{ "cells": [ { "cell_type": "markdown", "id": "ce7a2652-9948-4c4a-a29f-1c603c688a0a", "metadata": {}, "source": [ "# 00-Finance Tutorial - Quantum Amplitude Estimation\n", "### Quantum Rings toolkit for Qiskit 2.x" ] }, { "cell_type": "code", "execution_count": 1, "id": "67c069e3-2d16-4d7d-9301-a96cd3a117f7", "metadata": {}, "outputs": [], "source": [ "# This tutorial is from:\n", "# https://qiskit-community.github.io/qiskit-finance/tutorials/00_amplitude_estimation.html\n", "\n", "# Modified for use with Quantum Rings toolkit" ] }, { "cell_type": "code", "execution_count": 2, "id": "d802a5ea-ae6d-41db-aec0-095cd4b48326", "metadata": {}, "outputs": [], "source": [ "#\n", "# Setup your account\n", "# You can also save your account locally using the class method QrRuntimeService.save_account(...) and\n", "# invoke the QrRuntimeService class constructor without any arguments.\n", "#\n", "import os\n", "\n", "my_token = os.environ[\"QR_TOKEN\"]\n", "my_name = os.environ[\"QR_ACCOUNT\"]\n", "\n", "#\n", "# Set the backend of your choice, depending upon the task and your hardware configuration.\n", "# See SDK documentation for additional help.\n", "#\n", "\n", "my_backend = \"scarlet_quantum_rings\"" ] }, { "cell_type": "code", "execution_count": 3, "id": "080a03dc-7f23-400d-8cb4-f66708e358a3", "metadata": {}, "outputs": [], "source": [ "p = 0.2" ] }, { "cell_type": "code", "execution_count": 4, "id": "443049e2-9f55-4212-85e0-06eaae386671", "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "from qiskit.circuit import QuantumCircuit\n", "\n", "\n", "class BernoulliA(QuantumCircuit):\n", " \"\"\"A circuit representing the Bernoulli A operator.\"\"\"\n", "\n", " def __init__(self, probability):\n", " super().__init__(1) # circuit on 1 qubit\n", "\n", " theta_p = 2 * np.arcsin(np.sqrt(probability))\n", " self.ry(theta_p, 0)\n", "\n", "\n", "class BernoulliQ(QuantumCircuit):\n", " \"\"\"A circuit representing the Bernoulli Q operator.\"\"\"\n", "\n", " def __init__(self, probability):\n", " super().__init__(1) # circuit on 1 qubit\n", "\n", " self._theta_p = 2 * np.arcsin(np.sqrt(probability))\n", " self.ry(2 * self._theta_p, 0)\n", "\n", " def power(self, k):\n", " # implement the efficient power of Q\n", " q_k = QuantumCircuit(1)\n", " q_k.ry(2 * k * self._theta_p, 0)\n", " return q_k" ] }, { "cell_type": "code", "execution_count": 5, "id": "7fcd0abc-0142-4cfe-828f-d82f88e64825", "metadata": {}, "outputs": [], "source": [ "A = BernoulliA(p)\n", "Q = BernoulliQ(p)" ] }, { "cell_type": "code", "execution_count": 6, "id": "d89eec0f-3d31-4ac2-87fe-9497915752a3", "metadata": {}, "outputs": [], "source": [ "from qiskit_algorithms import EstimationProblem\n", "\n", "problem = EstimationProblem(\n", " state_preparation=A, # A operator\n", " grover_operator=Q, # Q operator\n", " objective_qubits=[0], # the \"good\" state Psi1 is identified as measuring |1> in qubit 0\n", ")" ] }, { "cell_type": "code", "execution_count": 7, "id": "b55dbbad-113a-4297-819d-be919eecd5dd", "metadata": {}, "outputs": [], "source": [ "# change to Quantum Rings\n", "\n", "from quantumrings.toolkit.qiskit import QrRuntimeService\n", "from quantumrings.toolkit.qiskit import QrSamplerV2 as Sampler\n", "\n", "qr_services = QrRuntimeService(name = my_name, token = my_token)\n", "qr_backend = qr_services.backend(name = my_backend, precision = \"single\")\n", "\n", "sampler = Sampler(backend = qr_backend, run_options = {\"performance\":\"HighestEfficiency\"})\n" ] }, { "cell_type": "code", "execution_count": 8, "id": "5c58fe3e-b29d-437b-8707-d6c31d9e1b32", "metadata": {}, "outputs": [], "source": [ "from qiskit_algorithms import AmplitudeEstimation\n", "\n", "ae = AmplitudeEstimation(\n", " num_eval_qubits=3, # the number of evaluation qubits specifies circuit width and accuracy\n", " sampler=sampler,\n", ")" ] }, { "cell_type": "code", "execution_count": 9, "id": "5458a06b-5049-4433-8358-cf4a752052f8", "metadata": {}, "outputs": [], "source": [ "ae_result = ae.estimate(problem)" ] }, { "cell_type": "code", "execution_count": 10, "id": "87756b67-59c2-4e14-be0e-b3e33c7a4d2d", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0.1464466\n" ] } ], "source": [ "print(ae_result.estimation)" ] }, { "cell_type": "code", "execution_count": 11, "id": "edef85e3-911a-48c3-b13b-71cfebd9df3f", "metadata": { "jupyter": { "source_hidden": true } }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import matplotlib.pyplot as plt\n", "\n", "# plot estimated values\n", "gridpoints = list(ae_result.samples.keys())\n", "probabilities = list(ae_result.samples.values())\n", "\n", "plt.bar(gridpoints, probabilities, width=0.5 / len(probabilities))\n", "plt.axvline(p, color=\"r\", ls=\"--\")\n", "plt.xticks(size=15)\n", "plt.yticks([0, 0.25, 0.5, 0.75, 1], size=15)\n", "plt.title(\"Estimated Values\", size=15)\n", "plt.ylabel(\"Probability\", size=15)\n", "plt.xlabel(r\"Amplitude $a$\", size=15)\n", "plt.ylim((0, 1))\n", "plt.grid()\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 12, "id": "642f785c-58ee-45b4-bae4-dcff848b495f", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Interpolated MLE estimator: 0.20390400135509223\n" ] } ], "source": [ "print(\"Interpolated MLE estimator:\", ae_result.mle)" ] }, { "cell_type": "code", "execution_count": 13, "id": "05c00de7-6974-4373-877d-f2ab2c632e24", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" } ], "source": [ "ae_circuit = ae.construct_circuit(problem)\n", "ae_circuit.decompose().draw(\n", " \"mpl\", style=\"clifford\"\n", ") " ] }, { "cell_type": "code", "execution_count": 14, "id": "1ddba7c1-93e1-4d39-96b0-074f184b083e", "metadata": {}, "outputs": [ { "data": { "image/png": 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" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from qiskit import transpile\n", "\n", "\n", "basis_gates = [\"h\", \"ry\", \"cry\", \"cx\", \"ccx\", \"p\", \"cp\", \"x\", \"s\", \"sdg\", \"y\", \"t\", \"cz\"]\n", "transpile(ae_circuit, basis_gates=basis_gates, optimization_level=2).draw(\"mpl\", style=\"clifford\")" ] }, { "cell_type": "code", "execution_count": 15, "id": "14bce09f-1caf-4903-be2a-2da9f40a0def", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Estimate: 0.19815668312207185\n" ] } ], "source": [ "from qiskit_algorithms import IterativeAmplitudeEstimation\n", "\n", "iae = IterativeAmplitudeEstimation(\n", " epsilon_target=0.01, # target accuracy\n", " alpha=0.05, # width of the confidence interval\n", " sampler=sampler,\n", ")\n", "iae_result = iae.estimate(problem)\n", "\n", "print(\"Estimate:\", iae_result.estimation)" ] }, { "cell_type": "code", "execution_count": 16, "id": "00315994-c932-4860-ba55-b328fc64177b", "metadata": {}, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "
" ] }, "execution_count": 16, "metadata": {}, "output_type": "execute_result" } ], "source": [ "iae_circuit = iae.construct_circuit(problem, k=3)\n", "iae_circuit.draw(\"mpl\", style=\"clifford\")" ] }, { "cell_type": "code", "execution_count": 17, "id": "7060f132-f433-4507-b2f5-25fff7d9269a", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Estimate: 0.1982888862395154\n" ] } ], "source": [ "from qiskit_algorithms import MaximumLikelihoodAmplitudeEstimation\n", "\n", "mlae = MaximumLikelihoodAmplitudeEstimation(\n", " evaluation_schedule=3, # log2 of the maximal Grover power\n", " sampler=sampler,\n", ")\n", "mlae_result = mlae.estimate(problem)\n", "\n", "print(\"Estimate:\", mlae_result.estimation)" ] }, { "cell_type": "code", "execution_count": 18, "id": "7d365427-e1e5-40f5-8ae4-61baa1759690", "metadata": {}, "outputs": [], "source": [ "# Example output:\n", "\n", "# Estimate: 0.19824310837835082" ] }, { "cell_type": "code", "execution_count": 19, "id": "2afb7c4c-ea63-4901-97e0-9dda8db82d92", "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "C:\\Users\\vkasi\\.conda\\envs\\Qiskit20\\Lib\\site-packages\\qiskit_algorithms\\amplitude_estimators\\estimation_problem.py:215: UserWarning: Rescaling discards the Grover operator.\n", " warnings.warn(\"Rescaling discards the Grover operator.\")\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Estimate: 0.19970946558781444\n" ] } ], "source": [ "from qiskit_algorithms import FasterAmplitudeEstimation\n", "\n", "fae = FasterAmplitudeEstimation(\n", " delta=0.01, # target accuracy\n", " maxiter=3, # determines the maximal power of the Grover operator\n", " sampler=sampler,\n", ")\n", "fae_result = fae.estimate(problem)\n", "\n", "print(\"Estimate:\", fae_result.estimation)" ] }, { "cell_type": "code", "execution_count": 20, "id": "8db49f53-3875-44b2-81e9-5736e7ec2e97", "metadata": {}, "outputs": [], "source": [ "# Example output:\n", "\n", "# Estimate: 0.013153220143990535" ] }, { "cell_type": "code", "execution_count": 21, "id": "3b4b9b83-985c-4aab-9f18-e9601693dae5", "metadata": {}, "outputs": [ { "data": { "text/html": [ "

Version Information

SoftwareVersion
qiskit2.2.1
qiskit_aer0.17.1
qiskit_ibm_runtime0.40.1
qiskit_algorithms0.4.0
System information
Python version3.12.9
OSWindows
Thu Oct 16 10:50:02 2025 Mountain Daylight Time
" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ "

Quantum Rings Version Information

SoftwareVersion
QuantumRingsLib0.11.0
quantumrings-toolkit-qiskit0.1.10
" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ "

This code is a part of a Qiskit project

© Copyright IBM 2017, 2025.

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.

Modifications Copyright Quantum Rings Inc, 2025
Modified from the originals
Added support for Quantum Rings QrEstimatorV2 class.

" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import tutorial_magics\n", "\n", "%qiskit_version_table\n", "%quantumrings_version_table\n", "%qiskit_copyright" ] }, { "cell_type": "code", "execution_count": null, "id": "cb4709a6-e890-43df-8fb9-a2f6a6fe6679", "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.12.9" } }, "nbformat": 4, "nbformat_minor": 5 }