From 731385b1f63502320f0e8160c374d786caab54d7 Mon Sep 17 00:00:00 2001 From: Kaelyn Ferris Date: Wed, 10 Apr 2024 18:01:35 -0400 Subject: [PATCH 01/25] Update hello-world to work with coding with qiskit --- docs/start/hello-world.ipynb | 333 +++++++++++++++++++++--- public/images/start/qiskit-patterns.png | Bin 0 -> 242605 bytes 2 files changed, 295 insertions(+), 38 deletions(-) create mode 100644 public/images/start/qiskit-patterns.png diff --git a/docs/start/hello-world.ipynb b/docs/start/hello-world.ipynb index 11d6200582f..e0958754880 100644 --- a/docs/start/hello-world.ipynb +++ b/docs/start/hello-world.ipynb @@ -13,7 +13,7 @@ "\n", "To learn about quantum computing in general, check out the [Basics of quantum information course](https://learning.quantum.ibm.com/course/basics-of-quantum-information) in IBM Quantum Learning.\n", "\n", - "The four steps to writing a quantum program are\n", + "The four steps to writing a quantum program using Qiskit Patterns are:\n", "\n", "1. Map the problem to a quantum-native format\n", "\n", @@ -23,6 +23,7 @@ "\n", "4. Analyze the results\n", "\n", + "\n", "## Step 1. Map the problem to a quantum-native format" ] }, @@ -41,7 +42,7 @@ "id": "21f7a26c", "metadata": {}, "source": [ - "The following code cell creates a circuit that produces a *Bell state,* which is a specific two-qubit entangled state.\n", + "The following code cell creates a circuit that produces a *Bell state,* which is a state wherein two (or more) qubits are fully entangled with each other.\n", "\n", "\n", " The Qiskit SDK uses the LSb 0 bit numbering where the $n^{th}$ digit has value $1 \\ll n$ or $2^n$. Because we usually write numbers on paper with the most significant digits to the left and the least significant digits to the right (in the Hindu-Arabic system used in most of the world), this has the consequence that the bits are labeled with indices increasing from right to left. This LSb 0 convention makes mathematics easier and is the most commonly used for modern digital electronics, although the opposite convention MSb 0 is also found in some domains. Converting the $i^{th}$ index between LSb 0 and MSb 0 conventions on an $n$-bit register is as simple as $i \\rightarrow n-i-1$. This differs across authors and software packages, so be aware! For more details, see the [Bit-ordering in the Qiskit SDK](../build/bit-ordering) topic.\n", @@ -50,7 +51,7 @@ }, { "cell_type": "code", - "execution_count": 2, + "execution_count": 1, "id": "930ca3b6", "metadata": { "tags": [] @@ -58,12 +59,12 @@ "outputs": [ { "data": { - "image/png": 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+ "image/png": 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"text/plain": [ "
" ] }, - "execution_count": 2, + "execution_count": 1, "metadata": {}, "output_type": "execute_result" } @@ -104,12 +105,14 @@ "id": "f3ef4248-7938-44c1-85f1-edc997f0edcd", "metadata": {}, "source": [ - "The following code cell uses the `quantum_info` package to create six two-qubit Pauli operators. The ZZ operator means Z on qubit 0 and Z on qubit 1. If the state is entangled, then the correlation between qubit 0 and qubit 1 is one." + "The following code cell uses the `quantum_info` package to create six two-qubit Pauli operators. The ZZ operator is a shorthand for the tensor product $Z\\otimes Z$ which essentially means measuring Z on qubit 0 and Z on qubit 1 together and obtaining information about the correlation between qubit 0 and qubit 1. Expectation values like this are also typically written as $\\langle Z_0 Z_1 \\rangle$.\n", + "\n", + "If the state is entangled, then the measurement of $\\langle Z_0 Z_1 \\rangle$ should be equal to 1." ] }, { "cell_type": "code", - "execution_count": 3, + "execution_count": 19, "id": "c57b261c-b757-4432-beab-61b526c98a41", "metadata": { "tags": [] @@ -117,7 +120,17 @@ "outputs": [], "source": [ "# Set up six different observables.\n", - "observables_labels = [\"ZZ\", \"ZI\", \"IZ\", \"XX\", \"XI\"]\n", + "from qiskit.quantum_info import Pauli\n", + "\n", + "ZZ = Pauli('ZZ')\n", + "ZI = Pauli('ZI')\n", + "IZ = Pauli('IZ')\n", + "XX = Pauli('XX')\n", + "XI = Pauli('XI')\n", + "IX = Pauli('IX')\n", + "\n", + "observables = [IZ, IX, ZI, XI, ZZ, XX]\n", + "observables_labels = [\"IZ\", \"IX\", \"ZI\", \"XI\", \"ZZ\", \"XX\"]\n", "observables = [SparsePauliOp(label) for label in observables_labels]" ] }, @@ -150,18 +163,18 @@ }, { "cell_type": "code", - "execution_count": 5, + "execution_count": 20, "id": "9a901271", "metadata": {}, "outputs": [ { "data": { - "image/png": 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", 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", 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" ] }, - "execution_count": 5, + "execution_count": 20, "metadata": {}, "output_type": "execute_result" } @@ -171,9 +184,6 @@ "# service = QiskitRuntimeService(channel=\"ibm_quantum\", token=\"\")\n", "service = QiskitRuntimeService()\n", "\n", - "# Use the following code instead if you want to run on a simulator:\n", - "# from qiskit_ibm_runtime.fake_provider import FakeCairoV2\n", - "# backend = FakeCairoV2()\n", "\n", "# Run on the least-busy backend you have access to\n", "backend = service.least_busy(simulator=False, operational=True)\n", @@ -190,42 +200,101 @@ "id": "9acac1d4", "metadata": {}, "source": [ - "## Step 3. Execute using a quantum primitive function\n", + "## Step 3. Execute using the quantum primitives\n", "\n", "Quantum computers can produce random results, so you'll often want to collect a sample of the outputs by running the circuit many times. You can estimate the value of the observable using the `Estimator` class. `Estimator` is one of our two [primitives](../run/primitives-get-started); the other is `Sampler`, which can be used to get data from a quantum computer. These objects possess a `run()` method that executes the selection of circuits, observables, and parameters (if applicable), using what's known as a [primitive unified bloc (PUB)](../run/primitives#sampler-v2)." ] }, { "cell_type": "code", - "execution_count": 3, + "execution_count": 21, "id": "62c4ca44", "metadata": { "tags": [] }, "outputs": [ { - "name": "stderr", + "name": "stdout", "output_type": "stream", "text": [ - "qiskit_runtime_service.__init__:INFO:2024-03-11 20:15:06,834: Default instance: ibm-q-internal/deployed/default\n", - "base_primitive._run:INFO:2024-03-11 20:15:30,536: Submitting job using options {'options': {'default_shots': 5000}, 'version': 2, 'support_qiskit': True, 'resilience_level': 1}\n", - "qiskit_runtime_service.run:INFO:2024-03-11 20:15:30,537: Instance selected: ibm-q-internal/live-data/live-data-demo\n" + ">>> Job ID: crbfya9djmqg008kd5p0\n" ] } ], "source": [ "# Construct the Estimator instance we want to use.\n", + "from qiskit_ibm_runtime import EstimatorV2 as Estimator\n", "\n", - "estimator = Estimator(backend)\n", + "estimator = Estimator(backend=backend)\n", "estimator.options.resilience_level = 1\n", "estimator.options.default_shots = 5000\n", "\n", - "observables = [\n", + "mapped_observables = [\n", " observable.apply_layout(isa_circuit.layout) for observable in observables\n", "]\n", "\n", "# One pub, with one circuit to run against five different observables.\n", - "job = estimator.run([(isa_circuit, observables)])\n", + "job = estimator.run([(isa_circuit, mapped_observables)])\n", + "\n", + "# Use the job id in order to retrieve your job data at a later time\n", + "print(f\">>> Job ID: {job.job_id()}\")" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "792d2f01", + "metadata": {}, + "outputs": [], + "source": [ + "# This is the result of the entire submission. We submitted one Pub,\n", + "# so this contains one inner result (and some metadata of its own).\n", + "job_result = job.result()\n", + "\n", + "# This is the result from our single pub, which had five observables,\n", + "# so contains information on all five.\n", + "pub_result = job.result()[0]" + ] + }, + { + "cell_type": "markdown", + "id": "48317a25", + "metadata": {}, + "source": [ + "\n", + "\n", + "Often times you will find that jobs will sit in the queue for some time. If you'd like to quickly get results back for this small example circuit, use the code block provided below which utilizes the [`fake_provider`](../api/qiskit-ibm-runtime/fake_provider) submodule.\n", + "\n", + "" + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "id": "057f38f1", + "metadata": {}, + "outputs": [], + "source": [ + "# Use the following code instead if you want to run on a simulator:\n", + "\n", + "\n", + "from qiskit_ibm_runtime.fake_provider import FakeAlmadenV2\n", + "backend = FakeAlmadenV2()\n", + "\n", + "estimator = Estimator(backend)\n", + "\n", + "\n", + "# Convert to an ISA circuit and layout-mapped observables.\n", + "pm = generate_preset_pass_manager(backend=backend, optimization_level=1)\n", + "isa_circuit = pm.run(qc)\n", + "\n", + "mapped_observables = [\n", + " observable.apply_layout(isa_circuit.layout) for observable in observables\n", + "]\n", + "\n", + "job = estimator.run([(isa_circuit, mapped_observables)])\n", + "result = job.result()\n", + "\n", "\n", "# This is the result of the entire submission. We submitted one Pub,\n", "# so this contains one inner result (and some metadata of its own).\n", @@ -258,7 +327,7 @@ }, { "cell_type": "code", - "execution_count": 4, + "execution_count": 23, "id": "87143fcc", "metadata": { "tags": [] @@ -266,17 +335,7 @@ "outputs": [ { "data": { - "text/plain": [ - "" - ] - }, - "execution_count": 4, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "image/png": 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", + "image/png": 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", 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" ] @@ -290,12 +349,17 @@ "\n", "from matplotlib import pyplot as plt\n", "\n", - "data = observables_labels\n", "values = pub_result.data.evs\n", "\n", - "errors = pub_result.data.ensemble_standard_error\n", + "errors = pub_result.data.stds\n", + "\n", + "#plt.errorbar(observables_labels, values, yerr=errors, fmt=\"o\")\n", "\n", - "plt.errorbar(observables_labels, values, yerr=errors, fmt=\"o\")" + "# plotting graph\n", + "plt.plot(observables_labels, values, '-o')\n", + "plt.xlabel('Observables')\n", + "plt.ylabel('Values')\n", + "plt.show()" ] }, { @@ -306,6 +370,199 @@ "Here we see that for qubits 0 and 1, the independent values of both X and Z are 0, while the correlations are 1. This is a hallmark of quantum entanglement." ] }, + { + "cell_type": "markdown", + "id": "0bc582d8", + "metadata": {}, + "source": [ + "---\n", + "\n", + "# Scale to $n$-qubits\n", + "\n", + "In order to accomplish utility-scale work, we will need to scale up this simple circuit to use many more qubits. To begin thinking about how to accomplish this, we will create a 100-qubit Bell state and measure the observable . In the code blocks below, we'll follow the same steps in the Qiskit Patterns workflow and measure the expectation value $\\langle Z_0 Z_i $\\rangle for each qubit.\n", + "\n", + "## Step 1. Map the problem\n", + "\n", + "First we will prepare a function that will return a `QuantumCircuit` which prepares an $n$-qubit Bell state. We will then use this function to prepare a 100-qubit Bell state, and collect all the observables that we will plan to measure." + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "id": "2ac02692", + "metadata": {}, + "outputs": [], + "source": [ + "from qiskit import QuantumCircuit\n", + "\n", + "def get_qc_for_n_qubit_Bell_state(n: int) -> QuantumCircuit:\n", + " \"\"\"This function will create a qiskit.QuantumCircuit (qc) for an n-qubit Bell state.\n", + "\n", + " Args:\n", + " n (int): Number of qubits in the n-qubit Bell state\n", + "\n", + " Returns:\n", + " QuantumCircuit: Quantum circuit that generate the n-qubit Bell state, assuming all qubits start in the 0 state\n", + " \"\"\"\n", + " if isinstance(n, int) and n >= 2:\n", + " qc = QuantumCircuit(n)\n", + " qc.h(0)\n", + " for i in range(n-1):\n", + " qc.cx(i, i+1)\n", + " else:\n", + " raise Exception(\"n is not a valid input\")\n", + " return qc\n", + "\n", + "\n", + "from qiskit import QuantumCircuit\n", + "\n", + "# Create a new circuit with two qubits (first argument) and two classical\n", + "# bits (second argument)\n", + "n = 100\n", + "qc = get_qc_for_n_qubit_Bell_state(n)" + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "id": "863a4ec9", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "['ZZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'ZIZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'ZIIZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'ZIIIZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'ZIIIIZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'ZIIIIIZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 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'ZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZIIIIIIIIIII', 'ZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZIIIIIIIIII', 'ZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZIIIIIIIII', 'ZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZIIIIIIII', 'ZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZIIIIIII', 'ZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZIIIIII', 'ZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZIIIII', 'ZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZIIII', 'ZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZIII', 'ZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZII', 'ZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZI', 'ZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZ']\n", + "99\n" + ] + } + ], + "source": [ + "from qiskit.quantum_info import SparsePauliOp\n", + "\n", + "# ZZII...II, ZIZI...II, ... , ZIII...ZZ\n", + "operator_strings = ['Z' + 'I'*i + 'Z' + 'I'*(n-2-i) for i in range(n-1)]\n", + "print(operator_strings)\n", + "print(len(operator_strings))\n", + "\n", + "operators = [SparsePauliOp(operator) for operator in operator_strings]" + ] + }, + { + "cell_type": "markdown", + "id": "a0b462ce", + "metadata": {}, + "source": [ + "## Step 2. Optimize the problem for execution on quantum hardware\n", + "\n", + "We will next transpile this circuit and map the observables to the layout of the hardware." + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "id": "428f05e7", + "metadata": {}, + "outputs": [], + "source": [ + "from qiskit_ibm_runtime import QiskitRuntimeService\n", + "from qiskit.transpiler.preset_passmanagers import generate_preset_pass_manager\n", + "\n", + "backend_name = \"ibm_brisbane\"\n", + "backend = QiskitRuntimeService().get_backend(backend_name)\n", + "pm = generate_preset_pass_manager(optimization_level=1, backend=backend)\n", + "\n", + "qc_transpiled = pm.run(qc)\n", + "operators_transpiled_list = [op.apply_layout(qc_transpiled.layout) for op in operators]" + ] + }, + { + "cell_type": "markdown", + "id": "2d2b5065", + "metadata": {}, + "source": [ + "## Step 3. Execute on hardware\n", + "\n", + "Once the circuit and observables are prepared, we then submit the job and enable error suppression via [dynamical decoupling](../api/qiskit-ibm-runtime/qiskit_ibm_runtime.options.DynamicalDecouplingOptions)." + ] + }, + { + "cell_type": "code", + "execution_count": 27, + "id": "3aaa5025", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "crbgpcsdqdn000832tq0\n" + ] + } + ], + "source": [ + "from qiskit_ibm_runtime import QiskitRuntimeService, EstimatorOptions\n", + "from qiskit_ibm_runtime import EstimatorV2 as Estimator\n", + "\n", + "service = QiskitRuntimeService()\n", + "\n", + "# backend = service.get_backend('ibm_sherbrooke')\n", + "backend = service.get_backend('ibm_brisbane')\n", + "\n", + "options = EstimatorOptions()\n", + "options.resilience_level = 1\n", + "options.optimization_level = 0\n", + "options.dynamical_decoupling.enable = True\n", + "options.dynamical_decoupling.sequence_type = \"XY4\"\n", + "\n", + "# Create an Estimator object\n", + "estimator = Estimator(backend, options=options)\n", + "\n", + "# Submit the circuit to Estimator\n", + "job = estimator.run([(qc_transpiled, operators_transpiled_list)])\n", + "job_id = job.job_id()\n", + "print(job_id)" + ] + }, + { + "cell_type": "markdown", + "id": "0bc64091", + "metadata": {}, + "source": [ + "## Step 4. Post-process results\n", + "\n", + "Once the job has completed, we can plot the results and see that $\\langle Z_0 Z_i \\rangle$ decreases with increasing $i$, even though in an ideal simulation we should see that all $\\langle Z_0 Z_i \\rangle$ should be 1." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "de91ebd0", + "metadata": {}, + "outputs": [], + "source": [ + "import matplotlib.pyplot as plt\n", + "import numpy as np\n", + "from qiskit_ibm_runtime import QiskitRuntimeService\n", + "\n", + "service = QiskitRuntimeService()\n", + "job = service.job(job_id)\n", + "\n", + "# data\n", + "data = list(range(1, len(operators)+1))\n", + "result = job.result()[0] # Estimator V2\n", + "values = result.data.evs # Estimator V2\n", + "# values = job.result().values # EstimatorV1\n", + "values = [v / values[0] for v in values]\n", + "\n", + "# plotting graph\n", + "plt.scatter(data, values, marker='o', label='ibm_sherbrooke')\n", + "plt.xlabel('Distance between qubits $i$')\n", + "plt.ylabel(r'$\\langle Z_0 Z_i \\rangle / \\langle Z_0 Z_1 \\rangle $')\n", + "plt.legend()\n", + "plt.show()" + ] + }, { "cell_type": "markdown", "id": "e7c24c81", diff --git a/public/images/start/qiskit-patterns.png b/public/images/start/qiskit-patterns.png new file mode 100644 index 0000000000000000000000000000000000000000..149956b267597f0cb989240691e04a535def2b9e GIT binary patch literal 242605 zcmY(qWmFtb@HI?;KyY^p65QPhut?D04j}|sB)Gc-w-78492S@01QvG)?zUKPS$xsm zH;?^)dCz?4GjqDtF?0&v6@Pyv4`rGbhp8c}IX`{pn)dgXU%cXWJB3oUpkXkxMF#<$= z(y1+{6KxBrwlQ|jg3f$C8zpx0v^_>x94nX{l}J>u zBAJz!n0QV~?f>}+Gk>NRm=uHQr+sB*Vgd(~upD7$O28n#T~)y~Hx@@N(ocLEIKi>| z=t0Rqu?v`a$Mt@mSI}$xSE$ILZ~u40B8Mns`R6|L?WP5;Z1jH}{`Nc1BKQ*hf4cwQ zQMDA)4uL%@I-8$zQEIPSQwkS+4Wi8joYbY@Bb|uDIpc}3tI<2V#e2J4ESamIr_|#v z)7q#_41#~&t3&?@@ITY|U+?u9_o1L5C|x2c8dWP(qF|%DN%64=+L>?r9d-o1Xkl4U zdpP_lsiDEExog*C95Ps$cPSVgh^FA#vBhiR|J|oin-%olxWJ>ISN+h#m{mx_z~@&c zTHlt-`rWY&ed>3=t1QZO@!f)-y0w>~X( 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Mon Sep 17 00:00:00 2001 From: Kaelyn Ferris Date: Wed, 10 Apr 2024 18:26:10 -0400 Subject: [PATCH 02/25] Add qiskit patterns image --- docs/start/hello-world.ipynb | 2 ++ .../start/hello-world/qiskit-patterns.png | Bin 0 -> 2213705 bytes public/images/start/qiskit-patterns.png | Bin 242605 -> 0 bytes 3 files changed, 2 insertions(+) create mode 100644 public/images/start/hello-world/qiskit-patterns.png delete mode 100644 public/images/start/qiskit-patterns.png diff --git a/docs/start/hello-world.ipynb b/docs/start/hello-world.ipynb index e0958754880..b3b36fe92e0 100644 --- a/docs/start/hello-world.ipynb +++ b/docs/start/hello-world.ipynb @@ -23,6 +23,8 @@ "\n", "4. Analyze the results\n", "\n", + "![Qiskit patterns](/images/start/hello-world/qiskit-patterns.png)\n", + "\n", "\n", "## Step 1. 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2001 From: Kaelyn Ferris <43348706+kaelynj@users.noreply.github.com> Date: Thu, 11 Apr 2024 09:50:04 -0400 Subject: [PATCH 03/25] Update docs/start/hello-world.ipynb Co-authored-by: Frank Harkins --- docs/start/hello-world.ipynb | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/docs/start/hello-world.ipynb b/docs/start/hello-world.ipynb index b3b36fe92e0..bc7a2be4e49 100644 --- a/docs/start/hello-world.ipynb +++ b/docs/start/hello-world.ipynb @@ -381,7 +381,7 @@ "\n", "# Scale to $n$-qubits\n", "\n", - "In order to accomplish utility-scale work, we will need to scale up this simple circuit to use many more qubits. To begin thinking about how to accomplish this, we will create a 100-qubit Bell state and measure the observable . In the code blocks below, we'll follow the same steps in the Qiskit Patterns workflow and measure the expectation value $\\langle Z_0 Z_i $\\rangle for each qubit.\n", + "In order to accomplish utility-scale work, we will need to scale up this simple circuit to use many more qubits. To begin thinking about how to accomplish this, we will create a 100-qubit Bell state and measure the observable . In the following code, we'll follow the same steps in the Qiskit Patterns workflow and measure the expectation value $\\langle Z_0 Z_i \\rangle $ for each qubit.\n", "\n", "## Step 1. Map the problem\n", "\n", From a6513715b54c1a2a9f6e2b58811b3a2acaf0ba8b Mon Sep 17 00:00:00 2001 From: Kaelyn Ferris <43348706+kaelynj@users.noreply.github.com> Date: Thu, 11 Apr 2024 09:50:10 -0400 Subject: [PATCH 04/25] Update docs/start/hello-world.ipynb Co-authored-by: Frank Harkins --- docs/start/hello-world.ipynb | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/docs/start/hello-world.ipynb b/docs/start/hello-world.ipynb index bc7a2be4e49..ec33ff2eceb 100644 --- a/docs/start/hello-world.ipynb +++ b/docs/start/hello-world.ipynb @@ -379,7 +379,7 @@ "source": [ "---\n", "\n", - "# Scale to $n$-qubits\n", + "# Scale to large numbers of qubits\n", "\n", "In order to accomplish utility-scale work, we will need to scale up this simple circuit to use many more qubits. To begin thinking about how to accomplish this, we will create a 100-qubit Bell state and measure the observable . In the following code, we'll follow the same steps in the Qiskit Patterns workflow and measure the expectation value $\\langle Z_0 Z_i \\rangle $ for each qubit.\n", "\n", From 15616bd3568f8750b836821f602accd571bcf1ae Mon Sep 17 00:00:00 2001 From: Kaelyn Ferris Date: Thu, 11 Apr 2024 16:09:21 -0400 Subject: [PATCH 05/25] Update section on executing with a simulator --- docs/start/hello-world.ipynb | 39 ++++++++++++++++++------------------ 1 file changed, 20 insertions(+), 19 deletions(-) diff --git a/docs/start/hello-world.ipynb b/docs/start/hello-world.ipynb index ec33ff2eceb..efd8afe5710 100644 --- a/docs/start/hello-world.ipynb +++ b/docs/start/hello-world.ipynb @@ -242,6 +242,16 @@ "print(f\">>> Job ID: {job.job_id()}\")" ] }, + { + "cell_type": "markdown", + "id": "47479e76", + "metadata": {}, + "source": [ + "Once a job is submitted, you can wait until either the job is completed within your current python instance, or use the `job_id` in order to retrieve the data at a later time. (See the [section on retrieving jobs](../run/monitor-job#retrieve-job-results-at-a-later-time) for more info)\n", + "\n", + "Once a job is completed, we can examine its output through the job's `result()` attribute shown below." + ] + }, { "cell_type": "code", "execution_count": null, @@ -263,20 +273,11 @@ "id": "48317a25", "metadata": {}, "source": [ - "\n", + "\n", "\n", "Often times you will find that jobs will sit in the queue for some time. If you'd like to quickly get results back for this small example circuit, use the code block provided below which utilizes the [`fake_provider`](../api/qiskit-ibm-runtime/fake_provider) submodule.\n", "\n", - "" - ] - }, - { - "cell_type": "code", - "execution_count": 22, - "id": "057f38f1", - "metadata": {}, - "outputs": [], - "source": [ + "```python\n", "# Use the following code instead if you want to run on a simulator:\n", "\n", "\n", @@ -304,7 +305,9 @@ "\n", "# This is the result from our single pub, which had five observables,\n", "# so contains information on all five.\n", - "pub_result = job.result()[0]" + "pub_result = job.result()[0]\n", + "```\n", + "" ] }, { @@ -355,8 +358,6 @@ "\n", "errors = pub_result.data.stds\n", "\n", - "#plt.errorbar(observables_labels, values, yerr=errors, fmt=\"o\")\n", - "\n", "# plotting graph\n", "plt.plot(observables_labels, values, '-o')\n", "plt.xlabel('Observables')\n", @@ -379,11 +380,11 @@ "source": [ "---\n", "\n", - "# Scale to large numbers of qubits\n", + "## Scale to large numbers of qubits\n", "\n", "In order to accomplish utility-scale work, we will need to scale up this simple circuit to use many more qubits. To begin thinking about how to accomplish this, we will create a 100-qubit Bell state and measure the observable . In the following code, we'll follow the same steps in the Qiskit Patterns workflow and measure the expectation value $\\langle Z_0 Z_i \\rangle $ for each qubit.\n", "\n", - "## Step 1. Map the problem\n", + "### Step 1. Map the problem\n", "\n", "First we will prepare a function that will return a `QuantumCircuit` which prepares an $n$-qubit Bell state. We will then use this function to prepare a 100-qubit Bell state, and collect all the observables that we will plan to measure." ] @@ -455,7 +456,7 @@ "id": "a0b462ce", "metadata": {}, "source": [ - "## Step 2. Optimize the problem for execution on quantum hardware\n", + "### Step 2. Optimize the problem for execution on quantum hardware\n", "\n", "We will next transpile this circuit and map the observables to the layout of the hardware." ] @@ -483,7 +484,7 @@ "id": "2d2b5065", "metadata": {}, "source": [ - "## Step 3. Execute on hardware\n", + "### Step 3. Execute on hardware\n", "\n", "Once the circuit and observables are prepared, we then submit the job and enable error suppression via [dynamical decoupling](../api/qiskit-ibm-runtime/qiskit_ibm_runtime.options.DynamicalDecouplingOptions)." ] @@ -531,7 +532,7 @@ "id": "0bc64091", "metadata": {}, "source": [ - "## Step 4. Post-process results\n", + "### Step 4. Post-process results\n", "\n", "Once the job has completed, we can plot the results and see that $\\langle Z_0 Z_i \\rangle$ decreases with increasing $i$, even though in an ideal simulation we should see that all $\\langle Z_0 Z_i \\rangle$ should be 1." ] From 92672629b8fe6b86516206ec2a2f05548ab41ba0 Mon Sep 17 00:00:00 2001 From: Kaelyn Ferris Date: Wed, 17 Apr 2024 17:36:14 -0400 Subject: [PATCH 06/25] Improve pedagogy page --- docs/start/hello-world.ipynb | 63 +++++++++++++++++------------------- 1 file changed, 30 insertions(+), 33 deletions(-) diff --git a/docs/start/hello-world.ipynb b/docs/start/hello-world.ipynb index efd8afe5710..0db7c257c26 100644 --- a/docs/start/hello-world.ipynb +++ b/docs/start/hello-world.ipynb @@ -7,9 +7,12 @@ "source": [ "# Hello world\n", "\n", - "This Hello world example creates a simple quantum program and runs it on a quantum system. Begin with following the [Install and set up](install) instructions if you haven't already, including the steps to [Set up to use IBM Quantum™ Platform](setup-channel#set-up-to-use-ibm-quantum-platform).\n", + "This Hello world example comes in two parts: creating a simple quantum program and running it on a quantum system followed by a demonstration of how to scale it up to a utility level program (found in the section titled [Scale to large numbers of qubits](#scale-to-large-numbers-of-qubits)).\n", + "\n", + " First, begin by following the [Install and set up](install) instructions if you haven't already, including the steps to [Set up to use IBM Quantum™ Platform](setup-channel#set-up-to-use-ibm-quantum-platform).\n", + "\n", + "We recommend that you use the [Jupyter](https://jupyter.org/install) development environment to interact with quantum computers. Be sure to install the recommended extra visualization support (`pip install qiskit[visualization]`), and note that zsh users need to put `'qiskit[visualization]'` in single quotes. You'll also need the `matplotlib` package for the second part of this example.\n", "\n", - "We recommend that you use the [Jupyter](https://jupyter.org/install) development environment to interact with quantum computers. Be sure to install the recommended extra visualization support (`pip install qiskit[visualization]`), and note that zsh users need to put `'qiskit[visualization]'` in single quotes.\n", "\n", "To learn about quantum computing in general, check out the [Basics of quantum information course](https://learning.quantum.ibm.com/course/basics-of-quantum-information) in IBM Quantum Learning.\n", "\n", @@ -23,10 +26,8 @@ "\n", "4. Analyze the results\n", "\n", - "![Qiskit patterns](/images/start/hello-world/qiskit-patterns.png)\n", "\n", - "\n", - "## Step 1. Map the problem to a quantum-native format" + "\n" ] }, { @@ -36,6 +37,8 @@ "raw_mimetype": "text/restructuredtext" }, "source": [ + "## Step 1. Map the problem to a quantum-native format\n", + "\n", "In a quantum program, *quantum circuits* are the native format in which to represent quantum instructions, and *operators* represent the observables to be measured. When creating a circuit, you'll usually create a new [`QuantumCircuit`](/api/qiskit/qiskit.circuit.QuantumCircuit#quantumcircuit) object, then add instructions to it in sequence." ] }, @@ -99,7 +102,9 @@ "raw_mimetype": "text/restructuredtext" }, "source": [ - "See [`QuantumCircuit`](/api/qiskit/qiskit.circuit.QuantumCircuit#quantumcircuit) in the documentation for all available operations." + "See [`QuantumCircuit`](/api/qiskit/qiskit.circuit.QuantumCircuit#quantumcircuit) in the documentation for all available operations.\n", + "\n", + "---" ] }, { @@ -107,9 +112,9 @@ "id": "f3ef4248-7938-44c1-85f1-edc997f0edcd", "metadata": {}, "source": [ - "The following code cell uses the `quantum_info` package to create six two-qubit Pauli operators. The ZZ operator is a shorthand for the tensor product $Z\\otimes Z$ which essentially means measuring Z on qubit 0 and Z on qubit 1 together and obtaining information about the correlation between qubit 0 and qubit 1. Expectation values like this are also typically written as $\\langle Z_0 Z_1 \\rangle$.\n", + "While creating quantum circuits, we also must consider what type of data we want to get back after execution, and there are are two ways to do so within Qiskit. You can either obtain a probability distribution for a set of qubits you choose to measure, or obtain the expectation value of an observable. Preparing your workload to measure your circuit in one of these two ways is done through the [Qiskit primitives](../run/primitives-get-started) (explained in detail in [Step 3](#step-3-execute-using-the-quantum-primitives) of this page).\n", "\n", - "If the state is entangled, then the measurement of $\\langle Z_0 Z_1 \\rangle$ should be equal to 1." + "For this example, we will be measuring some expectation values using the `qiskit.quantum_info` submodule which will be specified using operators (these are mathematical objects used to represent an action or process which changes a quantum state). The following code cell creates six two-qubit Pauli operators: `IZ`, `IX`, `ZI`, `XI`, `ZZ`, and `XX`. \n" ] }, { @@ -138,18 +143,16 @@ }, { "cell_type": "markdown", - "id": "674b4019", + "id": "47150779", "metadata": {}, "source": [ - "\n", - " To ensure faster and more efficient results, as of 1 March 2024, circuits and observables need to be transformed to only use instructions supported by the system (referred to as *instruction set architecture (ISA)* circuits and observables) before being submitted to the Qiskit Runtime primitives. See the [transpilation documentation](../transpile) for instructions to transform circuits. Due to this change, the primitives will no longer perform layout or routing operations. Consequently, transpilation options referring to those tasks will no longer have any effect. By default, all primitives except Sampler V2 still optimize the input circuits. To bypass all optimization, set `optimization_level=0`.\n", "\n", - "*Exception*: When you initialize the Qiskit Runtime Service with the Q-CTRL channel strategy (example below), abstract circuits are still supported.\n", + "\n", + "\n", + "Here, something like the `ZZ` operator is a shorthand for the tensor product $Z\\otimes Z$ which essentially means measuring Z on qubit 0 and Z on qubit 1 together and obtaining information about the correlation between qubit 0 and qubit 1. Expectation values like this are also typically written as $\\langle Z_0 Z_1 \\rangle$.\n", + "\n", + "If the state is entangled, then the measurement of $\\langle Z_0 Z_1 \\rangle$ should be equal to 1.\n", "\n", - "> ``` python\n", - "> service = QiskitRuntimeService(channel=\"ibm_cloud\", channel_strategy=\"q-ctrl\")\n", - "> ```\n", - ">\n", "" ] }, @@ -160,7 +163,9 @@ "source": [ "## Step 2. Optimize the circuits and operators\n", "\n", - "Even though the circuit and operators for this example are quite simple, we still need to convert its instructions into those of a backend device's [Instruction Set Architecture (ISA)](../transpile/#instruction-set-architecture). This ensures the circuit complies with the constraints of a device (namely its native basis gates and qubit connectivity)." + "When executing circuits on a device, it is an important step to optimize the set of instructions which the circuit contains and work to minimize the overall depth (roughly the number of instructions) of the circuit. This ensures that you obtain the best results possible by reducing the effects of error and noise. Additionally, the circuit's instructions must conform to a backend device's [Instruction Set Architecture (ISA)](../transpile/#instruction-set-architecture) and takes both the device's basis gates as well as its qubit connectivity into account. \n", + "\n", + "The code snippet below will instantiate a real device to submit a job to and transform the circuit to match that backend's ISA." ] }, { @@ -204,7 +209,7 @@ "source": [ "## Step 3. Execute using the quantum primitives\n", "\n", - "Quantum computers can produce random results, so you'll often want to collect a sample of the outputs by running the circuit many times. You can estimate the value of the observable using the `Estimator` class. `Estimator` is one of our two [primitives](../run/primitives-get-started); the other is `Sampler`, which can be used to get data from a quantum computer. These objects possess a `run()` method that executes the selection of circuits, observables, and parameters (if applicable), using what's known as a [primitive unified bloc (PUB)](../run/primitives#sampler-v2)." + "Quantum computers can produce random results, so you'll often want to collect a sample of the outputs by running the circuit many times. You can estimate the value of the observable using the `Estimator` class. `Estimator` is one of two [primitives](../run/primitives-get-started); the other is `Sampler`, which can be used to get data from a quantum computer. These objects possess a `run()` method that executes the selection of circuits, observables, and parameters (if applicable), using what's known as a [primitive unified bloc (PUB)](../run/primitives#sampler-v2)." ] }, { @@ -275,7 +280,7 @@ "source": [ "\n", "\n", - "Often times you will find that jobs will sit in the queue for some time. If you'd like to quickly get results back for this small example circuit, use the code block provided below which utilizes the [`fake_provider`](../api/qiskit-ibm-runtime/fake_provider) submodule.\n", + "When running your quantum program on a real device your workload must wait in a queue before it is run. If you would like to save some time with this example, you can instead use the following code to run this small workload on a local simulator (using the [`fake_provider`](../api/qiskit-ibm-runtime/fake_provider)). Bear in mind this will only work for this small circuit, but when you scale up in the next section you will need to use a real device.\n", "\n", "```python\n", "# Use the following code instead if you want to run on a simulator:\n", @@ -310,24 +315,16 @@ "" ] }, - { - "cell_type": "markdown", - "id": "0d5ea9a0", - "metadata": {}, - "source": [ - "## Step 4. Analyze the results" - ] - }, { "cell_type": "markdown", "id": "d200d1f8", "metadata": {}, "source": [ - "\n", - " You might need to run `pip install matplotlib` if you do not already have it installed.\n", - "\n", + "## Step 4. Analyze the results\n", "\n", - "The `values` property is a list of expectation values for each of the observables we provided." + "The analyze step is typically where you might postprocess your results using something like measurement error mitigation or zero noise extrapolation. You might feed these results into another workflow for further analysis or prepare a plot of the key values and data. In general this will be specific to your problem and so for this example,we'll simply plot each of the expectation values that were measured for our circuit. \n", + "\n", + "The expectation values and standard deviations for the observables you specified are accessed through the `PubResult.data.evs` and `PubResult.data.stds` attributes of the job results. To obtain the results from the sampler, use the `PubResult.data.meas.get_counts()` function which will return a `dict` of measurements in the form of bitstrings as keys and counts as their corresponding values." ] }, { @@ -370,7 +367,7 @@ "id": "e6a9ba84", "metadata": {}, "source": [ - "Here we see that for qubits 0 and 1, the independent values of both X and Z are 0, while the correlations are 1. This is a hallmark of quantum entanglement." + "Here we see that for qubits 0 and 1, the independent expectation values of both X and Z are 0, while the correlations (`XX` and `ZZ`) are 1. This is a hallmark of quantum entanglement." ] }, { @@ -378,7 +375,7 @@ "id": "0bc582d8", "metadata": {}, "source": [ - "---\n", + "\n", "\n", "## Scale to large numbers of qubits\n", "\n", From e7f93d8bb9afa983733cb634412f39854d4b5233 Mon Sep 17 00:00:00 2001 From: Kaelyn Ferris Date: Wed, 17 Apr 2024 17:39:26 -0400 Subject: [PATCH 07/25] Lint notebook --- docs/start/hello-world.ipynb | 14 ++++---------- 1 file changed, 4 insertions(+), 10 deletions(-) diff --git a/docs/start/hello-world.ipynb b/docs/start/hello-world.ipynb index 0db7c257c26..25132e1c666 100644 --- a/docs/start/hello-world.ipynb +++ b/docs/start/hello-world.ipynb @@ -24,10 +24,7 @@ "\n", "3. Execute using a quantum primitive function\n", "\n", - "4. Analyze the results\n", - "\n", - "\n", - "\n" + "4. Analyze the results" ] }, { @@ -114,7 +111,7 @@ "source": [ "While creating quantum circuits, we also must consider what type of data we want to get back after execution, and there are are two ways to do so within Qiskit. You can either obtain a probability distribution for a set of qubits you choose to measure, or obtain the expectation value of an observable. Preparing your workload to measure your circuit in one of these two ways is done through the [Qiskit primitives](../run/primitives-get-started) (explained in detail in [Step 3](#step-3-execute-using-the-quantum-primitives) of this page).\n", "\n", - "For this example, we will be measuring some expectation values using the `qiskit.quantum_info` submodule which will be specified using operators (these are mathematical objects used to represent an action or process which changes a quantum state). The following code cell creates six two-qubit Pauli operators: `IZ`, `IX`, `ZI`, `XI`, `ZZ`, and `XX`. \n" + "For this example, we will be measuring some expectation values using the `qiskit.quantum_info` submodule which will be specified using operators (these are mathematical objects used to represent an action or process which changes a quantum state). The following code cell creates six two-qubit Pauli operators: `IZ`, `IX`, `ZI`, `XI`, `ZZ`, and `XX`." ] }, { @@ -146,7 +143,6 @@ "id": "47150779", "metadata": {}, "source": [ - "\n", "\n", "\n", "Here, something like the `ZZ` operator is a shorthand for the tensor product $Z\\otimes Z$ which essentially means measuring Z on qubit 0 and Z on qubit 1 together and obtaining information about the correlation between qubit 0 and qubit 1. Expectation values like this are also typically written as $\\langle Z_0 Z_1 \\rangle$.\n", @@ -163,7 +159,7 @@ "source": [ "## Step 2. Optimize the circuits and operators\n", "\n", - "When executing circuits on a device, it is an important step to optimize the set of instructions which the circuit contains and work to minimize the overall depth (roughly the number of instructions) of the circuit. This ensures that you obtain the best results possible by reducing the effects of error and noise. Additionally, the circuit's instructions must conform to a backend device's [Instruction Set Architecture (ISA)](../transpile/#instruction-set-architecture) and takes both the device's basis gates as well as its qubit connectivity into account. \n", + "When executing circuits on a device, it is an important step to optimize the set of instructions which the circuit contains and work to minimize the overall depth (roughly the number of instructions) of the circuit. This ensures that you obtain the best results possible by reducing the effects of error and noise. Additionally, the circuit's instructions must conform to a backend device's [Instruction Set Architecture (ISA)](../transpile/#instruction-set-architecture) and takes both the device's basis gates as well as its qubit connectivity into account.\n", "\n", "The code snippet below will instantiate a real device to submit a job to and transform the circuit to match that backend's ISA." ] @@ -322,7 +318,7 @@ "source": [ "## Step 4. Analyze the results\n", "\n", - "The analyze step is typically where you might postprocess your results using something like measurement error mitigation or zero noise extrapolation. You might feed these results into another workflow for further analysis or prepare a plot of the key values and data. In general this will be specific to your problem and so for this example,we'll simply plot each of the expectation values that were measured for our circuit. \n", + "The analyze step is typically where you might postprocess your results using something like measurement error mitigation or zero noise extrapolation. You might feed these results into another workflow for further analysis or prepare a plot of the key values and data. In general this will be specific to your problem and so for this example,we'll simply plot each of the expectation values that were measured for our circuit.\n", "\n", "The expectation values and standard deviations for the observables you specified are accessed through the `PubResult.data.evs` and `PubResult.data.stds` attributes of the job results. To obtain the results from the sampler, use the `PubResult.data.meas.get_counts()` function which will return a `dict` of measurements in the form of bitstrings as keys and counts as their corresponding values." ] @@ -375,8 +371,6 @@ "id": "0bc582d8", "metadata": {}, "source": [ - "\n", - "\n", "## Scale to large numbers of qubits\n", "\n", "In order to accomplish utility-scale work, we will need to scale up this simple circuit to use many more qubits. To begin thinking about how to accomplish this, we will create a 100-qubit Bell state and measure the observable . In the following code, we'll follow the same steps in the Qiskit Patterns workflow and measure the expectation value $\\langle Z_0 Z_i \\rangle $ for each qubit.\n", From 2aeb5c9d11eedc6f28e307a3e03b9dd5ec973fcb Mon Sep 17 00:00:00 2001 From: Rebecca Dimock Date: Mon, 22 Apr 2024 15:47:51 -0500 Subject: [PATCH 08/25] Add video and some more explanations --- docs/start/hello-world.ipynb | 50 +++++++++++++++++++++++++++--------- 1 file changed, 38 insertions(+), 12 deletions(-) diff --git a/docs/start/hello-world.ipynb b/docs/start/hello-world.ipynb index 25132e1c666..0f3bf77e414 100644 --- a/docs/start/hello-world.ipynb +++ b/docs/start/hello-world.ipynb @@ -7,9 +7,28 @@ "source": [ "# Hello world\n", "\n", - "This Hello world example comes in two parts: creating a simple quantum program and running it on a quantum system followed by a demonstration of how to scale it up to a utility level program (found in the section titled [Scale to large numbers of qubits](#scale-to-large-numbers-of-qubits)).\n", + "This example contains two parts: you will first create a simple quantum program and run it on a quantum system. Because actual quantum research requires much more robust programs, in the [Scale to large numbers of qubits](#scale-to-large-numbers-of-qubits) section, you will scale the simple program up to utility level. You can also watch this Hello World in practice in the Hello World episode of the Coding with Qiskit video series. " + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "7973a948", + "metadata": {}, + "outputs": [], + "source": [ + "%%html\n", + "" + ] + }, + { + "cell_type": "markdown", + "id": "7b65f7e0", + "metadata": {}, + "source": [ + "## Before you begin\n", "\n", - " First, begin by following the [Install and set up](install) instructions if you haven't already, including the steps to [Set up to use IBM Quantum™ Platform](setup-channel#set-up-to-use-ibm-quantum-platform).\n", + "Follow the [Install and set up](install) instructions if you haven't already, including the steps to [Set up to use IBM Quantum™ Platform](setup-channel#set-up-to-use-ibm-quantum-platform).\n", "\n", "We recommend that you use the [Jupyter](https://jupyter.org/install) development environment to interact with quantum computers. Be sure to install the recommended extra visualization support (`pip install qiskit[visualization]`), and note that zsh users need to put `'qiskit[visualization]'` in single quotes. You'll also need the `matplotlib` package for the second part of this example.\n", "\n", @@ -27,6 +46,14 @@ "4. Analyze the results" ] }, + { + "cell_type": "markdown", + "id": "80471a0a", + "metadata": {}, + "source": [ + "## Create and run a simple quantum program" + ] + }, { "cell_type": "markdown", "id": "85fe979e", @@ -34,7 +61,7 @@ "raw_mimetype": "text/restructuredtext" }, "source": [ - "## Step 1. Map the problem to a quantum-native format\n", + "### Step 1. Map the problem to a quantum-native format\n", "\n", "In a quantum program, *quantum circuits* are the native format in which to represent quantum instructions, and *operators* represent the observables to be measured. When creating a circuit, you'll usually create a new [`QuantumCircuit`](/api/qiskit/qiskit.circuit.QuantumCircuit#quantumcircuit) object, then add instructions to it in sequence." ] @@ -157,7 +184,7 @@ "id": "83bf9151-3bc9-40d2-8615-31570238b08e", "metadata": {}, "source": [ - "## Step 2. Optimize the circuits and operators\n", + "### Step 2. Optimize the circuits and operators\n", "\n", "When executing circuits on a device, it is an important step to optimize the set of instructions which the circuit contains and work to minimize the overall depth (roughly the number of instructions) of the circuit. This ensures that you obtain the best results possible by reducing the effects of error and noise. Additionally, the circuit's instructions must conform to a backend device's [Instruction Set Architecture (ISA)](../transpile/#instruction-set-architecture) and takes both the device's basis gates as well as its qubit connectivity into account.\n", "\n", @@ -203,7 +230,7 @@ "id": "9acac1d4", "metadata": {}, "source": [ - "## Step 3. Execute using the quantum primitives\n", + "### Step 3. Execute using the quantum primitives\n", "\n", "Quantum computers can produce random results, so you'll often want to collect a sample of the outputs by running the circuit many times. You can estimate the value of the observable using the `Estimator` class. `Estimator` is one of two [primitives](../run/primitives-get-started); the other is `Sampler`, which can be used to get data from a quantum computer. These objects possess a `run()` method that executes the selection of circuits, observables, and parameters (if applicable), using what's known as a [primitive unified bloc (PUB)](../run/primitives#sampler-v2)." ] @@ -316,7 +343,7 @@ "id": "d200d1f8", "metadata": {}, "source": [ - "## Step 4. Analyze the results\n", + "### Step 4. Analyze the results\n", "\n", "The analyze step is typically where you might postprocess your results using something like measurement error mitigation or zero noise extrapolation. You might feed these results into another workflow for further analysis or prepare a plot of the key values and data. In general this will be specific to your problem and so for this example,we'll simply plot each of the expectation values that were measured for our circuit.\n", "\n", @@ -373,11 +400,11 @@ "source": [ "## Scale to large numbers of qubits\n", "\n", - "In order to accomplish utility-scale work, we will need to scale up this simple circuit to use many more qubits. To begin thinking about how to accomplish this, we will create a 100-qubit Bell state and measure the observable . In the following code, we'll follow the same steps in the Qiskit Patterns workflow and measure the expectation value $\\langle Z_0 Z_i \\rangle $ for each qubit.\n", + "In quantum computing, utility-scale work is crucial for making progress in the field. Such work requires computations to be done on a much larger scale; working with circuits that might use over 100 qubits and over 1000 gates. This example demonstrates how you can accomplish utility-scale work on IBM Quantum systems by working with a 100-qubit Bell state. It uses the Qiskit Patterns workflow and ends by measuring the expectation value $\\langle Z_0 Z_i \\rangle $ for each qubit.\n", "\n", "### Step 1. Map the problem\n", "\n", - "First we will prepare a function that will return a `QuantumCircuit` which prepares an $n$-qubit Bell state. We will then use this function to prepare a 100-qubit Bell state, and collect all the observables that we will plan to measure." + "Write a function that returns a `QuantumCircuit` that prepares an $n$-qubit Bell state then use that function to prepare a 100-qubit Bell state and collect the observables to be measured." ] }, { @@ -449,7 +476,7 @@ "source": [ "### Step 2. Optimize the problem for execution on quantum hardware\n", "\n", - "We will next transpile this circuit and map the observables to the layout of the hardware." + "Transpile this circuit and map the observables to the hardware's layout." ] }, { @@ -477,7 +504,7 @@ "source": [ "### Step 3. Execute on hardware\n", "\n", - "Once the circuit and observables are prepared, we then submit the job and enable error suppression via [dynamical decoupling](../api/qiskit-ibm-runtime/qiskit_ibm_runtime.options.DynamicalDecouplingOptions)." + "Submit the job and enable error suppression by using a technique to reduce errors called [dynamical decoupling.](../api/qiskit-ibm-runtime/qiskit_ibm_runtime.options.DynamicalDecouplingOptions) " ] }, { @@ -525,7 +552,7 @@ "source": [ "### Step 4. Post-process results\n", "\n", - "Once the job has completed, we can plot the results and see that $\\langle Z_0 Z_i \\rangle$ decreases with increasing $i$, even though in an ideal simulation we should see that all $\\langle Z_0 Z_i \\rangle$ should be 1." + "After the job has completed, we can plot the results and see that $\\langle Z_0 Z_i \\rangle$ decreases with increasing $i$, even though in an ideal simulation we should see that all $\\langle Z_0 Z_i \\rangle$ should be 1." ] }, { @@ -566,7 +593,6 @@ "\n", "\n", " * Learn how to [build circuits](../build/) in more detail.\n", - "\n", " * Try one of the [workflow example tutorials.](https://learning.quantum.ibm.com/catalog/tutorials?category=workflow-example)\n", "" ] From c0b7fc427b75ce11b1b6fa0e2b35047e7b1cd1bc Mon Sep 17 00:00:00 2001 From: Rebecca Dimock Date: Mon, 22 Apr 2024 17:55:24 -0500 Subject: [PATCH 09/25] add some more explanation and links --- docs/start/hello-world.ipynb | 36 ++++++++++++++++++++++++++---------- 1 file changed, 26 insertions(+), 10 deletions(-) diff --git a/docs/start/hello-world.ipynb b/docs/start/hello-world.ipynb index 0f3bf77e414..89b01912f0d 100644 --- a/docs/start/hello-world.ipynb +++ b/docs/start/hello-world.ipynb @@ -7,7 +7,7 @@ "source": [ "# Hello world\n", "\n", - "This example contains two parts: you will first create a simple quantum program and run it on a quantum system. Because actual quantum research requires much more robust programs, in the [Scale to large numbers of qubits](#scale-to-large-numbers-of-qubits) section, you will scale the simple program up to utility level. You can also watch this Hello World in practice in the Hello World episode of the Coding with Qiskit video series. " + "This example contains two parts: you will first create a simple quantum program and run it on a quantum system. Because actual quantum research requires much more robust programs, in the [Scale to large numbers of qubits](#scale-to-large-numbers-of-qubits) section, you will scale the simple program up to utility level. You can also watch this Hello World in practice in the Hello World episode of the Coding with Qiskit 1.0 video series. " ] }, { @@ -188,7 +188,7 @@ "\n", "When executing circuits on a device, it is an important step to optimize the set of instructions which the circuit contains and work to minimize the overall depth (roughly the number of instructions) of the circuit. This ensures that you obtain the best results possible by reducing the effects of error and noise. Additionally, the circuit's instructions must conform to a backend device's [Instruction Set Architecture (ISA)](../transpile/#instruction-set-architecture) and takes both the device's basis gates as well as its qubit connectivity into account.\n", "\n", - "The code snippet below will instantiate a real device to submit a job to and transform the circuit to match that backend's ISA." + "The following code instantiates a real device to submit a job to and transform the circuit to match that backend's ISA." ] }, { @@ -443,6 +443,14 @@ "qc = get_qc_for_n_qubit_Bell_state(n)" ] }, + { + "cell_type": "markdown", + "id": "5b3d0d74", + "metadata": {}, + "source": [ + "Next, map to the operators of interest. This example uses the `ZZ` operators between qubits to examine the behavior as they get farther apart. Increasingly inaccurate (corrupted) expectation values between distant qubits would reveal the level of noise on the system. The `ZZ` operator between the 0th and 1st qubit should be the largest, and the `ZZ` operator between the 0th qubit and the 100th qubit should be the smallest." + ] + }, { "cell_type": "code", "execution_count": 25, @@ -476,7 +484,7 @@ "source": [ "### Step 2. Optimize the problem for execution on quantum hardware\n", "\n", - "Transpile this circuit and map the observables to the hardware's layout." + "Transpile this circuit and map the observables to the hardware's layout (ISA). " ] }, { @@ -504,7 +512,7 @@ "source": [ "### Step 3. Execute on hardware\n", "\n", - "Submit the job and enable error suppression by using a technique to reduce errors called [dynamical decoupling.](../api/qiskit-ibm-runtime/qiskit_ibm_runtime.options.DynamicalDecouplingOptions) " + "Submit the job and enable error suppression by using a technique to reduce errors called [dynamical decoupling.](../api/qiskit-ibm-runtime/qiskit_ibm_runtime.options.DynamicalDecouplingOptions) The resilience level specifies how much resilience to build against errors. Higher levels generate more accurate results, at the expense of longer processing times. For further explanation of the options set in the following code, see [Configure error mitigation for Qiskit Runtime.](../run/configure-error-mitigation)" ] }, { @@ -552,7 +560,7 @@ "source": [ "### Step 4. Post-process results\n", "\n", - "After the job has completed, we can plot the results and see that $\\langle Z_0 Z_i \\rangle$ decreases with increasing $i$, even though in an ideal simulation we should see that all $\\langle Z_0 Z_i \\rangle$ should be 1." + "After the job completes, plot the results and notice that $\\langle Z_0 Z_i \\rangle$ decreases with increasing $i$, even though in an ideal simulation we should see that all $\\langle Z_0 Z_i \\rangle$ should be 1. " ] }, { @@ -570,11 +578,11 @@ "job = service.job(job_id)\n", "\n", "# data\n", - "data = list(range(1, len(operators)+1))\n", - "result = job.result()[0] # Estimator V2\n", - "values = result.data.evs # Estimator V2\n", - "# values = job.result().values # EstimatorV1\n", - "values = [v / values[0] for v in values]\n", + "data = list(range(1, len(operators)+1)) # Distance between the Z operators\n", + "result = job.result()[0] # Use for EstimatorV2.\n", + "values = result.data.evs # Expectation value at each Z operator. Use for Estimator V2.\n", + "# values = job.result().values # Use for EstimatorV1\n", + "values = [v / values[0] for v in values] # Normalize the expectation values to evaluate how they decay with distance.\n", "\n", "# plotting graph\n", "plt.scatter(data, values, marker='o', label='ibm_sherbrooke')\n", @@ -584,6 +592,14 @@ "plt.show()" ] }, + { + "cell_type": "markdown", + "id": "0afc307c", + "metadata": {}, + "source": [ + "The previous plot shows that as the distance between qubits increases, the signal decays because there is noise on the system. " + ] + }, { "cell_type": "markdown", "id": "e7c24c81", From 0335fc2796548526bbb7b8c584ab5b1109aef1d3 Mon Sep 17 00:00:00 2001 From: Rebecca Dimock Date: Mon, 22 Apr 2024 18:03:46 -0500 Subject: [PATCH 10/25] Re-upload after downloading artifact from github --- docs/start/hello-world.ipynb | 5 +++-- 1 file changed, 3 insertions(+), 2 deletions(-) diff --git a/docs/start/hello-world.ipynb b/docs/start/hello-world.ipynb index 89b01912f0d..eb1042733ae 100644 --- a/docs/start/hello-world.ipynb +++ b/docs/start/hello-world.ipynb @@ -608,8 +608,9 @@ "## Next steps\n", "\n", "\n", - " * Learn how to [build circuits](../build/) in more detail.\n", - " * Try one of the [workflow example tutorials.](https://learning.quantum.ibm.com/catalog/tutorials?category=workflow-example)\n", + " - Learn how to [build circuits](../build/) in more detail.\n", + " \n", + " - Try one of the [workflow example tutorials.](https://learning.quantum.ibm.com/catalog/tutorials?category=workflow-example)\n", "" ] } From 7ac8d8fe6ddfe0bc979efe4ed736ff7ad87a2da8 Mon Sep 17 00:00:00 2001 From: Rebecca Dimock Date: Tue, 23 Apr 2024 09:37:14 -0500 Subject: [PATCH 11/25] edits --- docs/start/hello-world.ipynb | 61 ++++++++++++++++++------------------ 1 file changed, 31 insertions(+), 30 deletions(-) diff --git a/docs/start/hello-world.ipynb b/docs/start/hello-world.ipynb index eb1042733ae..198b00df8b1 100644 --- a/docs/start/hello-world.ipynb +++ b/docs/start/hello-world.ipynb @@ -30,7 +30,7 @@ "\n", "Follow the [Install and set up](install) instructions if you haven't already, including the steps to [Set up to use IBM Quantum™ Platform](setup-channel#set-up-to-use-ibm-quantum-platform).\n", "\n", - "We recommend that you use the [Jupyter](https://jupyter.org/install) development environment to interact with quantum computers. Be sure to install the recommended extra visualization support (`pip install qiskit[visualization]`), and note that zsh users need to put `'qiskit[visualization]'` in single quotes. You'll also need the `matplotlib` package for the second part of this example.\n", + "It is recommended that you use the [Jupyter](https://jupyter.org/install) development environment to interact with quantum computers. Be sure to install the recommended extra visualization support (`pip install qiskit[visualization]`), and note that zsh users need to put `'qiskit[visualization]'` in single quotes. You'll also need the `matplotlib` package for the second part of this example.\n", "\n", "\n", "To learn about quantum computing in general, check out the [Basics of quantum information course](https://learning.quantum.ibm.com/course/basics-of-quantum-information) in IBM Quantum Learning.\n", @@ -74,7 +74,7 @@ "The following code cell creates a circuit that produces a *Bell state,* which is a state wherein two (or more) qubits are fully entangled with each other.\n", "\n", "\n", - " The Qiskit SDK uses the LSb 0 bit numbering where the $n^{th}$ digit has value $1 \\ll n$ or $2^n$. Because we usually write numbers on paper with the most significant digits to the left and the least significant digits to the right (in the Hindu-Arabic system used in most of the world), this has the consequence that the bits are labeled with indices increasing from right to left. This LSb 0 convention makes mathematics easier and is the most commonly used for modern digital electronics, although the opposite convention MSb 0 is also found in some domains. Converting the $i^{th}$ index between LSb 0 and MSb 0 conventions on an $n$-bit register is as simple as $i \\rightarrow n-i-1$. This differs across authors and software packages, so be aware! For more details, see the [Bit-ordering in the Qiskit SDK](../build/bit-ordering) topic.\n", + " The Qiskit SDK uses the LSb 0 bit numbering where the $n^{th}$ digit has value $1 \\ll n$ or $2^n$. Because you usually write numbers with the most significant digits to the left and the least significant digits to the right (in the Hindu-Arabic system used in most of the world), this has the consequence that the bits are labeled with indices increasing from right to left. This LSb 0 convention makes mathematics easier and is the most commonly used for modern digital electronics, although the opposite convention MSb 0 is also found in some domains. Converting the $i^{th}$ index between LSb 0 and MSb 0 conventions on an $n$-bit register is as simple as $i \\rightarrow n-i-1$. This differs across authors and software packages, so be aware! For more details, see the [Bit-ordering in the Qiskit SDK](../build/bit-ordering) topic.\n", "" ] }, @@ -102,7 +102,7 @@ "from qiskit import QuantumCircuit\n", "from qiskit.quantum_info import SparsePauliOp\n", "from qiskit.transpiler.preset_passmanagers import generate_preset_pass_manager\n", - "from qiskit_ibm_runtime import QiskitRuntimeService, EstimatorV2 as Estimator\n", + "from qiskit_ibm_runtime import EstimatorV2 as Estimator\n", "\n", "# Create a new circuit with two qubits\n", "qc = QuantumCircuit(2)\n", @@ -136,9 +136,9 @@ "id": "f3ef4248-7938-44c1-85f1-edc997f0edcd", "metadata": {}, "source": [ - "While creating quantum circuits, we also must consider what type of data we want to get back after execution, and there are are two ways to do so within Qiskit. You can either obtain a probability distribution for a set of qubits you choose to measure, or obtain the expectation value of an observable. Preparing your workload to measure your circuit in one of these two ways is done through the [Qiskit primitives](../run/primitives-get-started) (explained in detail in [Step 3](#step-3-execute-using-the-quantum-primitives) of this page).\n", + "While creating quantum circuits, you must also consider what type of data you want to get back after execution, and there are are two ways to do so within Qiskit. You can either obtain a probability distribution for a set of qubits you choose to measure, or obtain the expectation value of an observable. Preparing your workload to measure your circuit in one of these two ways is done through the [Qiskit primitives](../run/primitives-get-started) (explained in detail in [Step 3](#step-3-execute-using-the-quantum-primitives) of this page).\n", "\n", - "For this example, we will be measuring some expectation values using the `qiskit.quantum_info` submodule which will be specified using operators (these are mathematical objects used to represent an action or process which changes a quantum state). The following code cell creates six two-qubit Pauli operators: `IZ`, `IX`, `ZI`, `XI`, `ZZ`, and `XX`." + "This example measures expectation values by using the `qiskit.quantum_info` submodule, which is specified by using operators (mathematical objects used to represent an action or process that changes a quantum state). The following code cell creates six two-qubit Pauli operators: `IZ`, `IX`, `ZI`, `XI`, `ZZ`, and `XX`." ] }, { @@ -162,7 +162,7 @@ "\n", "observables = [IZ, IX, ZI, XI, ZZ, XX]\n", "observables_labels = [\"IZ\", \"IX\", \"ZI\", \"XI\", \"ZZ\", \"XX\"]\n", - "observables = [SparsePauliOp(label) for label in observables_labels]" + "observables = [SparsePauliOp(label) for label in observables_labels]GHZ" ] }, { @@ -188,7 +188,7 @@ "\n", "When executing circuits on a device, it is an important step to optimize the set of instructions which the circuit contains and work to minimize the overall depth (roughly the number of instructions) of the circuit. This ensures that you obtain the best results possible by reducing the effects of error and noise. Additionally, the circuit's instructions must conform to a backend device's [Instruction Set Architecture (ISA)](../transpile/#instruction-set-architecture) and takes both the device's basis gates as well as its qubit connectivity into account.\n", "\n", - "The following code instantiates a real device to submit a job to and transform the circuit to match that backend's ISA." + "The following code instantiates a real device to submit a job to and transform the circuit and observables to match that backend's ISA." ] }, { @@ -210,6 +210,8 @@ } ], "source": [ + "from qiskit_ibm_runtime import QiskitRuntimeService\n", + "\n", "# If you did not previously save your credentials, use the following line instead:\n", "# service = QiskitRuntimeService(channel=\"ibm_quantum\", token=\"\")\n", "service = QiskitRuntimeService()\n", @@ -252,7 +254,7 @@ } ], "source": [ - "# Construct the Estimator instance we want to use.\n", + "# Construct the Estimator instance.\n", "from qiskit_ibm_runtime import EstimatorV2 as Estimator\n", "\n", "estimator = Estimator(backend=backend)\n", @@ -266,7 +268,7 @@ "# One pub, with one circuit to run against five different observables.\n", "job = estimator.run([(isa_circuit, mapped_observables)])\n", "\n", - "# Use the job id in order to retrieve your job data at a later time\n", + "# Use the job ID to retrieve your job data later\n", "print(f\">>> Job ID: {job.job_id()}\")" ] }, @@ -277,7 +279,7 @@ "source": [ "Once a job is submitted, you can wait until either the job is completed within your current python instance, or use the `job_id` in order to retrieve the data at a later time. (See the [section on retrieving jobs](../run/monitor-job#retrieve-job-results-at-a-later-time) for more info)\n", "\n", - "Once a job is completed, we can examine its output through the job's `result()` attribute shown below." + "Once a job is completed, examine its output through the job's `result()` attribute shown below." ] }, { @@ -287,7 +289,7 @@ "metadata": {}, "outputs": [], "source": [ - "# This is the result of the entire submission. We submitted one Pub,\n", + "# This is the result of the entire submission. You submitted one Pub,\n", "# so this contains one inner result (and some metadata of its own).\n", "job_result = job.result()\n", "\n", @@ -327,7 +329,7 @@ "result = job.result()\n", "\n", "\n", - "# This is the result of the entire submission. We submitted one Pub,\n", + "# This is the result of the entire submission. You submitted one Pub,\n", "# so this contains one inner result (and some metadata of its own).\n", "job_result = job.result()\n", "\n", @@ -390,7 +392,7 @@ "id": "e6a9ba84", "metadata": {}, "source": [ - "Here we see that for qubits 0 and 1, the independent expectation values of both X and Z are 0, while the correlations (`XX` and `ZZ`) are 1. This is a hallmark of quantum entanglement." + "Notice that for qubits 0 and 1, the independent expectation values of both X and Z are 0, while the correlations (`XX` and `ZZ`) are 1. This is a hallmark of quantum entanglement." ] }, { @@ -400,11 +402,11 @@ "source": [ "## Scale to large numbers of qubits\n", "\n", - "In quantum computing, utility-scale work is crucial for making progress in the field. Such work requires computations to be done on a much larger scale; working with circuits that might use over 100 qubits and over 1000 gates. This example demonstrates how you can accomplish utility-scale work on IBM Quantum systems by working with a 100-qubit Bell state. It uses the Qiskit Patterns workflow and ends by measuring the expectation value $\\langle Z_0 Z_i \\rangle $ for each qubit.\n", + "In quantum computing, utility-scale work is crucial for making progress in the field. Such work requires computations to be done on a much larger scale; working with circuits that might use over 100 qubits and over 1000 gates. This example demonstrates how you can accomplish utility-scale work on IBM Quantum systems by working with a 100-qubit GHZ state. It uses the Qiskit Patterns workflow and ends by measuring the expectation value $\\langle Z_0 Z_i \\rangle $ for each qubit.\n", "\n", "### Step 1. Map the problem\n", "\n", - "Write a function that returns a `QuantumCircuit` that prepares an $n$-qubit Bell state then use that function to prepare a 100-qubit Bell state and collect the observables to be measured." + "Write a function that returns a `QuantumCircuit` that prepares an $n$-qubit GHZ state (essentially an extended Bell state), then use that function to prepare a 100-qubit GHZ state and collect the observables to be measured." ] }, { @@ -416,14 +418,14 @@ "source": [ "from qiskit import QuantumCircuit\n", "\n", - "def get_qc_for_n_qubit_Bell_state(n: int) -> QuantumCircuit:\n", - " \"\"\"This function will create a qiskit.QuantumCircuit (qc) for an n-qubit Bell state.\n", + "def get_qc_for_n_qubit_GHZ_state(n: int) -> QuantumCircuit:\n", + " \"\"\"This function will create a qiskit.QuantumCircuit (qc) for an n-qubit GHZ state.\n", "\n", " Args:\n", - " n (int): Number of qubits in the n-qubit Bell state\n", + " n (int): Number of qubits in the n-qubit GHZ state\n", "\n", " Returns:\n", - " QuantumCircuit: Quantum circuit that generate the n-qubit Bell state, assuming all qubits start in the 0 state\n", + " QuantumCircuit: Quantum circuit that generate the n-qubit GHZ state, assuming all qubits start in the 0 state\n", " \"\"\"\n", " if isinstance(n, int) and n >= 2:\n", " qc = QuantumCircuit(n)\n", @@ -440,7 +442,7 @@ "# Create a new circuit with two qubits (first argument) and two classical\n", "# bits (second argument)\n", "n = 100\n", - "qc = get_qc_for_n_qubit_Bell_state(n)" + "qc = get_qc_for_n_qubit_GHZ_state(n)" ] }, { @@ -484,7 +486,7 @@ "source": [ "### Step 2. Optimize the problem for execution on quantum hardware\n", "\n", - "Transpile this circuit and map the observables to the hardware's layout (ISA). " + "Transform the circuit and observables to match the backend's ISA. " ] }, { @@ -494,15 +496,17 @@ "metadata": {}, "outputs": [], "source": [ - "from qiskit_ibm_runtime import QiskitRuntimeService\n", "from qiskit.transpiler.preset_passmanagers import generate_preset_pass_manager\n", + "from qiskit_ibm_runtime import QiskitRuntimeService\n", + "\n", + "service = QiskitRuntimeService()\n", "\n", "backend_name = \"ibm_brisbane\"\n", "backend = QiskitRuntimeService().get_backend(backend_name)\n", "pm = generate_preset_pass_manager(optimization_level=1, backend=backend)\n", "\n", - "qc_transpiled = pm.run(qc)\n", - "operators_transpiled_list = [op.apply_layout(qc_transpiled.layout) for op in operators]" + "isa_circuit = pm.run(qc)\n", + "isa_operators_list = [op.apply_layout(isa_circuit.layout) for op in operators]" ] }, { @@ -530,12 +534,9 @@ } ], "source": [ - "from qiskit_ibm_runtime import QiskitRuntimeService, EstimatorOptions\n", + "from qiskit_ibm_runtime import EstimatorOptions\n", "from qiskit_ibm_runtime import EstimatorV2 as Estimator\n", "\n", - "service = QiskitRuntimeService()\n", - "\n", - "# backend = service.get_backend('ibm_sherbrooke')\n", "backend = service.get_backend('ibm_brisbane')\n", "\n", "options = EstimatorOptions()\n", @@ -548,7 +549,7 @@ "estimator = Estimator(backend, options=options)\n", "\n", "# Submit the circuit to Estimator\n", - "job = estimator.run([(qc_transpiled, operators_transpiled_list)])\n", + "job = estimator.run([(isa_circuit, isa_operators_list)])\n", "job_id = job.job_id()\n", "print(job_id)" ] @@ -560,7 +561,7 @@ "source": [ "### Step 4. Post-process results\n", "\n", - "After the job completes, plot the results and notice that $\\langle Z_0 Z_i \\rangle$ decreases with increasing $i$, even though in an ideal simulation we should see that all $\\langle Z_0 Z_i \\rangle$ should be 1. " + "After the job completes, plot the results and notice that $\\langle Z_0 Z_i \\rangle$ decreases with increasing $i$, even though in an ideal simulation all $\\langle Z_0 Z_i \\rangle$ should be 1." ] }, { From d991d6c036c254f42fe900a5840a630c43b7a120 Mon Sep 17 00:00:00 2001 From: Rebecca Dimock Date: Tue, 23 Apr 2024 13:15:03 -0500 Subject: [PATCH 12/25] Get output --- docs/start/hello-world.ipynb | 93 ++++++++++++++++++++++-------------- 1 file changed, 58 insertions(+), 35 deletions(-) diff --git a/docs/start/hello-world.ipynb b/docs/start/hello-world.ipynb index 198b00df8b1..7c456a47ef9 100644 --- a/docs/start/hello-world.ipynb +++ b/docs/start/hello-world.ipynb @@ -12,10 +12,23 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 1, "id": "7973a948", "metadata": {}, - "outputs": [], + "outputs": [ + { + "data": { + "text/html": [ + "\n" + ], + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], "source": [ "%%html\n", "" @@ -80,7 +93,7 @@ }, { "cell_type": "code", - "execution_count": 1, + "execution_count": 2, "id": "930ca3b6", "metadata": { "tags": [] @@ -88,12 +101,12 @@ "outputs": [ { "data": { - "image/png": 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R4BgxkeAYMZHgGDGR4BgxkeAYMZHgGDGR4BgxkeAYMZHgGDGR4BgxkeAYMZHgGDGR4BgxkeAYMZHgGDGR4BgxkeAYMZHgGDGR4BgxkeAYMZHgGDGR4BgxkeD+DyBtQk9i1toDAAAAAElFTkSuQmCC", "text/plain": [ "
" ] }, - "execution_count": 1, + "execution_count": 2, "metadata": {}, "output_type": "execute_result" } @@ -143,7 +156,7 @@ }, { "cell_type": "code", - "execution_count": 19, + "execution_count": 3, "id": "c57b261c-b757-4432-beab-61b526c98a41", "metadata": { "tags": [] @@ -162,7 +175,7 @@ "\n", "observables = [IZ, IX, ZI, XI, ZZ, XX]\n", "observables_labels = [\"IZ\", \"IX\", \"ZI\", \"XI\", \"ZZ\", \"XX\"]\n", - "observables = [SparsePauliOp(label) for label in observables_labels]GHZ" + "observables = [SparsePauliOp(label) for label in observables_labels]" ] }, { @@ -193,18 +206,18 @@ }, { "cell_type": "code", - "execution_count": 20, + "execution_count": 4, "id": "9a901271", "metadata": {}, "outputs": [ { "data": { - "image/png": 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", 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", 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" ] }, - "execution_count": 20, + "execution_count": 4, "metadata": {}, "output_type": "execute_result" } @@ -216,8 +229,6 @@ "# service = QiskitRuntimeService(channel=\"ibm_quantum\", token=\"\")\n", "service = QiskitRuntimeService()\n", "\n", - "\n", - "# Run on the least-busy backend you have access to\n", "backend = service.least_busy(simulator=False, operational=True)\n", "\n", "# Convert to an ISA circuit and layout-mapped observables.\n", @@ -239,7 +250,7 @@ }, { "cell_type": "code", - "execution_count": 21, + "execution_count": 5, "id": "62c4ca44", "metadata": { "tags": [] @@ -249,7 +260,7 @@ "name": "stdout", "output_type": "stream", "text": [ - ">>> Job ID: crbfya9djmqg008kd5p0\n" + ">>> Job ID: crkzbr74r70g0088t3ng\n" ] } ], @@ -284,7 +295,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 6, "id": "792d2f01", "metadata": {}, "outputs": [], @@ -354,7 +365,7 @@ }, { "cell_type": "code", - "execution_count": 23, + "execution_count": 7, "id": "87143fcc", "metadata": { "tags": [] @@ -362,7 +373,7 @@ "outputs": [ { "data": { - "image/png": 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", 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", 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" ] @@ -411,7 +422,7 @@ }, { "cell_type": "code", - "execution_count": 24, + "execution_count": 8, "id": "2ac02692", "metadata": {}, "outputs": [], @@ -455,7 +466,7 @@ }, { "cell_type": "code", - "execution_count": 25, + "execution_count": 9, "id": "863a4ec9", "metadata": {}, "outputs": [ @@ -491,7 +502,7 @@ }, { "cell_type": "code", - "execution_count": 26, + "execution_count": 10, "id": "428f05e7", "metadata": {}, "outputs": [], @@ -499,10 +510,11 @@ "from qiskit.transpiler.preset_passmanagers import generate_preset_pass_manager\n", "from qiskit_ibm_runtime import QiskitRuntimeService\n", "\n", + "# If you did not previously save your credentials, use the following line instead:\n", + "# service = QiskitRuntimeService(channel=\"ibm_quantum\", token=\"\")\n", "service = QiskitRuntimeService()\n", "\n", - "backend_name = \"ibm_brisbane\"\n", - "backend = QiskitRuntimeService().get_backend(backend_name)\n", + "backend = service.least_busy(simulator=False, operational=True, min_num_qubits=100)\n", "pm = generate_preset_pass_manager(optimization_level=1, backend=backend)\n", "\n", "isa_circuit = pm.run(qc)\n", @@ -521,7 +533,7 @@ }, { "cell_type": "code", - "execution_count": 27, + "execution_count": 11, "id": "3aaa5025", "metadata": {}, "outputs": [ @@ -529,7 +541,7 @@ "name": "stdout", "output_type": "stream", "text": [ - "crbgpcsdqdn000832tq0\n" + "crkzc58akhw0008exd0g\n" ] } ], @@ -537,8 +549,6 @@ "from qiskit_ibm_runtime import EstimatorOptions\n", "from qiskit_ibm_runtime import EstimatorV2 as Estimator\n", "\n", - "backend = service.get_backend('ibm_brisbane')\n", - "\n", "options = EstimatorOptions()\n", "options.resilience_level = 1\n", "options.optimization_level = 0\n", @@ -566,18 +576,26 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 12, "id": "de91ebd0", "metadata": {}, - "outputs": [], + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], "source": [ "import matplotlib.pyplot as plt\n", "import numpy as np\n", "from qiskit_ibm_runtime import QiskitRuntimeService\n", "\n", - "service = QiskitRuntimeService()\n", - "job = service.job(job_id)\n", - "\n", "# data\n", "data = list(range(1, len(operators)+1)) # Distance between the Z operators\n", "result = job.result()[0] # Use for EstimatorV2.\n", @@ -586,7 +604,7 @@ "values = [v / values[0] for v in values] # Normalize the expectation values to evaluate how they decay with distance.\n", "\n", "# plotting graph\n", - "plt.scatter(data, values, marker='o', label='ibm_sherbrooke')\n", + "plt.scatter(data, values, marker='o', label='100-qubit GHZ state')\n", "plt.xlabel('Distance between qubits $i$')\n", "plt.ylabel(r'$\\langle Z_0 Z_i \\rangle / \\langle Z_0 Z_1 \\rangle $')\n", "plt.legend()\n", @@ -610,17 +628,22 @@ "\n", "\n", " - Learn how to [build circuits](../build/) in more detail.\n", - " \n", " - Try one of the [workflow example tutorials.](https://learning.quantum.ibm.com/catalog/tutorials?category=workflow-example)\n", "" ] + }, + { + "cell_type": "markdown", + "id": "24510d4b", + "metadata": {}, + "source": [] } ], "metadata": { "celltoolbar": "Raw Cell Format", "description": "Get started using Qiskit with IBM Quantum hardware in this Hello World example", "kernelspec": { - "display_name": "Python 3", + "display_name": "Python 3 (ipykernel)", "language": "python", "name": "python3" }, @@ -634,7 +657,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3" + "version": "3.12.2" }, "title": "Hello world", "widgets": { From 5e96a9c86e7ff8b726f3ae9d93e3d78dbd834a24 Mon Sep 17 00:00:00 2001 From: Rebecca Dimock Date: Tue, 23 Apr 2024 13:28:07 -0500 Subject: [PATCH 13/25] update video code --- docs/start/hello-world.ipynb | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/docs/start/hello-world.ipynb b/docs/start/hello-world.ipynb index 7c456a47ef9..26397732afc 100644 --- a/docs/start/hello-world.ipynb +++ b/docs/start/hello-world.ipynb @@ -31,7 +31,7 @@ ], "source": [ "%%html\n", - "" + "" ] }, { From 1fcf7a6eb68ceb69f316e80e6c9569f05ca6ab0c Mon Sep 17 00:00:00 2001 From: Rebecca Dimock Date: Tue, 23 Apr 2024 14:01:05 -0500 Subject: [PATCH 14/25] Final edits --- docs/start/hello-world.ipynb | 40 +++++++++++++++--------------------- 1 file changed, 17 insertions(+), 23 deletions(-) diff --git a/docs/start/hello-world.ipynb b/docs/start/hello-world.ipynb index 26397732afc..f29c974a3c8 100644 --- a/docs/start/hello-world.ipynb +++ b/docs/start/hello-world.ipynb @@ -50,13 +50,13 @@ "\n", "The four steps to writing a quantum program using Qiskit Patterns are:\n", "\n", - "1. Map the problem to a quantum-native format\n", + "1. Map the problem to a quantum-native format.\n", "\n", - "2. Optimize the circuits and operators\n", + "2. Optimize the circuits and operators.\n", "\n", - "3. Execute using a quantum primitive function\n", + "3. Execute using a quantum primitive function.\n", "\n", - "4. Analyze the results" + "4. Analyze the results." ] }, { @@ -149,7 +149,7 @@ "id": "f3ef4248-7938-44c1-85f1-edc997f0edcd", "metadata": {}, "source": [ - "While creating quantum circuits, you must also consider what type of data you want to get back after execution, and there are are two ways to do so within Qiskit. You can either obtain a probability distribution for a set of qubits you choose to measure, or obtain the expectation value of an observable. Preparing your workload to measure your circuit in one of these two ways is done through the [Qiskit primitives](../run/primitives-get-started) (explained in detail in [Step 3](#step-3-execute-using-the-quantum-primitives) of this page).\n", + "While creating quantum circuits, you must also consider what type of data you want returned after execution, and there are are two ways to do so within Qiskit. You can obtain a probability distribution for a set of qubits you choose to measure, or you can obtain the expectation value of an observable. Preparing your workload to measure your circuit in one of these two ways is done through the [Qiskit primitives](../run/primitives-get-started) (explained in detail in [Step 3](#step-3-execute-using-the-quantum-primitives)).\n", "\n", "This example measures expectation values by using the `qiskit.quantum_info` submodule, which is specified by using operators (mathematical objects used to represent an action or process that changes a quantum state). The following code cell creates six two-qubit Pauli operators: `IZ`, `IX`, `ZI`, `XI`, `ZZ`, and `XX`." ] @@ -185,9 +185,9 @@ "source": [ "\n", "\n", - "Here, something like the `ZZ` operator is a shorthand for the tensor product $Z\\otimes Z$ which essentially means measuring Z on qubit 0 and Z on qubit 1 together and obtaining information about the correlation between qubit 0 and qubit 1. Expectation values like this are also typically written as $\\langle Z_0 Z_1 \\rangle$.\n", + "Here, something like the `ZZ` operator is a shorthand for the tensor product $Z\\otimes Z$, which essentially means measuring Z on qubit 0 and Z on qubit 1 together, and obtaining information about the correlation between qubit 0 and qubit 1. Expectation values like this are also typically written as $\\langle Z_0 Z_1 \\rangle$.\n", "\n", - "If the state is entangled, then the measurement of $\\langle Z_0 Z_1 \\rangle$ should be equal to 1.\n", + "If the state is entangled, then the measurement of $\\langle Z_0 Z_1 \\rangle$ should be 1.\n", "\n", "" ] @@ -199,9 +199,9 @@ "source": [ "### Step 2. Optimize the circuits and operators\n", "\n", - "When executing circuits on a device, it is an important step to optimize the set of instructions which the circuit contains and work to minimize the overall depth (roughly the number of instructions) of the circuit. This ensures that you obtain the best results possible by reducing the effects of error and noise. Additionally, the circuit's instructions must conform to a backend device's [Instruction Set Architecture (ISA)](../transpile/#instruction-set-architecture) and takes both the device's basis gates as well as its qubit connectivity into account.\n", + "When executing circuits on a device, it is an important step to optimize the set of instructions that the circuit contains and work to minimize the overall depth (roughly the number of instructions) of the circuit. This ensures that you obtain the best results possible by reducing the effects of error and noise. Additionally, the circuit's instructions must conform to a backend device's [Instruction Set Architecture (ISA)](../transpile/#instruction-set-architecture) and must consider the device's basis gates and qubit connectivity.\n", "\n", - "The following code instantiates a real device to submit a job to and transform the circuit and observables to match that backend's ISA." + "The following code instantiates a real device to submit a job to and transforms the circuit and observables to match that backend's ISA." ] }, { @@ -245,7 +245,7 @@ "source": [ "### Step 3. Execute using the quantum primitives\n", "\n", - "Quantum computers can produce random results, so you'll often want to collect a sample of the outputs by running the circuit many times. You can estimate the value of the observable using the `Estimator` class. `Estimator` is one of two [primitives](../run/primitives-get-started); the other is `Sampler`, which can be used to get data from a quantum computer. These objects possess a `run()` method that executes the selection of circuits, observables, and parameters (if applicable), using what's known as a [primitive unified bloc (PUB)](../run/primitives#sampler-v2)." + "Quantum computers can produce random results, so you usually collect a sample of the outputs by running the circuit many times. You can estimate the value of the observable by using the `Estimator` class. `Estimator` is one of two [primitives](../run/primitives-get-started); the other is `Sampler`, which can be used to get data from a quantum computer. These objects possess a `run()` method that executes the selection of circuits, observables, and parameters (if applicable), using what's known as a [primitive unified bloc (PUB).](../run/primitives#sampler-v2)" ] }, { @@ -288,9 +288,9 @@ "id": "47479e76", "metadata": {}, "source": [ - "Once a job is submitted, you can wait until either the job is completed within your current python instance, or use the `job_id` in order to retrieve the data at a later time. (See the [section on retrieving jobs](../run/monitor-job#retrieve-job-results-at-a-later-time) for more info)\n", + "After a job is submitted, you can wait until either the job is completed within your current python instance, or use the `job_id` in order to retrieve the data at a later time. (See the [section on retrieving jobs](../run/monitor-job#retrieve-job-results-at-a-later-time) for details.)\n", "\n", - "Once a job is completed, examine its output through the job's `result()` attribute shown below." + "After the job completes, examine its output through the job's `result()` attribute." ] }, { @@ -316,7 +316,7 @@ "source": [ "\n", "\n", - "When running your quantum program on a real device your workload must wait in a queue before it is run. If you would like to save some time with this example, you can instead use the following code to run this small workload on a local simulator (using the [`fake_provider`](../api/qiskit-ibm-runtime/fake_provider)). Bear in mind this will only work for this small circuit, but when you scale up in the next section you will need to use a real device.\n", + "When running your quantum program on a real device, your workload must wait in a queue before it is run. To save some time, you can instead use the following code to run this small workload on in the Qiskit Runtime local testing mode to use the [`fake_provider`.](../api/qiskit-ibm-runtime/fake_provider) Note that this is only possible for a small circuit. When you scale up in the next section you will need to use a real device.\n", "\n", "```python\n", "# Use the following code instead if you want to run on a simulator:\n", @@ -358,9 +358,9 @@ "source": [ "### Step 4. Analyze the results\n", "\n", - "The analyze step is typically where you might postprocess your results using something like measurement error mitigation or zero noise extrapolation. You might feed these results into another workflow for further analysis or prepare a plot of the key values and data. In general this will be specific to your problem and so for this example,we'll simply plot each of the expectation values that were measured for our circuit.\n", + "The analyze step is typically where you might postprocess your results using something like measurement error mitigation or zero noise extrapolation (ZNE). You might feed these results into another workflow for further analysis or prepare a plot of the key values and data. In general, this step is specific to your problem. For this example, plot each of the expectation values that were measured for our circuit.\n", "\n", - "The expectation values and standard deviations for the observables you specified are accessed through the `PubResult.data.evs` and `PubResult.data.stds` attributes of the job results. To obtain the results from the sampler, use the `PubResult.data.meas.get_counts()` function which will return a `dict` of measurements in the form of bitstrings as keys and counts as their corresponding values." + "The expectation values and standard deviations for the observables you specified to Estimator are accessed through the job result's `PubResult.data.evs` and `PubResult.data.stds` attributes. To obtain the results from the Sampler, use the `PubResult.data.meas.get_counts()` function, which will return a `dict` of measurements in the form of bitstrings as keys and counts as their corresponding values. For more information, see [Get started with Sampler.](/run/primitives-get-started#get-started-with-sampler)" ] }, { @@ -413,7 +413,7 @@ "source": [ "## Scale to large numbers of qubits\n", "\n", - "In quantum computing, utility-scale work is crucial for making progress in the field. Such work requires computations to be done on a much larger scale; working with circuits that might use over 100 qubits and over 1000 gates. This example demonstrates how you can accomplish utility-scale work on IBM Quantum systems by working with a 100-qubit GHZ state. It uses the Qiskit Patterns workflow and ends by measuring the expectation value $\\langle Z_0 Z_i \\rangle $ for each qubit.\n", + "In quantum computing, utility-scale work is crucial for making progress in the field. Such work requires computations to be done on a much larger scale; working with circuits that might use over 100 qubits and over 1000 gates. This example demonstrates how you can accomplish utility-scale work on IBM Quantum systems by creating and analyzing a 100-qubit GHZ state. It uses the Qiskit Patterns workflow and ends by measuring the expectation value $\\langle Z_0 Z_i \\rangle $ for each qubit.\n", "\n", "### Step 1. Map the problem\n", "\n", @@ -461,7 +461,7 @@ "id": "5b3d0d74", "metadata": {}, "source": [ - "Next, map to the operators of interest. This example uses the `ZZ` operators between qubits to examine the behavior as they get farther apart. Increasingly inaccurate (corrupted) expectation values between distant qubits would reveal the level of noise on the system. The `ZZ` operator between the 0th and 1st qubit should be the largest, and the `ZZ` operator between the 0th qubit and the 100th qubit should be the smallest." + "Next, map to the operators of interest. This example uses the `ZZ` operators between qubits to examine the behavior as they get farther apart. Increasingly inaccurate (corrupted) expectation values between distant qubits would reveal the level of noise on the system. " ] }, { @@ -631,12 +631,6 @@ " - Try one of the [workflow example tutorials.](https://learning.quantum.ibm.com/catalog/tutorials?category=workflow-example)\n", "" ] - }, - { - "cell_type": "markdown", - "id": "24510d4b", - "metadata": {}, - "source": [] } ], "metadata": { From 4d3ebb00f265bfe24e526d69db3e2a4118e69fb3 Mon Sep 17 00:00:00 2001 From: Rebecca Dimock Date: Tue, 23 Apr 2024 14:17:07 -0500 Subject: [PATCH 15/25] Trying to fix the video code --- docs/start/hello-world.ipynb | 5 ++--- 1 file changed, 2 insertions(+), 3 deletions(-) diff --git a/docs/start/hello-world.ipynb b/docs/start/hello-world.ipynb index f29c974a3c8..b13dfb5352f 100644 --- a/docs/start/hello-world.ipynb +++ b/docs/start/hello-world.ipynb @@ -7,7 +7,7 @@ "source": [ "# Hello world\n", "\n", - "This example contains two parts: you will first create a simple quantum program and run it on a quantum system. Because actual quantum research requires much more robust programs, in the [Scale to large numbers of qubits](#scale-to-large-numbers-of-qubits) section, you will scale the simple program up to utility level. You can also watch this Hello World in practice in the Hello World episode of the Coding with Qiskit 1.0 video series. " + "This example contains two parts: you will first create a simple quantum program and run it on a quantum system. Because actual quantum research requires much more robust programs, in the [Scale to large numbers of qubits](#scale-to-large-numbers-of-qubits) section, you will scale the simple program up to utility level. You can also follow along with the Hello World episode of the Coding with Qiskit 1.0 video series. " ] }, { @@ -30,8 +30,7 @@ } ], "source": [ - "%%html\n", - "" + "" ] }, { From 8e5252ae427a76d370b9ea37849c8530664e42b6 Mon Sep 17 00:00:00 2001 From: Rebecca Dimock Date: Tue, 23 Apr 2024 14:20:22 -0500 Subject: [PATCH 16/25] typo --- docs/start/hello-world.ipynb | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/docs/start/hello-world.ipynb b/docs/start/hello-world.ipynb index b13dfb5352f..e8ed6c19da6 100644 --- a/docs/start/hello-world.ipynb +++ b/docs/start/hello-world.ipynb @@ -315,7 +315,7 @@ "source": [ "\n", "\n", - "When running your quantum program on a real device, your workload must wait in a queue before it is run. To save some time, you can instead use the following code to run this small workload on in the Qiskit Runtime local testing mode to use the [`fake_provider`.](../api/qiskit-ibm-runtime/fake_provider) Note that this is only possible for a small circuit. When you scale up in the next section you will need to use a real device.\n", + "When running your quantum program on a real device, your workload must wait in a queue before it is run. To save some time, you can instead use the following code to run this small workload in the Qiskit Runtime local testing mode to use the [`fake_provider`.](../api/qiskit-ibm-runtime/fake_provider) Note that this is only possible for a small circuit. When you scale up in the next section you will need to use a real device.\n", "\n", "```python\n", "# Use the following code instead if you want to run on a simulator:\n", From 90c5f6dc5e904c9e1f0594f6bd2150ba9a38f01a Mon Sep 17 00:00:00 2001 From: Eric Arellano <14852634+Eric-Arellano@users.noreply.github.com> Date: Tue, 23 Apr 2024 15:31:43 -0400 Subject: [PATCH 17/25] Fix video + run squeaky --- docs/start/hello-world.ipynb | 38 ++++++++---------------------------- 1 file changed, 8 insertions(+), 30 deletions(-) diff --git a/docs/start/hello-world.ipynb b/docs/start/hello-world.ipynb index f29c974a3c8..c88c125e91d 100644 --- a/docs/start/hello-world.ipynb +++ b/docs/start/hello-world.ipynb @@ -7,31 +7,9 @@ "source": [ "# Hello world\n", "\n", - "This example contains two parts: you will first create a simple quantum program and run it on a quantum system. Because actual quantum research requires much more robust programs, in the [Scale to large numbers of qubits](#scale-to-large-numbers-of-qubits) section, you will scale the simple program up to utility level. You can also watch this Hello World in practice in the Hello World episode of the Coding with Qiskit 1.0 video series. " - ] - }, - { - "cell_type": "code", - "execution_count": 1, - "id": "7973a948", - "metadata": {}, - "outputs": [ - { - "data": { - "text/html": [ - "\n" - ], - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "%%html\n", - "" + "This example contains two parts: you will first create a simple quantum program and run it on a quantum system. Because actual quantum research requires much more robust programs, in the [Scale to large numbers of qubits](#scale-to-large-numbers-of-qubits) section, you will scale the simple program up to utility level. You can also watch this Hello World in practice in the Hello World episode of the Coding with Qiskit 1.0 video series.\n", + "\n", + "" ] }, { @@ -461,7 +439,7 @@ "id": "5b3d0d74", "metadata": {}, "source": [ - "Next, map to the operators of interest. This example uses the `ZZ` operators between qubits to examine the behavior as they get farther apart. Increasingly inaccurate (corrupted) expectation values between distant qubits would reveal the level of noise on the system. " + "Next, map to the operators of interest. This example uses the `ZZ` operators between qubits to examine the behavior as they get farther apart. Increasingly inaccurate (corrupted) expectation values between distant qubits would reveal the level of noise on the system." ] }, { @@ -497,7 +475,7 @@ "source": [ "### Step 2. Optimize the problem for execution on quantum hardware\n", "\n", - "Transform the circuit and observables to match the backend's ISA. " + "Transform the circuit and observables to match the backend's ISA." ] }, { @@ -616,7 +594,7 @@ "id": "0afc307c", "metadata": {}, "source": [ - "The previous plot shows that as the distance between qubits increases, the signal decays because there is noise on the system. " + "The previous plot shows that as the distance between qubits increases, the signal decays because there is noise on the system." ] }, { @@ -637,7 +615,7 @@ "celltoolbar": "Raw Cell Format", "description": "Get started using Qiskit with IBM Quantum hardware in this Hello World example", "kernelspec": { - "display_name": "Python 3 (ipykernel)", + "display_name": "Python 3", "language": "python", "name": "python3" }, @@ -651,7 +629,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.12.2" + "version": "3" }, "title": "Hello world", "widgets": { From 32836b821e4853424ac3882f13929e2339084b14 Mon Sep 17 00:00:00 2001 From: Rebecca Dimock Date: Tue, 23 Apr 2024 15:00:52 -0500 Subject: [PATCH 18/25] fix video and put back in edits --- docs/start/hello-world.ipynb | 8 ++++---- 1 file changed, 4 insertions(+), 4 deletions(-) diff --git a/docs/start/hello-world.ipynb b/docs/start/hello-world.ipynb index 7e61b607fab..9e0201dd9ae 100644 --- a/docs/start/hello-world.ipynb +++ b/docs/start/hello-world.ipynb @@ -7,9 +7,9 @@ "source": [ "# Hello world\n", "\n", - "This example contains two parts: you will first create a simple quantum program and run it on a quantum system. Because actual quantum research requires much more robust programs, in the [Scale to large numbers of qubits](#scale-to-large-numbers-of-qubits) section, you will scale the simple program up to utility level. You can also watch this Hello World in practice in the Hello World episode of the Coding with Qiskit 1.0 video series.\n", + "This example contains two parts: you will first create a simple quantum program and run it on a quantum system. Because actual quantum research requires much more robust programs, in the [Scale to large numbers of qubits](#scale-to-large-numbers-of-qubits) section, you will scale the simple program up to utility level. You can also follow along with the Hello World episode of the Coding with Qiskit 1.0 video series. \n", "\n", - "" + "ame width=\"560\" height=\"315\" src=\"https://www.youtube.com/embed/93-zLTppFZw?si=whJzB_FrpuorerTv\" title=\"Hello World\" frameborder=\"0\" allow=\"accelerometer; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen>" ] }, { @@ -615,7 +615,7 @@ "celltoolbar": "Raw Cell Format", "description": "Get started using Qiskit with IBM Quantum hardware in this Hello World example", "kernelspec": { - "display_name": "Python 3", + "display_name": "Python 3 (ipykernel)", "language": "python", "name": "python3" }, @@ -629,7 +629,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3" + "version": "3.12.2" }, "title": "Hello world", "widgets": { From 3b1aadfc09da384e6972697a7f8999511e6ad1ce Mon Sep 17 00:00:00 2001 From: Rebecca Dimock Date: Tue, 23 Apr 2024 15:15:01 -0500 Subject: [PATCH 19/25] edit --- docs/start/hello-world.ipynb | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/docs/start/hello-world.ipynb b/docs/start/hello-world.ipynb index 9e0201dd9ae..b24c09146c9 100644 --- a/docs/start/hello-world.ipynb +++ b/docs/start/hello-world.ipynb @@ -9,7 +9,7 @@ "\n", "This example contains two parts: you will first create a simple quantum program and run it on a quantum system. Because actual quantum research requires much more robust programs, in the [Scale to large numbers of qubits](#scale-to-large-numbers-of-qubits) section, you will scale the simple program up to utility level. You can also follow along with the Hello World episode of the Coding with Qiskit 1.0 video series. \n", "\n", - "ame width=\"560\" height=\"315\" src=\"https://www.youtube.com/embed/93-zLTppFZw?si=whJzB_FrpuorerTv\" title=\"Hello World\" frameborder=\"0\" allow=\"accelerometer; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen>" + "" ] }, { From 66961a497f9340fc22e280924e345a8bab678376 Mon Sep 17 00:00:00 2001 From: Rebecca Dimock <66339736+beckykd@users.noreply.github.com> Date: Tue, 23 Apr 2024 16:10:12 -0500 Subject: [PATCH 20/25] Update docs/start/hello-world.ipynb Co-authored-by: abbycross --- docs/start/hello-world.ipynb | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/docs/start/hello-world.ipynb b/docs/start/hello-world.ipynb index b24c09146c9..7071fbb4c23 100644 --- a/docs/start/hello-world.ipynb +++ b/docs/start/hello-world.ipynb @@ -127,7 +127,7 @@ "id": "f3ef4248-7938-44c1-85f1-edc997f0edcd", "metadata": {}, "source": [ - "While creating quantum circuits, you must also consider what type of data you want returned after execution, and there are are two ways to do so within Qiskit. You can obtain a probability distribution for a set of qubits you choose to measure, or you can obtain the expectation value of an observable. Preparing your workload to measure your circuit in one of these two ways is done through the [Qiskit primitives](../run/primitives-get-started) (explained in detail in [Step 3](#step-3-execute-using-the-quantum-primitives)).\n", + "When creating quantum circuits, you must also consider what type of data you want returned after execution. Qiskit provides two ways to return data: you can obtain a probability distribution for a set of qubits you choose to measure, or you can obtain the expectation value of an observable. Prepare your workload to measure your circuit in one of these two ways with [Qiskit primitives](../run/primitives-get-started) (explained in detail in [Step 3](#step-3-execute-using-the-quantum-primitives)).\n", "\n", "This example measures expectation values by using the `qiskit.quantum_info` submodule, which is specified by using operators (mathematical objects used to represent an action or process that changes a quantum state). The following code cell creates six two-qubit Pauli operators: `IZ`, `IX`, `ZI`, `XI`, `ZZ`, and `XX`." ] From 0e034bf9c63090558cae128e0eaff02aa27a33c5 Mon Sep 17 00:00:00 2001 From: Rebecca Dimock <66339736+beckykd@users.noreply.github.com> Date: Tue, 23 Apr 2024 16:10:28 -0500 Subject: [PATCH 21/25] Update docs/start/hello-world.ipynb Co-authored-by: abbycross --- docs/start/hello-world.ipynb | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/docs/start/hello-world.ipynb b/docs/start/hello-world.ipynb index 7071fbb4c23..63649290534 100644 --- a/docs/start/hello-world.ipynb +++ b/docs/start/hello-world.ipynb @@ -163,7 +163,7 @@ "source": [ "\n", "\n", - "Here, something like the `ZZ` operator is a shorthand for the tensor product $Z\\otimes Z$, which essentially means measuring Z on qubit 0 and Z on qubit 1 together, and obtaining information about the correlation between qubit 0 and qubit 1. Expectation values like this are also typically written as $\\langle Z_0 Z_1 \\rangle$.\n", + "Here, something like the `ZZ` operator is a shorthand for the tensor product $Z\\otimes Z$, which means measuring Z on qubit 0 and Z on qubit 1 together, and obtaining information about the correlation between qubit 0 and qubit 1. Expectation values like this are also typically written as $\\langle Z_0 Z_1 \\rangle$.\n", "\n", "If the state is entangled, then the measurement of $\\langle Z_0 Z_1 \\rangle$ should be 1.\n", "\n", From b5d41f4d6b853eb306108abd84a623652e8a1993 Mon Sep 17 00:00:00 2001 From: Rebecca Dimock <66339736+beckykd@users.noreply.github.com> Date: Tue, 23 Apr 2024 16:10:41 -0500 Subject: [PATCH 22/25] Update docs/start/hello-world.ipynb Co-authored-by: abbycross --- docs/start/hello-world.ipynb | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/docs/start/hello-world.ipynb b/docs/start/hello-world.ipynb index 63649290534..44bcb3b9316 100644 --- a/docs/start/hello-world.ipynb +++ b/docs/start/hello-world.ipynb @@ -177,7 +177,7 @@ "source": [ "### Step 2. Optimize the circuits and operators\n", "\n", - "When executing circuits on a device, it is an important step to optimize the set of instructions that the circuit contains and work to minimize the overall depth (roughly the number of instructions) of the circuit. This ensures that you obtain the best results possible by reducing the effects of error and noise. Additionally, the circuit's instructions must conform to a backend device's [Instruction Set Architecture (ISA)](../transpile/#instruction-set-architecture) and must consider the device's basis gates and qubit connectivity.\n", + "When executing circuits on a device, it is important to optimize the set of instructions that the circuit contains and minimize the overall depth (roughly the number of instructions) of the circuit. This ensures that you obtain the best results possible by reducing the effects of error and noise. Additionally, the circuit's instructions must conform to a backend device's [Instruction Set Architecture (ISA)](../transpile/#instruction-set-architecture) and must consider the device's basis gates and qubit connectivity.\n", "\n", "The following code instantiates a real device to submit a job to and transforms the circuit and observables to match that backend's ISA." ] From b8774f06e2f2ca3c33a2aeaad5b6988ce801cc9e Mon Sep 17 00:00:00 2001 From: Rebecca Dimock <66339736+beckykd@users.noreply.github.com> Date: Tue, 23 Apr 2024 16:13:07 -0500 Subject: [PATCH 23/25] Apply suggestions from code review Co-authored-by: Eric Arellano <14852634+Eric-Arellano@users.noreply.github.com> Co-authored-by: abbycross --- docs/start/hello-world.ipynb | 10 +++++----- 1 file changed, 5 insertions(+), 5 deletions(-) diff --git a/docs/start/hello-world.ipynb b/docs/start/hello-world.ipynb index 44bcb3b9316..dba404a6cb3 100644 --- a/docs/start/hello-world.ipynb +++ b/docs/start/hello-world.ipynb @@ -9,7 +9,7 @@ "\n", "This example contains two parts: you will first create a simple quantum program and run it on a quantum system. Because actual quantum research requires much more robust programs, in the [Scale to large numbers of qubits](#scale-to-large-numbers-of-qubits) section, you will scale the simple program up to utility level. You can also follow along with the Hello World episode of the Coding with Qiskit 1.0 video series. \n", "\n", - "" + "" ] }, { @@ -266,7 +266,7 @@ "id": "47479e76", "metadata": {}, "source": [ - "After a job is submitted, you can wait until either the job is completed within your current python instance, or use the `job_id` in order to retrieve the data at a later time. (See the [section on retrieving jobs](../run/monitor-job#retrieve-job-results-at-a-later-time) for details.)\n", + "After a job is submitted, you can wait until either the job is completed within your current python instance, or use the `job_id` to retrieve the data at a later time. (See the [section on retrieving jobs](../run/monitor-job#retrieve-job-results-at-a-later-time) for details.)\n", "\n", "After the job completes, examine its output through the job's `result()` attribute." ] @@ -294,7 +294,7 @@ "source": [ "\n", "\n", - "When running your quantum program on a real device, your workload must wait in a queue before it is run. To save some time, you can instead use the following code to run this small workload in the Qiskit Runtime local testing mode to use the [`fake_provider`.](../api/qiskit-ibm-runtime/fake_provider) Note that this is only possible for a small circuit. When you scale up in the next section you will need to use a real device.\n", + "When you run your quantum program on a real device, your workload must wait in a queue before it runs. To save time, you can instead use the following code to run this small workload on the [`fake_provider`](../api/qiskit-ibm-runtime/fake_provider) with the Qiskit Runtime local testing mode. Note that this is only possible for a small circuit. When you scale up in the next section, you will need to use a real device.\n", "\n", "```python\n", "# Use the following code instead if you want to run on a simulator:\n", @@ -336,9 +336,9 @@ "source": [ "### Step 4. Analyze the results\n", "\n", - "The analyze step is typically where you might postprocess your results using something like measurement error mitigation or zero noise extrapolation (ZNE). You might feed these results into another workflow for further analysis or prepare a plot of the key values and data. In general, this step is specific to your problem. For this example, plot each of the expectation values that were measured for our circuit.\n", + "The analyze step is typically where you might postprocess your results using, for example, measurement error mitigation or zero noise extrapolation (ZNE). You might feed these results into another workflow for further analysis or prepare a plot of the key values and data. In general, this step is specific to your problem. For this example, plot each of the expectation values that were measured for our circuit.\n", "\n", - "The expectation values and standard deviations for the observables you specified to Estimator are accessed through the job result's `PubResult.data.evs` and `PubResult.data.stds` attributes. To obtain the results from the Sampler, use the `PubResult.data.meas.get_counts()` function, which will return a `dict` of measurements in the form of bitstrings as keys and counts as their corresponding values. For more information, see [Get started with Sampler.](/run/primitives-get-started#get-started-with-sampler)" + "The expectation values and standard deviations for the observables you specified to Estimator are accessed through the job result's `PubResult.data.evs` and `PubResult.data.stds` attributes. To obtain the results from Sampler, use the `PubResult.data.meas.get_counts()` function, which will return a `dict` of measurements in the form of bitstrings as keys and counts as their corresponding values. For more information, see [Get started with Sampler.](/run/primitives-get-started#get-started-with-sampler)" ] }, { From ae81d01b971791fb245ecb95d062ef432f7f6afc Mon Sep 17 00:00:00 2001 From: Rebecca Dimock Date: Tue, 23 Apr 2024 16:14:12 -0500 Subject: [PATCH 24/25] Final final edits --- docs/start/hello-world.ipynb | 6 +++--- 1 file changed, 3 insertions(+), 3 deletions(-) diff --git a/docs/start/hello-world.ipynb b/docs/start/hello-world.ipynb index dba404a6cb3..4cd0b606e60 100644 --- a/docs/start/hello-world.ipynb +++ b/docs/start/hello-world.ipynb @@ -7,7 +7,7 @@ "source": [ "# Hello world\n", "\n", - "This example contains two parts: you will first create a simple quantum program and run it on a quantum system. Because actual quantum research requires much more robust programs, in the [Scale to large numbers of qubits](#scale-to-large-numbers-of-qubits) section, you will scale the simple program up to utility level. You can also follow along with the Hello World episode of the Coding with Qiskit 1.0 video series. \n", + "This example contains two parts. You will first create a simple quantum program and run it on a quantum system. Because actual quantum research requires much more robust programs, in the second section ([Scale to large numbers of qubits](#scale-to-large-numbers-of-qubits)), you will scale the simple program up to utility level. You can also follow along with the Hello World episode of the Coding with Qiskit 1.0 video series. \n", "\n", "" ] @@ -24,7 +24,7 @@ "It is recommended that you use the [Jupyter](https://jupyter.org/install) development environment to interact with quantum computers. Be sure to install the recommended extra visualization support (`pip install qiskit[visualization]`), and note that zsh users need to put `'qiskit[visualization]'` in single quotes. You'll also need the `matplotlib` package for the second part of this example.\n", "\n", "\n", - "To learn about quantum computing in general, check out the [Basics of quantum information course](https://learning.quantum.ibm.com/course/basics-of-quantum-information) in IBM Quantum Learning.\n", + "To learn about quantum computing in general, visit the [Basics of quantum information course](https://learning.quantum.ibm.com/course/basics-of-quantum-information) in IBM Quantum Learning.\n", "\n", "The four steps to writing a quantum program using Qiskit Patterns are:\n", "\n", @@ -65,7 +65,7 @@ "The following code cell creates a circuit that produces a *Bell state,* which is a state wherein two (or more) qubits are fully entangled with each other.\n", "\n", "\n", - " The Qiskit SDK uses the LSb 0 bit numbering where the $n^{th}$ digit has value $1 \\ll n$ or $2^n$. Because you usually write numbers with the most significant digits to the left and the least significant digits to the right (in the Hindu-Arabic system used in most of the world), this has the consequence that the bits are labeled with indices increasing from right to left. This LSb 0 convention makes mathematics easier and is the most commonly used for modern digital electronics, although the opposite convention MSb 0 is also found in some domains. Converting the $i^{th}$ index between LSb 0 and MSb 0 conventions on an $n$-bit register is as simple as $i \\rightarrow n-i-1$. This differs across authors and software packages, so be aware! For more details, see the [Bit-ordering in the Qiskit SDK](../build/bit-ordering) topic.\n", + " The Qiskit SDK uses the LSb 0 bit numbering where the $n^{th}$ digit has value $1 \\ll n$ or $2^n$. For more details, see the [Bit-ordering in the Qiskit SDK](../build/bit-ordering) topic.\n", "" ] }, From 3da6b8446fef31383df68ed1f41f59b8ba613851 Mon Sep 17 00:00:00 2001 From: Rebecca Dimock Date: Tue, 23 Apr 2024 16:28:54 -0500 Subject: [PATCH 25/25] Ran squeaky and am crossing fingers --- docs/start/hello-world.ipynb | 6 +++--- 1 file changed, 3 insertions(+), 3 deletions(-) diff --git a/docs/start/hello-world.ipynb b/docs/start/hello-world.ipynb index 4cd0b606e60..54fa81f2f95 100644 --- a/docs/start/hello-world.ipynb +++ b/docs/start/hello-world.ipynb @@ -7,7 +7,7 @@ "source": [ "# Hello world\n", "\n", - "This example contains two parts. You will first create a simple quantum program and run it on a quantum system. Because actual quantum research requires much more robust programs, in the second section ([Scale to large numbers of qubits](#scale-to-large-numbers-of-qubits)), you will scale the simple program up to utility level. You can also follow along with the Hello World episode of the Coding with Qiskit 1.0 video series. \n", + "This example contains two parts. You will first create a simple quantum program and run it on a quantum system. Because actual quantum research requires much more robust programs, in the second section ([Scale to large numbers of qubits](#scale-to-large-numbers-of-qubits)), you will scale the simple program up to utility level. You can also follow along with the Hello World episode of the Coding with Qiskit 1.0 video series.\n", "\n", "" ] @@ -615,7 +615,7 @@ "celltoolbar": "Raw Cell Format", "description": "Get started using Qiskit with IBM Quantum hardware in this Hello World example", "kernelspec": { - "display_name": "Python 3 (ipykernel)", + "display_name": "Python 3", "language": "python", "name": "python3" }, @@ -629,7 +629,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.12.2" + "version": "3" }, "title": "Hello world", "widgets": {

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