diff --git a/docs/index.rst b/docs/index.rst index e517c59d0..c13bec99a 100644 --- a/docs/index.rst +++ b/docs/index.rst @@ -64,13 +64,11 @@ Next steps :caption: Tutorials Get started with Estimator + Get started with Sampler Get started with error suppression and error mitigation - VQE with Estimator CHSH with Estimator - Get started with Sampler - QPE with Sampler + VQE with Estimator Grover with Sampler - SEA with Sampler QAOA with Primitives Submit user-transpiled circuits using primitives All tutorials diff --git a/docs/tutorials.rst b/docs/tutorials.rst index 550a6cfba..1a7fed645 100644 --- a/docs/tutorials.rst +++ b/docs/tutorials.rst @@ -11,8 +11,8 @@ Estimator tutorials/how-to-getting-started-with-estimator tutorials/Error-Suppression-and-Error-Mitigation - tutorials/vqe_with_estimator tutorials/chsh_with_estimator + tutorials/vqe_with_estimator Sampler ================================= @@ -22,8 +22,6 @@ Sampler tutorials/how-to-getting-started-with-sampler tutorials/grover_with_sampler tutorials/user-transpiled-circuits - tutorials/sea_with_sampler - tutorials/qpe_with_sampler tutorials/qaoa_with_primitives diff --git a/docs/tutorials/qpe_with_sampler.ipynb b/docs/tutorials/qpe_with_sampler.ipynb deleted file mode 100644 index 1d95b545b..000000000 --- a/docs/tutorials/qpe_with_sampler.ipynb +++ /dev/null @@ -1,677 +0,0 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "id": "665555c8", - "metadata": {}, - "source": [ - "# Quantum phase estimation using the Sampler primitive\n", - "\n", - "The quantum phase estimation (QPE) algorithm is an important subroutine in quantum computation. It serves as a central building block of many quantum algorithms including the Shor's factoring algorithm and the quantum algorithm for linear systems of equations (HHL algorithm). In this tutorial, you will build a parameterized version of QPE circuit and run it using the Sampler primitive, which makes running parameterized circuits very easy." - ] - }, - { - "cell_type": "markdown", - "id": "420d1072", - "metadata": {}, - "source": [ - "## Before you begin\n", - "\n", - "This tutorial requires a Qiskit Runtime service instance. If you haven't done so already, follow the instructions in the Qiskit [Getting started guide](https://qiskit.org/documentation/partners/qiskit_ibm_runtime/getting_started.html) to set one up." - ] - }, - { - "cell_type": "markdown", - "id": "ab166e9d", - "metadata": {}, - "source": [ - "## Background information" - ] - }, - { - "cell_type": "markdown", - "id": "ea2f34b7", - "metadata": {}, - "source": [ - "### Quantum phase estimation algorithm\n", - "\n", - "\n", - "The QPE algorithm [1][2] estimates the value of theta, where a unitary operator $U$ has an eigenvector $|\\psi \\rangle$ with eigenvalue $e^{2\\pi i \\theta}$. To find the estimation, we assume we have black boxes (sometimes called *oracles*), that can prepare the state $|\\psi \\rangle$ and run a controlled-$U^{2^j}$ operation.\n", - "\n", - "Because it relies on black boxes, the QPE algorithm is not actually a complete algorithm, but can be thought of as a subroutine. It can work with other subroutines to perform other computations, such as Shor's factoring algorithm and the HHL algorithm.\n", - "\n", - "We are not going to explain the details of the QPE algorithm here. If you want to learn more, you can read the chapter about the QPE algorithm in [the Qiskit textbook](https://learn.qiskit.org/course/ch-algorithms/quantum-phase-estimation) [3]." - ] - }, - { - "cell_type": "markdown", - "id": "4b56062b", - "metadata": {}, - "source": [ - "## Overview\n", - "\n", - "As explained earlier, there are black boxes in the QPE algorithm to prepare the state $|\\psi \\rangle$ and perform the controlled-$U^{2^j}$ operation. In this tutorial, you will prepare a series of QPE circuits containing different black boxes corresponding to different phases. You will then run these circuits using the [Sampler primitive](https://qiskit.org/documentation/partners/qiskit_ibm_runtime/stubs/qiskit_ibm_runtime.Sampler.html) and analyze the results. As you will see, the Sampler primitive makes running parameterized circuits very easy. Rather than create a series of QPE circuits, you only need to create *one* QPE circuit with a parameter specifying the phase the black boxes generate and a series of phase values for the parameter.\n", - "\n", - "
\n", - "\n", - "Note\n", - "\n", - "In a typical usage of the QPE algorithm, such as the Shor's factoring algorithm, the black boxes are not configured by the user but instead are specified by other subroutines. However, the purpose of this tutorial is to use the QPE algorithm to illustrate the ease of running parameterized circuits by using the Sampler primitive.\n", - "\n", - "
\n", - "\n" - ] - }, - { - "cell_type": "markdown", - "id": "759a4f19", - "metadata": {}, - "source": [ - "## Step 1: Create QPE circuits" - ] - }, - { - "cell_type": "markdown", - "id": "a18bcbae", - "metadata": {}, - "source": [ - "### Create a parameterized QPE circuit\n", - "\n", - "The procedure of the QPE algorithm is as follows:\n", - "\n", - "1. Create a circuit with two quantum registers (the first for estimating the phase and the second for storing the eigenvector $|\\psi\\rangle$) and one classical register for readout.\n", - "2. Initialize the qubits in the first register as $|0\\rangle$ and the second register as $|\\psi\\rangle$.\n", - "3. Create a superposition in the first register.\n", - "4. Apply the controlled-$U^{2^j}$ black box.\n", - "5. Apply an inverse quantum Fourier transform (QFT) to the first register.\n", - "6. Measure the first register.\n", - "\n", - "The following code creates a function `create_qpe_circuit` for creating a QPE circuit given the keyword arguments `theta` and `num_qubits`. Note that `theta` doesn't contain the $2\\pi$ factor. The `num_qubits` argument specifies the number of qubits in the first register. More qubits will provide more precision for the phase estimation. " - ] - }, - { - "cell_type": "code", - "execution_count": 1, - "id": "fb79c13d", - "metadata": {}, - "outputs": [], - "source": [ - "import numpy as np\n", - "\n", - "from qiskit import QuantumRegister, ClassicalRegister, QuantumCircuit\n", - "from qiskit.circuit.library import QFT\n", - "\n", - "\n", - "def create_qpe_circuit(theta, num_qubits):\n", - " \"\"\"Creates a QPE circuit given theta and num_qubits.\"\"\"\n", - "\n", - " # Step 1: Create a circuit with two quantum registers and one classical register.\n", - " first = QuantumRegister(\n", - " size=num_qubits, name=\"first\"\n", - " ) # the first register for phase estimation\n", - " second = QuantumRegister(\n", - " size=1, name=\"second\"\n", - " ) # the second register for storing eigenvector |psi>\n", - " classical = ClassicalRegister(\n", - " size=num_qubits, name=\"readout\"\n", - " ) # classical register for readout\n", - " qpe_circuit = QuantumCircuit(first, second, classical)\n", - "\n", - " # Step 2: Initialize the qubits.\n", - " # All qubits are initialized in |0> by default, no extra code is needed to initialize the first register.\n", - " qpe_circuit.x(\n", - " second\n", - " ) # Initialize the second register with state |psi>, which is |1> in this example.\n", - "\n", - " # Step 3: Create superposition in the first register.\n", - " qpe_circuit.barrier() # Add barriers to separate each step of the algorithm for better visualization.\n", - " qpe_circuit.h(first)\n", - "\n", - " # Step 4: Apply a controlled-U^(2^j) black box.\n", - " qpe_circuit.barrier()\n", - " for j in range(num_qubits):\n", - " qpe_circuit.cp(\n", - " theta * 2 * np.pi * (2**j), j, num_qubits\n", - " ) # Theta doesn't contain the 2 pi factor.\n", - "\n", - " # Step 5: Apply an inverse QFT to the first register.\n", - " qpe_circuit.barrier()\n", - " qpe_circuit.compose(QFT(num_qubits, inverse=True), inplace=True)\n", - "\n", - " # Step 6: Measure the first register.\n", - " qpe_circuit.barrier()\n", - " qpe_circuit.measure(first, classical)\n", - "\n", - " return qpe_circuit" - ] - }, - { - "cell_type": "markdown", - "id": "5e6c71ee", - "metadata": {}, - "source": [ - "If you pass a real number to the `theta` argument in the `create_qpe_circuit` function, it will return a circuit with a fixed phase encoded." - ] - }, - { - "cell_type": "code", - "execution_count": 2, - "id": "c99e7a32", - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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", - "text/plain": [ - "
" - ] - }, - "execution_count": 2, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "num_qubits = 4\n", - "qpe_circuit_fixed_phase = create_qpe_circuit(\n", - " 1 / 2, num_qubits\n", - ") # Create a QPE circuit with fixed theta=1/2.\n", - "qpe_circuit_fixed_phase.draw(\"mpl\")" - ] - }, - { - "cell_type": "markdown", - "id": "6ca92036", - "metadata": {}, - "source": [ - "However, if you pass a [`Parameter`](https://qiskit.org/documentation/stubs/qiskit.circuit.Parameter.html) object instead, it will return a parameterized circuit whose parameter values can be assigned after the circuit has been created. You will use the parameterized version of the QPE circuit for the rest of the tutorial." - ] - }, - { - "cell_type": "code", - "execution_count": 3, - "id": "a80833a0", - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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- "text/plain": [ - "
" - ] - }, - "execution_count": 3, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "from qiskit.circuit import Parameter\n", - "\n", - "theta = Parameter(\n", - " \"theta\"\n", - ") # Create a parameter `theta` whose values can be assigned later.\n", - "qpe_circuit_parameterized = create_qpe_circuit(theta, num_qubits)\n", - "qpe_circuit_parameterized.draw(\"mpl\")" - ] - }, - { - "cell_type": "markdown", - "id": "b9e438a8", - "metadata": {}, - "source": [ - "### Create a list of phase values to be assigned later\n", - "\n", - "After creating the parameterized QPE circuit, you will create a list of phase values to be assigned to the circuit in the next step. You can use the following code to create a list of 21 phase values that range from `0` to `2` with equal spacing, that is, `0`, `0.1`, `0.2`, ..., `1.9`, `2.0`." - ] - }, - { - "cell_type": "code", - "execution_count": 4, - "id": "055469e4", - "metadata": {}, - "outputs": [], - "source": [ - "number_of_phases = 21\n", - "phases = np.linspace(0, 2, number_of_phases)\n", - "individual_phases = [\n", - " [ph] for ph in phases\n", - "] # Phases need to be expressed as a list of lists." - ] - }, - { - "cell_type": "markdown", - "id": "69b9c027", - "metadata": {}, - "source": [ - "## Step 2: Submit the circuits to a quantum computer on the cloud" - ] - }, - { - "cell_type": "markdown", - "id": "3f33a206", - "metadata": {}, - "source": [ - "### Connect to the Qiskit Runtime service \n", - "\n", - "First, you will connect to the Qiskit Runtime service instance that you created in [the first step](#Before-you-begin). We will use `ibmq_qasm_simulator` to run this tutorial." - ] - }, - { - "cell_type": "code", - "execution_count": 5, - "id": "ac4773b1", - "metadata": {}, - "outputs": [], - "source": [ - "from qiskit_ibm_runtime import QiskitRuntimeService\n", - "\n", - "service = QiskitRuntimeService()\n", - "backend = \"ibmq_qasm_simulator\" # use the simulator" - ] - }, - { - "cell_type": "markdown", - "id": "d2b00453", - "metadata": {}, - "source": [ - "### Run the parameterized circuits by using the Sampler primitive\n", - "\n", - "With the Qiskit Runtime service connected, a parameterized QPE circuit, and a list of parameter values, you are now ready to use the Sampler primitive to run the QPE circuits. The `with ...` syntax opens a Qiskit Runtime session. Within the session, you will run the parameterized QPE circuit with 21 parameter values with just one line of code. The Sampler primitive will take the parameter values, assign them to the circuit and run it as 21 circuits with fixed parameter values and return a single job result containing the (quasi-)probabilities of bit strings. This saves you from writing dozens of lines of code.\n", - "\n", - "The `Estimator` primitive has a similar API interface for parameterized circuits. See [the API reference](https://qiskit.org/documentation/partners/qiskit_ibm_runtime/stubs/qiskit_ibm_runtime.Estimator.html) for more details." - ] - }, - { - "cell_type": "code", - "execution_count": 6, - "id": "8ee9e102", - "metadata": {}, - "outputs": [], - "source": [ - "from qiskit_ibm_runtime import Sampler, Session\n", - "\n", - "with Session(service=service, backend=backend):\n", - " results = (\n", - " Sampler()\n", - " .run(\n", - " [qpe_circuit_parameterized] * len(individual_phases),\n", - " parameter_values=individual_phases,\n", - " )\n", - " .result()\n", - " )" - ] - }, - { - "cell_type": "markdown", - "id": "9e9f7b84", - "metadata": {}, - "source": [ - "## Step 3: Analyze the results\n" - ] - }, - { - "cell_type": "markdown", - "id": "30ec2d15", - "metadata": {}, - "source": [ - "### Analyze the results of one circuit\n", - "\n", - "After the job has been completed, you can start analyzing the results by looking at the histogram of one of the circuits. The (quasi-)probability distribution of the measurement outcome is stored in `results.quasi_dists` and you can access results from an individual circuit by passing the index of the circuit ($idx=6$ in the following example) you are interested in. " - ] - }, - { - "cell_type": "code", - "execution_count": 7, - "id": "638f7657", - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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", 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" - ] - }, - "execution_count": 7, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "from qiskit.tools.visualization import plot_histogram\n", - "\n", - "idx = 6\n", - "plot_histogram(\n", - " results.quasi_dists[idx].binary_probabilities(),\n", - " legend=[f\"$\\\\theta$={phases[idx]:.3f}\"],\n", - ")" - ] - }, - { - "cell_type": "markdown", - "id": "9f4ff7b3", - "metadata": {}, - "source": [ - "To estimate $\\theta$, you need to divide the most likely outcome $N_1$ (`1010` in binary or `10` in decimal) by $2^n$, where $n$ is the number of qubits in the first register ($n=4$ in our example):\n", - "\n", - "$$\\theta = \\frac{N_1}{2^n} = \\frac{10}{2^4} = 0.625. $$\n", - "\n", - "This is close to the expected value of $0.6$, but you can get a better estimate by taking the weighted average of the most likely outcome (`1010` in binary or `10` in decimal) and the second most likely outcome (`1001` in binary or `9` in decimal):\n", - "\n", - "$$\\theta = \\frac{P_1 \\times \\frac{N_1}{2^n} + P_2 \\times \\frac{N_2}{2^n}}{P_1 + P_2} = \\frac{0.554 \\times \\frac{10}{2^4} + 0.269 \\times \\frac{9}{2^4}}{0.554 + 0.269} = 0.605,$$\n", - "\n", - "where $N_1$ and $P_1$ are the most likely outcome and its probability and $N_2$ and $P_2$ are the second most likely outcome and its probability. The result, $0.605$, is much closer to the expected value of $0.6$. We will use this method to analyze the results from all circuits." - ] - }, - { - "cell_type": "markdown", - "id": "4f6350cf", - "metadata": {}, - "source": [ - "### Analyze the results of all circuits\n", - "\n", - "You can use the following helper functions to find the values for $N_1$, $P_1$, $N_2$, and $P_2$ for a phase and calculate the estimated $\\theta$. Ideally $N_2$ should be a \"neighbor\" of $N_1$ (for example, the neighbors of `1010` are `1001` and `1011`). However, due to the presence of noise, the second most likely outcome may not be a neighbor of $N_1$ if the results were obtained from a real quantum system. The helper functions take the $N_2$ value only from $N_1$'s neighbors." - ] - }, - { - "cell_type": "code", - "execution_count": 8, - "id": "71483cfc", - "metadata": {}, - "outputs": [], - "source": [ - "def most_likely_bitstring(results_dict):\n", - " \"\"\"Finds the most likely outcome bit string from a result dictionary.\"\"\"\n", - " return max(results_dict, key=results_dict.get)\n", - "\n", - "\n", - "def find_neighbors(bitstring):\n", - " \"\"\"Finds the neighbors of a bit string.\n", - "\n", - " Example:\n", - " For bit string '1010', this function returns ('1001', '1011')\n", - " \"\"\"\n", - " if bitstring == len(bitstring) * \"0\":\n", - " neighbor_left = len(bitstring) * \"1\"\n", - " else:\n", - " neighbor_left = format((int(bitstring, 2) - 1), \"0%sb\" % len(bitstring))\n", - "\n", - " if bitstring == len(bitstring) * \"1\":\n", - " neighbor_right = len(bitstring) * \"0\"\n", - " else:\n", - " neighbor_right = format((int(bitstring, 2) + 1), \"0%sb\" % len(bitstring))\n", - "\n", - " return (neighbor_left, neighbor_right)\n", - "\n", - "\n", - "def estimate_phase(results_dict):\n", - " \"\"\"Estimates the phase from a result dictionary of a QPE circuit.\"\"\"\n", - "\n", - " # Find the most likely outcome bit string N1 and its neighbors.\n", - " num_1_key = most_likely_bitstring(results_dict)\n", - " neighbor_left, neighbor_right = find_neighbors(num_1_key)\n", - "\n", - " # Get probabilities of N1 and its neighbors.\n", - " num_1_prob = results_dict.get(num_1_key)\n", - " neighbor_left_prob = results_dict.get(neighbor_left)\n", - " neighbor_right_prob = results_dict.get(neighbor_right)\n", - "\n", - " # Find the second most likely outcome N2 and its probability P2 among the neighbors.\n", - " if neighbor_left_prob is None:\n", - " # neighbor_left doesn't exist\n", - " if neighbor_right_prob is None:\n", - " # both neighbors don't exist, N2 is N1\n", - " num_2_key = num_1_key\n", - " num_2_prob = num_1_prob\n", - " else:\n", - " # If only neighbor_left doesn't exist, N2 is neighbor_right.\n", - " num_2_key = neighbor_right\n", - " num_2_prob = neighbor_right_prob\n", - " elif neighbor_right_prob is None:\n", - " # If only neighbor_right doesn't exist, N2 is neighbor_left.\n", - " num_2_key = neighbor_left\n", - " num_2_prob = neighbor_left_prob\n", - " elif neighbor_left_prob > neighbor_right_prob:\n", - " # Both neighbors exist and neighbor_left has higher probability, so N2 is neighbor_left.\n", - " num_2_key = neighbor_left\n", - " num_2_prob = neighbor_left_prob\n", - " else:\n", - " # Both neighbors exist and neighbor_right has higher probability, so N2 is neighor_right.\n", - " num_2_key = neighbor_right\n", - " num_2_prob = neighbor_right_prob\n", - "\n", - " # Calculate the estimated phases for N1 and N2.\n", - " num_qubits = len(num_1_key)\n", - " num_1_phase = int(num_1_key, 2) / 2**num_qubits\n", - " num_2_phase = int(num_2_key, 2) / 2**num_qubits\n", - "\n", - " # Calculate the weighted average phase from N1 and N2.\n", - " phase_estimated = (num_1_phase * num_1_prob + num_2_phase * num_2_prob) / (\n", - " num_1_prob + num_2_prob\n", - " )\n", - "\n", - " return phase_estimated" - ] - }, - { - "cell_type": "markdown", - "id": "0b6eab31", - "metadata": {}, - "source": [ - "You can use the `estimate_phase` helper function to estimate phases from the results of all circuits." - ] - }, - { - "cell_type": "code", - "execution_count": 9, - "id": "dcd84b0f", - "metadata": {}, - "outputs": [], - "source": [ - "qpe_solutions = []\n", - "for idx, result_dict in enumerate(results.quasi_dists):\n", - " qpe_solutions.append(estimate_phase(result_dict.binary_probabilities()))" - ] - }, - { - "cell_type": "markdown", - "id": "3ed0fc7d", - "metadata": {}, - "source": [ - "The ideal solutions for the phases $\\theta$ are periodic with a period of `1` because the eigenvalue $e^{2 \\pi i \\theta}$ is $2 \\pi$ periodic. You can run the following cell to generate the ideal solutions for comparison with the solutions obtained from the QPE algorithm." - ] - }, - { - "cell_type": "code", - "execution_count": 10, - "id": "be048ddf", - "metadata": {}, - "outputs": [], - "source": [ - "ideal_solutions = np.append(\n", - " phases[: (number_of_phases - 1) // 2], # first period\n", - " np.subtract(phases[(number_of_phases - 1) // 2 : -1], 1), # second period\n", - ")\n", - "ideal_solutions = np.append(\n", - " ideal_solutions, np.subtract(phases[-1], 2)\n", - ") # starting point of the third period" - ] - }, - { - "cell_type": "markdown", - "id": "ac4b970c", - "metadata": {}, - "source": [ - "You can run the following code to visualize the solutions." - ] - }, - { - "cell_type": "code", - "execution_count": 11, - "id": "97b9ae1d", - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "" - ] - }, - "execution_count": 11, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - 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", 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" - ] - }, - "metadata": { - "needs_background": "light" - }, - "output_type": "display_data" - } - ], - "source": [ - "import matplotlib.pyplot as plt\n", - "\n", - "fig = plt.figure(figsize=(10, 6))\n", - "plt.plot(phases, ideal_solutions, \"--\", label=\"Ideal solutions\")\n", - "plt.plot(phases, qpe_solutions, \"o\", label=\"QPE solutions\")\n", - "\n", - "plt.title(\"Quantum Phase Estimation Algorithm\")\n", - "plt.xlabel(\"Input Phase\")\n", - "plt.ylabel(\"Output Phase\")\n", - "plt.legend()" - ] - }, - { - "cell_type": "markdown", - "id": "83308635", - "metadata": {}, - "source": [ - "As you can see, the solutions obtained from the QPE algorithm follow closely to the ideal solutions. Congratulations! You have successfully run the QPE algorithm and obtained good solutions!" - ] - }, - { - "cell_type": "markdown", - "id": "e81f1691", - "metadata": {}, - "source": [ - "## Summary\n", - "\n", - "In this tutorial, you have created a parameterized QPE circuit, run it using the Sampler primitive, analyzed the results, and obtained solutions that are closed to the ideal solutions. You can see that the Sampler primitive makes running parameterized circuits very easy." - ] - }, - { - "cell_type": "markdown", - "id": "6facf8bc", - "metadata": {}, - "source": [ - "## References\n", - "\n", - "1. Kitaev, A. Y. (1995). Quantum measurements and the Abelian stabilizer problem. arXiv preprint quant-ph/9511026.\n", - "1. Nielsen, M., & Chuang, I. (2010). Quantum computation and quantum information (2nd ed., pp. 221-226). Cambridge University Press.\n", - "1. Abbas, A., Andersson, S., Asfaw, A., Córcoles, A., Bello, L., Ben-Haim, Y., ... & Wootton, J. (2020). Learn quantum computation using qiskit. URL: https://qiskit.org/textbook/preface.html (accessed 07/14/2022)." - ] - }, - { - "cell_type": "markdown", - "id": "1041ed38", - "metadata": {}, - "source": [ - "## Qiskit versions and copyright" - ] - }, - { - "cell_type": "code", - "execution_count": 12, - "id": "5716f0da", - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "'0.7.0'" - ] - }, - "execution_count": 12, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "import qiskit_ibm_runtime\n", - "\n", - "qiskit_ibm_runtime.version.get_version_info()" - ] - }, - { - "cell_type": "code", - "execution_count": 13, - "id": "478c173c", - "metadata": {}, - "outputs": [ - { - "data": { - "text/html": [ - "

Version Information

Qiskit SoftwareVersion
qiskit-terra0.21.0
qiskit-aer0.10.4
qiskit-ibmq-provider0.19.2
qiskit0.37.0
System information
Python version3.9.12
Python compilerClang 12.0.0
Python buildmain, Apr 5 2022 01:53:17
OSDarwin
CPUs8
Memory (Gb)16.0
Tue Jul 12 11:40:25 2022 CEST
" - ], - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - }, - { - "data": { - "text/html": [ - "

This code is a part of Qiskit

© Copyright IBM 2017, 2022.

This code is licensed under the Apache License, Version 2.0. You may
obtain a copy of this license in the LICENSE.txt file in the root directory
of this source tree or at http://www.apache.org/licenses/LICENSE-2.0.

Any modifications or derivative works of this code must retain this
copyright notice, and modified files need to carry a notice indicating
that they have been altered from the originals.

" - ], - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "import qiskit.tools.jupyter\n", - "\n", - "%qiskit_version_table\n", - "%qiskit_copyright" - ] - } - ], - "metadata": { - "kernelspec": { - "display_name": "Python 3.10.5 ('qiskit-ibm-runtime-dev')", - "language": "python", - "name": "python3" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.10.5" - }, - "vscode": { - "interpreter": { - "hash": "cc844467c6cda8d9a2fa77409198df8dff1239931436dfda6dcae5790e79be65" - } - } - }, - "nbformat": 4, - "nbformat_minor": 5 -} diff --git a/docs/tutorials/sea_with_sampler.ipynb b/docs/tutorials/sea_with_sampler.ipynb deleted file mode 100644 index ed80c7dd2..000000000 --- a/docs/tutorials/sea_with_sampler.ipynb +++ /dev/null @@ -1,401 +0,0 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "id": "8be9226d", - "metadata": {}, - "source": [ - "# Spectroscopic Eigensolver Algorithm with Sampler\n", - "\n", - "This tutorial demonstrates the ability to send flexible circuits to the `Sampler` primitive by performing a simple example of the Spectroscopic Eigensolver Algorithm (SEA) ([arXiv:2202.12910](http://arxiv.org/abs/2202.12910)). The SEA is used for quantum simulation of model Hamiltonians, and works by interacting a \"probe\" auxiliary qubit with a simulation register. The energy of the probe qubit is swept and eigenvalues of the simulation Hamiltonian are observed as peaks or dips in the response, akin to the experimental tool of spectroscopy. Because each point (energy) is a different quantum circuit, this technique is expensive with respect to the number of circuits required. The `Sampler` provides the flexibility to send just a single circuit with the needed `Parameter`s passed." - ] - }, - { - "cell_type": "markdown", - "id": "72ab99fd", - "metadata": {}, - "source": [ - "## Set up your local development environment\n", - "\n", - "This tutorial requires a Qiskit Runtime service instance. If you haven’t done so already, follow [these steps](https://qiskit.org/documentation/partners/qiskit_ibm_runtime/getting_started.html) to set one up." - ] - }, - { - "cell_type": "code", - "execution_count": 1, - "id": "0f3b3a34", - "metadata": {}, - "outputs": [], - "source": [ - "# load necessary Runtime libraries\n", - "from qiskit_ibm_runtime import QiskitRuntimeService, Sampler, Session\n", - "\n", - "backend = \"ibmq_qasm_simulator\" # use the simulator" - ] - }, - { - "cell_type": "markdown", - "id": "ce7228b0", - "metadata": {}, - "source": [ - "## Simple Hamiltonian model\n", - "\n", - "Let us consider a Pauli-X matrix acting on a qubit,\n", - "$$\n", - "H_{\\rm Pauli}/\\hbar = \\mu X\n", - "$$\n", - "where we can set $\\mu$ later, or even sweep its values as well. The SEA works by taking the model Pauli (qubit) Hamiltonian and building a larger \"resonance\" Hamiltonian that includes both the simulation register and probe qubit `q0` through\n", - "$$\n", - "H_{\\rm res} / \\hbar = -\\frac{1}{2} \\omega IZ + c XX + H_{\\rm Pauli}/\\hbar \\otimes I\n", - "$$\n", - "where the angular frequency $\\omega$ corresponds to the energy of the probe qubit, and $c$ is the coupling between the probe qubit and a qubit in the simulation register (`q1` in this case). The letters $I$, $X$, and $Z$ correspond to the Pauli spin matrices and their order reflect which qubit they operate on (note that this notation is little-endian). We will set $\\hbar \\equiv 1$ in the following code.\n", - "\n", - "We can construct the SEA circuits with tools from Qiskit Opflow." - ] - }, - { - "cell_type": "code", - "execution_count": 2, - "id": "e98caf32", - "metadata": {}, - "outputs": [], - "source": [ - "from qiskit.circuit import Parameter\n", - "from qiskit.opflow import I, X, Z\n", - "\n", - "mu = Parameter(\"$\\\\mu$\")\n", - "ham_pauli = mu * X" - ] - }, - { - "cell_type": "code", - "execution_count": 3, - "id": "c9d2c3e8", - "metadata": {}, - "outputs": [], - "source": [ - "cc = Parameter(\"$c$\")\n", - "ww = Parameter(\"$\\\\omega$\")\n", - "\n", - "ham_res = -(1 / 2) * ww * (I ^ Z) + cc * (X ^ X) + (ham_pauli ^ I)" - ] - }, - { - "cell_type": "markdown", - "id": "68398382", - "metadata": {}, - "source": [ - "Time evolve the resonance Hamiltonian." - ] - }, - { - "cell_type": "code", - "execution_count": 4, - "id": "dec4884e", - "metadata": {}, - "outputs": [], - "source": [ - "tt = Parameter(\"$t$\")\n", - "U_ham = (tt * ham_res).exp_i()" - ] - }, - { - "cell_type": "markdown", - "id": "199fb538", - "metadata": {}, - "source": [ - "From the time-evolution operator $U_{\\rm ham}$, we use the Suzuki-Trotter expansion to convert this operator into quantum circuits that implement discrete time steps of the simulation. The smaller the time steps (more Trotter steps), the more accurate the quantum circuit, but also longer depth, which could introduce errors when executing on noisy quantum hardware. We then transpile the circuits to IBM backend basis gates and measure only the probe qubit `q0`." - ] - }, - { - "cell_type": "code", - "execution_count": 5, - "id": "f6b0c7d0", - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "" - ] - }, - "execution_count": 5, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "from qiskit import transpile\n", - "from qiskit.circuit import ClassicalRegister\n", - "from qiskit.opflow import PauliTrotterEvolution, Suzuki\n", - "import numpy as np\n", - "\n", - "num_trot_steps = 5\n", - "total_time = 10\n", - "cr = ClassicalRegister(1, \"c\")\n", - "\n", - "spec_op = PauliTrotterEvolution(\n", - " trotter_mode=Suzuki(order=2, reps=num_trot_steps)\n", - ").convert(U_ham)\n", - "spec_circ = spec_op.to_circuit()\n", - "spec_circ_t = transpile(spec_circ, basis_gates=[\"sx\", \"rz\", \"cx\"])\n", - "spec_circ_t.add_register(cr)\n", - "spec_circ_t.measure(0, cr[0])" - ] - }, - { - "cell_type": "code", - "execution_count": 6, - "id": "b8180337", - "metadata": { - "scrolled": true - }, - "outputs": [ - { - "data": { - "image/png": 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" - ] - }, - "execution_count": 6, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "spec_circ_t.draw(\"mpl\")" - ] - }, - { - "cell_type": "markdown", - "id": "95ff35f5", - "metadata": {}, - "source": [ - "Now let's fix our parameters and sweep over the frequency with several points `num_pts`. The eigenvalues of our model Hamiltonian $H_{\\rm Pauli}$ are $\\pm \\mu$, so we need to choose a range that includes those numbers.\n", - "\n", - "Note that the `Parameter`s' keys and values must be separated and converted into a `List` of `List`s. The keys give us the `Parameter`s inside each circuit. In this case, we only have a single circuit, so the `List` of keys contains a single `List`. For the `Parameter` values, there is a `List` for each value of `ww`. " - ] - }, - { - "cell_type": "code", - "execution_count": 7, - "id": "49563352", - "metadata": {}, - "outputs": [], - "source": [ - "# fixed Parameters\n", - "fixed_params = {cc: 0.3, mu: 0.7, tt: total_time}\n", - "# Parameter value for single circuit\n", - "param_keys = list(spec_circ_t.parameters)\n", - "\n", - "# run through all the ww values to create a List of Lists of Parameter value\n", - "num_pts = 101\n", - "wvals = np.linspace(-2, 2, num_pts)\n", - "param_vals = []\n", - "for wval in wvals:\n", - " all_params = {**fixed_params, **{ww: wval}}\n", - " param_vals.append([all_params[key] for key in param_keys])" - ] - }, - { - "cell_type": "markdown", - "id": "6a0ede58", - "metadata": {}, - "source": [ - "When calling the `sampler`, we specify a list of `circuits` pointing to the circuits desired to be run and the parameter values for each circuit." - ] - }, - { - "cell_type": "code", - "execution_count": 8, - "id": "377480fe", - "metadata": { - "scrolled": true - }, - "outputs": [], - "source": [ - "with Session(backend=backend):\n", - " sampler = Sampler()\n", - " job = sampler.run(\n", - " circuits=[spec_circ_t] * num_pts, parameter_values=param_vals, shots=1e5\n", - " )\n", - " result = job.result()" - ] - }, - { - "cell_type": "markdown", - "id": "16946678", - "metadata": {}, - "source": [ - "Build the $Z$ expectations by converting quasi-probabilities to $\\langle Z \\rangle$." - ] - }, - { - "cell_type": "code", - "execution_count": 9, - "id": "23643359", - "metadata": {}, - "outputs": [], - "source": [ - "Zexps = []\n", - "for dist in result.quasi_dists:\n", - " if 1 in dist:\n", - " Zexps.append(1 - 2 * dist[1])\n", - " else:\n", - " Zexps.append(1)" - ] - }, - { - "cell_type": "markdown", - "id": "f66fcbbe", - "metadata": {}, - "source": [ - "As a quick check, we'll calculate the exact expectation values with Qiskit Opflow." - ] - }, - { - "cell_type": "code", - "execution_count": 10, - "id": "48fd7854", - "metadata": {}, - "outputs": [], - "source": [ - "from qiskit.opflow import PauliExpectation, Zero\n", - "\n", - "param_bind = {cc: 0.3, mu: 0.7, tt: total_time}\n", - "\n", - "init_state = Zero ^ 2\n", - "obsv = I ^ Z\n", - "Zexp_exact = (U_ham @ init_state).adjoint() @ obsv @ (U_ham @ init_state)\n", - "\n", - "diag_meas_op = PauliExpectation().convert(Zexp_exact)\n", - "Zexact_values = []\n", - "for w_set in wvals:\n", - " param_bind[ww] = w_set\n", - " Zexact_values.append(np.real(diag_meas_op.bind_parameters(param_bind).eval()))" - ] - }, - { - "cell_type": "markdown", - "id": "1d8c2294", - "metadata": {}, - "source": [ - "And plotting everything together shows that the energy at which our peaks occurs to be $\\pm \\mu$." - ] - }, - { - "cell_type": "code", - "execution_count": 11, - "id": "084bad50", - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "" - ] - }, - "execution_count": 11, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "image/png": 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\n", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "import matplotlib.pyplot as plt\n", - "\n", - "plt.style.use(\"dark_background\")\n", - "\n", - "fig, ax = plt.subplots(dpi=100)\n", - "ax.plot([-param_bind[mu], -param_bind[mu]], [0, 1], ls=\"--\", color=\"purple\")\n", - "ax.plot([param_bind[mu], param_bind[mu]], [0, 1], ls=\"--\", color=\"purple\")\n", - "ax.plot(wvals, Zexact_values, label=\"Exact\")\n", - "ax.plot(wvals, Zexps, label=f\"{backend}\")\n", - "ax.set_xlabel(r\"$\\omega$ (arb)\")\n", - "ax.set_ylabel(r\"$\\langle Z \\rangle$ Expectation\")\n", - "ax.legend()" - ] - }, - { - "cell_type": "code", - "execution_count": 12, - "id": "8dac3031", - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "'0.7.0'" - ] - }, - "execution_count": 12, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "import qiskit_ibm_runtime\n", - "\n", - "qiskit_ibm_runtime.version.get_version_info()" - ] - }, - { - "cell_type": "code", - "execution_count": 13, - "id": "29b25d22", - "metadata": { - "scrolled": true - }, - "outputs": [ - { - "data": { - "text/html": [ - "

Version Information

Qiskit SoftwareVersion
qiskit-terra0.20.0
qiskit-aer0.10.3
qiskit-ignis0.7.0
qiskit-ibmq-provider0.18.3
qiskit0.35.0
System information
Python version3.9.10
Python compilerClang 11.1.0
Python buildmain, Feb 1 2022 21:27:48
OSDarwin
CPUs2
Memory (Gb)16.0
Mon Apr 11 16:17:45 2022 EDT
" - ], - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "from qiskit.tools.jupyter import *\n", - "\n", - "%qiskit_version_table" - ] - } - ], - "metadata": { - "kernelspec": { - "display_name": "primitives", - "language": "python", - "name": "primitives" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.9.7" - } - }, - "nbformat": 4, - "nbformat_minor": 5 -}