIIXIIX', '+XIIXIZI', '+XIIXXII', '+XIIXXZX', '-XIIYYXZ', '-XIIYYYY', '-XIIYZXY', '+XIIYZYZ', '+XIXIIII', '+XIXIIZX', '+XIXIXIX', '+XIXIXZI', '-XIXZYXY', '+XIXZYYZ', '+XIXZZXZ', '+XIXZZYY', '+XZIIIII', '+XZIIIZX', '+XZIIXIX', '+XZIIXZI', '-XZIZYXY', '+XZIZYYZ', '+XZIZZXZ', '+XZIZZYY', '+XZXXIIX', '+XZXXIZI', '+XZXXXII', '+XZXXXZX', '-XZXYYXZ', '-XZXYYYY', '-XZXYZXY', '+XZXYZYZ', '+YXYIYXY', '-YXYIYYZ', '-YXYIZXZ', '-YXYIZYY', '-YXYZIII', '-YXYZIZX', '-YXYZXIX', '-YXYZXZI', '-YXZXYXZ', '-YXZXYYY', '-YXZXZXY', '+YXZXZYZ', '-YXZYIIX', '-YXZYIZI', '-YXZYXII', '-YXZYXZX', '-YYYXYXZ', '-YYYXYYY', '-YYYXZXY', '+YYYXZYZ', '-YYYYIIX', '-YYYYIZI', '-YYYYXII', '-YYYYXZX', '-YYZIYXY', '+YYZIYYZ', '+YYZIZXZ', '+YYZIZYY', '+YYZZIII', '+YYZZIZX', '+YYZZXIX', '+YYZZXZI', '-ZXYXYXZ', '-ZXYXYYY', '-ZXYXZXY', '+ZXYXZYZ', '-ZXYYIIX', '-ZXYYIZI', '-ZXYYXII', '-ZXYYXZX', '-ZXZIYXY', '+ZXZIYYZ', '+ZXZIZXZ', '+ZXZIZYY', '+ZXZZIII', '+ZXZZIZX', '+ZXZZXIX', '+ZXZZXZI', '-ZYYIYXY', '+ZYYIYYZ', '+ZYYIZXZ', '+ZYYIZYY', '+ZYYZIII', '+ZYYZIZX', '+ZYYZXIX', '+ZYYZXZI', '+ZYZXYXZ', '+ZYZXYYY', '+ZYZXZXY', '-ZYZXZYZ', '+ZYZYIIX', '+ZYZYIZI', '+ZYZYXII', '+ZYZYXZX']\n", 261 | "Generators: ['IIIIIZX', 'IIIZZXZ', 'IIIIXZI', 'IZIXIZI', 'IZXIIII', 'ZXZZIII', 'XZIIIII']\n" 262 | ] 263 | } 264 | ], 265 | "source": [ 266 | "## Compute the stabilizers for this graph state\n", 267 | "generators = qi.Clifford(state_circuit).stabilizer.pauli.to_labels()\n", 268 | "stabilizers = compute_stabilizer_group(state_circuit)\n", 269 | "print('Stabilizers:', stabilizers)\n", 270 | "print('Generators:', generators)" 271 | ] 272 | }, 273 | { 274 | "cell_type": "code", 275 | "execution_count": 9, 276 | "metadata": {}, 277 | "outputs": [ 278 | { 279 | "data": { 280 | "image/png": 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\n", 281 | "text/plain": [ 282 | "
" 283 | ] 284 | }, 285 | "execution_count": 9, 286 | "metadata": {}, 287 | "output_type": "execute_result" 288 | } 289 | ], 290 | "source": [ 291 | "## Append the stabilizer measurements to the graph state circuit \n", 292 | "stabilizer_circuits = [stabilizer_measure_circuit(stab, state_circuit)\n", 293 | " for stab in stabilizers]\n", 294 | "\n", 295 | "stabilizer_circuits[0].draw()" 296 | ] 297 | }, 298 | { 299 | "cell_type": "markdown", 300 | "metadata": {}, 301 | "source": [ 302 | "## Measurement mitigation\n", 303 | "\n", 304 | "Noisy measurements impact our ability to accurately measure the state fidelity. For our default example we calibrate our measurements for the CTMP method using states with two-qubit excitations." 305 | ] 306 | }, 307 | { 308 | "cell_type": "code", 309 | "execution_count": 10, 310 | "metadata": {}, 311 | "outputs": [], 312 | "source": [ 313 | "labels = ['0000000', '0000011', '0000101', \n", 314 | " '0001001', '0001010', '0001100', \n", 315 | " '0010001', '0010010', '0010100', '0011000', \n", 316 | " '0100001', '0100010', '0100100', '0101000', '0110000', \n", 317 | " '1000001', '1000010', '1000100', '1001000', '1010000', '1100000', \n", 318 | " '1111111']\n", 319 | "meas_cal_circuits, metadata = mit.expval_meas_mitigator_circuits(num_qubits, labels=labels)" 320 | ] 321 | }, 322 | { 323 | "cell_type": "code", 324 | "execution_count": 11, 325 | "metadata": {}, 326 | "outputs": [], 327 | "source": [ 328 | "[meas_cal_circuits_full, state_labels] = mit.complete_meas_cal(range(num_qubits))" 329 | ] 330 | }, 331 | { 332 | "cell_type": "markdown", 333 | "metadata": {}, 334 | "source": [ 335 | "## Run the circuits" 336 | ] 337 | }, 338 | { 339 | "cell_type": "markdown", 340 | "metadata": {}, 341 | "source": [ 342 | "We will run the circuits on the `ibmq_casablanca` quantum system." 343 | ] 344 | }, 345 | { 346 | "cell_type": "markdown", 347 | "metadata": {}, 348 | "source": [ 349 | "In order to debug more quickly and avoid queues, you may consider using a simulator backend modeled after the real quantum system. This will use the noise model of `ibmq_casablanca` to do simulations. You may uncomment the line below to do so. **Note that the fidelities of your graph states will generally be higher on the simulator, but the Open Science Prize is awarded for the best fidelities on the real quantum system.**" 350 | ] 351 | }, 352 | { 353 | "cell_type": "code", 354 | "execution_count": 12, 355 | "metadata": {}, 356 | "outputs": [], 357 | "source": [ 358 | "# backend = QasmSimulator.from_backend(provider.get_backend('ibmq_casablanca'))" 359 | ] 360 | }, 361 | { 362 | "cell_type": "markdown", 363 | "metadata": {}, 364 | "source": [ 365 | "We run the measurement calibration circuits in a separate job from the graph state circuits. We repeat both 16 times and use the mean as the final value. \n", 366 | "\n", 367 | "In order to debug more quickly, you may consider reducing `reps` from 16 to 1. **Note that the final submissions will need to be executed with 16 repetitions.**" 368 | ] 369 | }, 370 | { 371 | "cell_type": "code", 372 | "execution_count": 13, 373 | "metadata": {}, 374 | "outputs": [], 375 | "source": [ 376 | "reps = 16" 377 | ] 378 | }, 379 | { 380 | "cell_type": "code", 381 | "execution_count": 14, 382 | "metadata": { 383 | "scrolled": false 384 | }, 385 | "outputs": [ 386 | { 387 | "name": "stdout", 388 | "output_type": "stream", 389 | "text": [ 390 | "Job IDs (1/16): \n", 391 | " measurement calibration: 5fc6ae9d667e1d0019e27c8d\n", 392 | " stabilizer measurements: 5fc6ae92409629001ab814fe\n", 393 | "Job IDs (2/16): \n", 394 | " measurement calibration: 5fc6aeb227482400199aa9fe\n", 395 | " stabilizer measurements: 5fc6aea77a8d9a0019d4c156\n", 396 | "Job IDs (3/16): \n", 397 | " measurement calibration: 5fc6aec7cb8ccc001a95c3ef\n", 398 | " stabilizer measurements: 5fc6aebd24c9e90019f924cb\n", 399 | "Job IDs (4/16): \n", 400 | " measurement calibration: 5fc6aedd46ea68001af54f10\n", 401 | " stabilizer measurements: 5fc6aed2409629001ab81501\n", 402 | "Job IDs (5/16): \n", 403 | " measurement calibration: 5fc6aef6cb8ccc001a95c3f2\n", 404 | " stabilizer measurements: 5fc6aeea409629001ab81503\n", 405 | "Job IDs (6/16): \n", 406 | " measurement calibration: 5fc6af0e667e1d0019e27c93\n", 407 | " stabilizer measurements: 5fc6af0327482400199aaa01\n", 408 | "Job IDs (7/16): \n", 409 | " measurement calibration: 5fc6af2924c9e90019f924d2\n", 410 | " stabilizer measurements: 5fc6af1b7a8d9a0019d4c15c\n", 411 | "Job IDs (8/16): \n", 412 | " measurement calibration: 5fc6af3ecb8ccc001a95c3f7\n", 413 | " stabilizer measurements: 5fc6af34667e1d0019e27c94\n", 414 | "Job IDs (9/16): \n", 415 | " measurement calibration: 5fc6af537a8d9a0019d4c160\n", 416 | " stabilizer measurements: 5fc6af496cd844001a3d2bd3\n", 417 | "Job IDs (10/16): \n", 418 | " measurement calibration: 5fc6af67cb8ccc001a95c3f9\n", 419 | " stabilizer measurements: 5fc6af5d6cd844001a3d2bd4\n", 420 | "Job IDs (11/16): \n", 421 | " measurement calibration: 5fc6af7c46ea68001af54f14\n", 422 | " stabilizer measurements: 5fc6af73f1eb23001a91aa73\n", 423 | "Job IDs (12/16): \n", 424 | " measurement calibration: 5fc6af8f667e1d0019e27c99\n", 425 | " stabilizer measurements: 5fc6af86f1eb23001a91aa75\n", 426 | "Job IDs (13/16): \n", 427 | " measurement calibration: 5fc6afa346ea68001af54f18\n", 428 | " stabilizer measurements: 5fc6af997a8d9a0019d4c166\n", 429 | "Job IDs (14/16): \n", 430 | " measurement calibration: 5fc6afb77a8d9a0019d4c167\n", 431 | " stabilizer measurements: 5fc6afad667e1d0019e27c9b\n", 432 | "Job IDs (15/16): \n", 433 | " measurement calibration: 5fc6afcbcb8ccc001a95c400\n", 434 | " stabilizer measurements: 5fc6afc27a8d9a0019d4c169\n", 435 | "Job IDs (16/16): \n", 436 | " measurement calibration: 5fc6afdf46ea68001af54f1e\n", 437 | " stabilizer measurements: 5fc6afd56cd844001a3d2bdb\n" 438 | ] 439 | } 440 | ], 441 | "source": [ 442 | "all_jobs = []\n", 443 | "all_jobs_mit = []\n", 444 | "\n", 445 | "for ii in range(reps):\n", 446 | "\n", 447 | " # Run QPT on backend\n", 448 | " shots = 8192\n", 449 | " il = [0,1,2,3,4,5,6]\n", 450 | " \n", 451 | " job_backend = execute(stabilizer_circuits, backend, shots=shots, initial_layout=il)\n", 452 | " job_mit_backend = execute(meas_cal_circuits, backend, shots=shots, initial_layout=il)\n", 453 | " print('Job IDs ({}/{}): \\n measurement calibration: {}\\n stabilizer measurements: {}'.format(\n", 454 | " ii+1, reps, job_mit_backend.job_id(), job_backend.job_id()))\n", 455 | "\n", 456 | " all_jobs.append(job_backend)\n", 457 | " all_jobs_mit.append(job_mit_backend)" 458 | ] 459 | }, 460 | { 461 | "cell_type": "markdown", 462 | "metadata": {}, 463 | "source": [ 464 | "We can monitor the status of the jobs using Qiskit's job monitoring tools." 465 | ] 466 | }, 467 | { 468 | "cell_type": "code", 469 | "execution_count": 15, 470 | "metadata": {}, 471 | "outputs": [ 472 | { 473 | "name": "stdout", 474 | "output_type": "stream", 475 | "text": [ 476 | "Job Status: job has successfully run\n", 477 | "Job Status: job has successfully run\n", 478 | "Job Status: job has successfully run\n", 479 | "Job Status: job has successfully run\n", 480 | "Job Status: job has successfully run\n", 481 | "Job Status: job has successfully run\n", 482 | "Job Status: job has successfully run\n", 483 | "Job Status: job has successfully run\n", 484 | "Job Status: job has successfully run\n", 485 | "Job Status: job has successfully run\n", 486 | "Job Status: job has successfully run\n", 487 | "Job Status: job has successfully run\n", 488 | "Job Status: job has successfully run\n", 489 | "Job Status: job has successfully run\n", 490 | "Job Status: job has successfully run\n", 491 | "Job Status: job has successfully run\n" 492 | ] 493 | } 494 | ], 495 | "source": [ 496 | "for job in all_jobs:\n", 497 | " job_monitor(job)\n", 498 | " try:\n", 499 | " if job.error_message() is not None:\n", 500 | " print(job.error_message())\n", 501 | " except:\n", 502 | " pass" 503 | ] 504 | }, 505 | { 506 | "cell_type": "markdown", 507 | "metadata": {}, 508 | "source": [ 509 | "## Post-processing and computing fidelities" 510 | ] 511 | }, 512 | { 513 | "cell_type": "markdown", 514 | "metadata": {}, 515 | "source": [ 516 | "Once the jobs are completed, we can get the results back as follows." 517 | ] 518 | }, 519 | { 520 | "cell_type": "code", 521 | "execution_count": 16, 522 | "metadata": {}, 523 | "outputs": [], 524 | "source": [ 525 | "result_backend = []\n", 526 | "result_mit_backend = []\n", 527 | "for job in all_jobs:\n", 528 | " # Retrieve results (this may take a while depending on the queue)\n", 529 | " result_backend.append(job.result())\n", 530 | " \n", 531 | "for job in all_jobs_mit:\n", 532 | " result_mit_backend.append(job.result())" 533 | ] 534 | }, 535 | { 536 | "cell_type": "markdown", 537 | "metadata": {}, 538 | "source": [ 539 | "Finally, we compute the fidelities of the graph states. You may consider creating your own method for error mitigation by updating the `stabilizer_expvals` function below. Here, we will use the default methods provided in Qiskit." 540 | ] 541 | }, 542 | { 543 | "cell_type": "code", 544 | "execution_count": 17, 545 | "metadata": {}, 546 | "outputs": [], 547 | "source": [ 548 | "def stabilizer_measure_diagonal(stabilizer):\n", 549 | " \"\"\"Return the diagonal vector for a stabilizer measurement.\n", 550 | " \n", 551 | " Args:\n", 552 | " stabilizer (str): a stabilizer string\n", 553 | " \n", 554 | " Returns:\n", 555 | " np.ndarray: the diagonal for measurement in the stabilizer basis.\n", 556 | " \"\"\"\n", 557 | " coeff, pauli = stabilizer_coeff_pauli(stabilizer)\n", 558 | " diag = np.array([1])\n", 559 | " for s in reversed(pauli):\n", 560 | " if s == 'I':\n", 561 | " tmp = np.array([1, 1])\n", 562 | " else:\n", 563 | " tmp = np.array([1, -1])\n", 564 | " diag = np.kron(tmp, diag)\n", 565 | " return coeff * diag\n", 566 | " \n", 567 | "def stabilizer_fidelity(expvals, stddevs=None):\n", 568 | " \"\"\"Compute stabilizer state fidelity from stabilizer expvals.\"\"\"\n", 569 | " mean = np.mean(expvals)\n", 570 | " if stddevs is None:\n", 571 | " return mean\n", 572 | " stddev = np.sqrt(np.sum(stddevs ** 2))\n", 573 | " return mean, stddev" 574 | ] 575 | }, 576 | { 577 | "cell_type": "markdown", 578 | "metadata": {}, 579 | "source": [ 580 | "### Your code goes here\n", 581 | "\n", 582 | "You may consider updating the function below to change how the measurement calibration circuits are used to compute the fidelity of the graph state." 583 | ] 584 | }, 585 | { 586 | "cell_type": "code", 587 | "execution_count": 18, 588 | "metadata": {}, 589 | "outputs": [], 590 | "source": [ 591 | "def stabilizer_expvals(result, stabilizers, meas_mitigator=None):\n", 592 | " \"\"\"Compute expectation values from stabilizer measurement results.\"\"\"\n", 593 | "\n", 594 | " ### YOUR CODE GOES HERE -- START\n", 595 | " \n", 596 | " expvals = []\n", 597 | " stddevs = []\n", 598 | " for i, stab in enumerate(stabilizers):\n", 599 | " expval, stddev = mit.expectation_value(\n", 600 | " result.get_counts(i),\n", 601 | " diagonal=stabilizer_measure_diagonal(stab),\n", 602 | " meas_mitigator=meas_mitigator)\n", 603 | " expvals.append(expval)\n", 604 | " stddevs.append(stddev)\n", 605 | " return np.array(expvals), np.array(stddevs)\n", 606 | "\n", 607 | " ### YOUR CODE GOES HERE -- END" 608 | ] 609 | }, 610 | { 611 | "cell_type": "code", 612 | "execution_count": 19, 613 | "metadata": {}, 614 | "outputs": [], 615 | "source": [ 616 | "## Mitigate the stabilizer expectation values \n", 617 | "F_nomit_backend = []\n", 618 | "F_mit_backend = []\n", 619 | "\n", 620 | "for ii in range(reps):\n", 621 | " # Unmitigated Expectation Values\n", 622 | " expvals_nomit_b, stddevs_nomit_b = stabilizer_expvals(\n", 623 | " result_backend[ii], stabilizers)\n", 624 | " \n", 625 | " # Fit measurement error mitigators\n", 626 | " mitigator_backend = mit.ExpvalMeasMitigatorFitter(result_mit_backend[ii], metadata).fit()\n", 627 | "\n", 628 | " # Measurement error mitigated expectation values\n", 629 | " expvals_mit_b, stddevs_mit_b = stabilizer_expvals(\n", 630 | " result_backend[ii], stabilizers, meas_mitigator=mitigator_backend)\n", 631 | " \n", 632 | " # save the fidelities for this iteration\n", 633 | " F_nomit_backend.append(stabilizer_fidelity(expvals_nomit_b, stddevs_nomit_b)[0])\n", 634 | " F_mit_backend.append(stabilizer_fidelity(expvals_mit_b, stddevs_mit_b)[0])" 635 | ] 636 | }, 637 | { 638 | "cell_type": "markdown", 639 | "metadata": {}, 640 | "source": [ 641 | "Report the fidelity estimates." 642 | ] 643 | }, 644 | { 645 | "cell_type": "code", 646 | "execution_count": 20, 647 | "metadata": {}, 648 | "outputs": [ 649 | { 650 | "name": "stdout", 651 | "output_type": "stream", 652 | "text": [ 653 | "Graph-state fidelity estimates\n", 654 | "\n", 655 | "No mitigation\n", 656 | "F(ibmq_casablanca) = 0.647 ± 0.016\n", 657 | "\n", 658 | "CTMP error mitigation\n", 659 | "F(ibmq_casablanca) = 0.782 ± 0.018\n" 660 | ] 661 | } 662 | ], 663 | "source": [ 664 | "## The final results\n", 665 | "\n", 666 | "print('Graph-state fidelity estimates')\n", 667 | "print('\\nNo mitigation')\n", 668 | "print('F({}) = {:.3f} \\u00B1 {:.3f}'.format(\n", 669 | " properties.backend_name, np.mean(F_nomit_backend), np.std(F_nomit_backend)))\n", 670 | "\n", 671 | "print('\\nCTMP error mitigation')\n", 672 | "print('F({}) = {:.3f} \\u00B1 {:.3f}'.format(\n", 673 | " properties.backend_name, np.mean(F_mit_backend), np.std(F_mit_backend)))" 674 | ] 675 | }, 676 | { 677 | "cell_type": "markdown", 678 | "metadata": {}, 679 | "source": [ 680 | "## Qiskit version" 681 | ] 682 | }, 683 | { 684 | "cell_type": "code", 685 | "execution_count": 21, 686 | "metadata": {}, 687 | "outputs": [ 688 | { 689 | "data": { 690 | "text/html": [ 691 | "

Version Information

Qiskit SoftwareVersion
Qiskit0.23.1
Terra0.16.1
Aer0.7.1
Ignis0.5.1
Aqua0.8.1
IBM Q Provider0.11.1
System information
Python3.8.2 (default, Mar 26 2020, 10:43:30) \n", 692 | "[Clang 4.0.1 (tags/RELEASE_401/final)]
OSDarwin
CPUs6
Memory (Gb)16.0
Tue Dec 01 18:16:41 2020 EST
" 693 | ], 694 | "text/plain": [ 695 | "" 696 | ] 697 | }, 698 | "metadata": {}, 699 | "output_type": "display_data" 700 | } 701 | ], 702 | "source": [ 703 | "import qiskit.tools.jupyter\n", 704 | "%qiskit_version_table" 705 | ] 706 | } 707 | ], 708 | "metadata": { 709 | "kernelspec": { 710 | "display_name": "Python 3", 711 | "language": "python", 712 | "name": "python3" 713 | }, 714 | "language_info": { 715 | "codemirror_mode": { 716 | "name": "ipython", 717 | "version": 3 718 | }, 719 | "file_extension": ".py", 720 | "mimetype": "text/x-python", 721 | "name": "python", 722 | "nbconvert_exporter": "python", 723 | "pygments_lexer": "ipython3", 724 | "version": "3.8.2" 725 | } 726 | }, 727 | "nbformat": 4, 728 | "nbformat_minor": 4 729 | } 730 | --------------------------------------------------------------------------------