{ "cells": [ { "cell_type": "markdown", "id": "68698a13-19c2-4246-bb56-b41a4bf7152c", "metadata": {}, "source": [ "# 06-Finance Tutorial- Pricing Basket Options\n", "### Modified for Quantum Rings toolkit for Qiskit 2.x" ] }, { "cell_type": "code", "execution_count": 1, "id": "2280ea7f-6ac9-48fd-8cc0-e39e3a497aed", "metadata": {}, "outputs": [], "source": [ "# This tutorial is from:\n", "# https://qiskit-community.github.io/qiskit-finance/tutorials/06_basket_option_pricing.html\n", "\n", "# Modified for use with Quantum Rings toolkit" ] }, { "cell_type": "code", "execution_count": 2, "id": "9eb6b896-d763-4553-a7d1-7b04534de4fe", "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", "\n", "import os\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": "ab8005d1-4568-49a7-83da-542fbb5b335d", "metadata": {}, "outputs": [], "source": [ "import matplotlib.pyplot as plt\n", "from scipy.interpolate import griddata\n", "\n", "%matplotlib inline\n", "import numpy as np\n", "\n", "from qiskit import QuantumRegister, QuantumCircuit, AncillaRegister, transpile\n", "from qiskit_algorithms import IterativeAmplitudeEstimation, EstimationProblem\n", "from qiskit.circuit.library import WeightedAdder, LinearAmplitudeFunction\n", "#from qiskit_aer.primitives import Sampler\n", "from qiskit_finance.circuit.library import LogNormalDistribution\n", "\n", "\n", "from quantumrings.toolkit.qiskit import QrRuntimeService\n", "from quantumrings.toolkit.qiskit import QrSamplerV2 as Sampler\n", "\n", "#\n", "# Acquire Quantum Rings Backend\n", "#\n", "\n", "qr_services = QrRuntimeService(name = my_name, token = my_token)\n", "qr_backend = qr_services.backend(name = my_backend, precision = \"single\")" ] }, { "cell_type": "code", "execution_count": 4, "id": "b8104753-4fc0-4064-97a4-be52af157306", "metadata": {}, "outputs": [], "source": [ "# number of qubits per dimension to represent the uncertainty\n", "num_uncertainty_qubits = 2\n", "\n", "# parameters for considered random distribution\n", "S = 2.0 # initial spot price\n", "vol = 0.4 # volatility of 40%\n", "r = 0.05 # annual interest rate of 4%\n", "T = 40 / 365 # 40 days to maturity\n", "\n", "# resulting parameters for log-normal distribution\n", "mu = (r - 0.5 * vol**2) * T + np.log(S)\n", "sigma = vol * np.sqrt(T)\n", "mean = np.exp(mu + sigma**2 / 2)\n", "variance = (np.exp(sigma**2) - 1) * np.exp(2 * mu + sigma**2)\n", "stddev = np.sqrt(variance)\n", "\n", "# lowest and highest value considered for the spot price; in between, an equidistant discretization is considered.\n", "low = np.maximum(0, mean - 3 * stddev)\n", "high = mean + 3 * stddev\n", "\n", "# map to higher dimensional distribution\n", "# for simplicity assuming dimensions are independent and identically distributed)\n", "dimension = 2\n", "num_qubits = [num_uncertainty_qubits] * dimension\n", "low = low * np.ones(dimension)\n", "high = high * np.ones(dimension)\n", "mu = mu * np.ones(dimension)\n", "cov = sigma**2 * np.eye(dimension)\n", "\n", "# construct circuit\n", "u = LogNormalDistribution(num_qubits=num_qubits, mu=mu, sigma=cov, bounds=list(zip(low, high)))" ] }, { "cell_type": "code", "execution_count": 5, "id": "49663f85-9934-4003-99b4-c11c545cb22c", "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "<>:13: SyntaxWarning: invalid escape sequence '\\$'\n", "<>:14: SyntaxWarning: invalid escape sequence '\\$'\n", "<>:15: SyntaxWarning: invalid escape sequence '\\%'\n", "<>:13: SyntaxWarning: invalid escape sequence '\\$'\n", "<>:14: SyntaxWarning: invalid escape sequence '\\$'\n", "<>:15: SyntaxWarning: invalid escape sequence '\\%'\n", "C:\\Users\\vkasi\\AppData\\Local\\Temp\\ipykernel_46620\\3600697497.py:13: SyntaxWarning: invalid escape sequence '\\$'\n", " ax.set_xlabel(\"Spot Price $S_T^1$ (\\$)\", size=15)\n", "C:\\Users\\vkasi\\AppData\\Local\\Temp\\ipykernel_46620\\3600697497.py:14: SyntaxWarning: invalid escape sequence '\\$'\n", " ax.set_ylabel(\"Spot Price $S_T^2$ (\\$)\", size=15)\n", "C:\\Users\\vkasi\\AppData\\Local\\Temp\\ipykernel_46620\\3600697497.py:15: SyntaxWarning: invalid escape sequence '\\%'\n", " ax.set_zlabel(\"Probability (\\%)\", size=15)\n" ] }, { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# plot PDF of uncertainty model\n", "x = [v[0] for v in u.values]\n", "y = [v[1] for v in u.values]\n", "z = u.probabilities\n", "# z = map(float, z)\n", "# z = list(map(float, z))\n", "resolution = np.array([2**n for n in num_qubits]) * 1j\n", "grid_x, grid_y = np.mgrid[min(x) : max(x) : resolution[0], min(y) : max(y) : resolution[1]]\n", "grid_z = griddata((x, y), z, (grid_x, grid_y))\n", "plt.figure(figsize=(10, 8))\n", "ax = plt.axes(projection=\"3d\")\n", "ax.plot_surface(grid_x, grid_y, grid_z, cmap=plt.cm.Spectral)\n", "ax.set_xlabel(\"Spot Price $S_T^1$ (\\$)\", size=15)\n", "ax.set_ylabel(\"Spot Price $S_T^2$ (\\$)\", size=15)\n", "ax.set_zlabel(\"Probability (\\%)\", size=15)\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 6, "id": "e3c00154-ed93-4693-9eae-f3c1bb39c6fc", "metadata": {}, "outputs": [], "source": [ "# determine number of qubits required to represent total loss\n", "weights = []\n", "for n in num_qubits:\n", " for i in range(n):\n", " weights += [2**i]\n", "\n", "# create aggregation circuit\n", "agg = WeightedAdder(sum(num_qubits), weights)\n", "n_s = agg.num_sum_qubits\n", "n_aux = agg.num_qubits - n_s - agg.num_state_qubits # number of additional qubits" ] }, { "cell_type": "code", "execution_count": 7, "id": "c02f496f-0683-400e-b8cd-47b4fa513070", "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "C:\\Users\\vkasi\\AppData\\Local\\Temp\\ipykernel_46620\\2529205002.py:21: DeprecationWarning: The class ``qiskit.circuit.library.arithmetic.linear_amplitude_function.LinearAmplitudeFunction`` is deprecated as of Qiskit 2.2. It will be removed in Qiskit 3.0. Use the class qiskit.circuit.library.LinearAmplitudeFunctionGate instead.\n", " basket_objective = LinearAmplitudeFunction(\n" ] } ], "source": [ "# set the strike price (should be within the low and the high value of the uncertainty)\n", "strike_price = 3.5\n", "\n", "# map strike price from [low, high] to {0, ..., 2^n-1}\n", "max_value = 2**n_s - 1\n", "low_ = low[0]\n", "high_ = high[0]\n", "mapped_strike_price = (\n", " (strike_price - dimension * low_) / (high_ - low_) * (2**num_uncertainty_qubits - 1)\n", ")\n", "\n", "# set the approximation scaling for the payoff function\n", "c_approx = 0.25\n", "\n", "# setup piecewise linear objective fcuntion\n", "breakpoints = [0, mapped_strike_price]\n", "slopes = [0, 1]\n", "offsets = [0, 0]\n", "f_min = 0\n", "f_max = 2 * (2**num_uncertainty_qubits - 1) - mapped_strike_price\n", "basket_objective = LinearAmplitudeFunction(\n", " n_s,\n", " slopes,\n", " offsets,\n", " domain=(0, max_value),\n", " image=(f_min, f_max),\n", " rescaling_factor=c_approx,\n", " breakpoints=breakpoints,\n", ")" ] }, { "cell_type": "code", "execution_count": 8, "id": "5ef2a6ac-fb4f-48cb-89de-4ab015dd3264", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " ┌───────┐┌────────┐ \n", "state_0: ┤0 ├┤0 ├──────\n", " │ ││ │ \n", "state_1: ┤1 ├┤1 ├──────\n", " │ P(X) ││ │ \n", "state_2: ┤2 ├┤2 ├──────\n", " │ ││ │ \n", "state_3: ┤3 ├┤3 ├──────\n", " └───────┘│ │┌────┐\n", " obj: ─────────┤ ├┤3 ├\n", " │ ││ │\n", " sum_0: ─────────┤4 adder ├┤0 ├\n", " │ ││ │\n", " sum_1: ─────────┤5 ├┤1 ├\n", " │ ││ │\n", " sum_2: ─────────┤6 ├┤2 F ├\n", " │ ││ │\n", " work_0: ─────────┤7 ├┤4 ├\n", " │ ││ │\n", " work_1: ─────────┤8 ├┤5 ├\n", " │ ││ │\n", " work_2: ─────────┤9 ├┤6 ├\n", " └────────┘└────┘\n", "objective qubit index 4\n" ] } ], "source": [ "# define overall multivariate problem\n", "qr_state = QuantumRegister(u.num_qubits, \"state\") # to load the probability distribution\n", "qr_obj = QuantumRegister(1, \"obj\") # to encode the function values\n", "ar_sum = AncillaRegister(n_s, \"sum\") # number of qubits used to encode the sum\n", "ar = AncillaRegister(max(n_aux, basket_objective.num_ancillas), \"work\") # additional qubits\n", "\n", "objective_index = u.num_qubits\n", "\n", "basket_option = QuantumCircuit(qr_state, qr_obj, ar_sum, ar)\n", "basket_option.append(u, qr_state)\n", "basket_option.append(agg, qr_state[:] + ar_sum[:] + ar[:n_aux])\n", "basket_option.append(basket_objective, ar_sum[:] + qr_obj[:] + ar[: basket_objective.num_ancillas])\n", "\n", "print(basket_option.draw())\n", "print(\"objective qubit index\", objective_index)" ] }, { "cell_type": "code", "execution_count": 9, "id": "01aab6f5-d077-4a2a-8b42-8e375b596df9", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# plot exact payoff function (evaluated on the grid of the uncertainty model)\n", "x = np.linspace(sum(low), sum(high))\n", "y = np.maximum(0, x - strike_price)\n", "plt.plot(x, y, \"r-\")\n", "plt.grid()\n", "plt.title(\"Payoff Function\", size=15)\n", "plt.xlabel(\"Sum of Spot Prices ($S_T^1 + S_T^2)$\", size=15)\n", "plt.ylabel(\"Payoff\", size=15)\n", "plt.xticks(size=15, rotation=90)\n", "plt.yticks(size=15)\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 10, "id": "2bbafdf2-a2bd-4034-a560-52c84801b498", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "exact expected value:\t0.4870\n" ] } ], "source": [ "# evaluate exact expected value\n", "sum_values = np.sum(u.values, axis=1)\n", "exact_value = np.dot(\n", " u.probabilities[sum_values >= strike_price],\n", " sum_values[sum_values >= strike_price] - strike_price,\n", ")\n", "print(\"exact expected value:\\t%.4f\" % exact_value)" ] }, { "cell_type": "code", "execution_count": 11, "id": "dee95c74-93b3-4730-a32f-71f2396a408f", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "state qubits: 5\n", "circuit width: 11\n", "circuit depth: 384\n" ] } ], "source": [ "num_state_qubits = basket_option.num_qubits - basket_option.num_ancillas\n", "print(\"state qubits: \", num_state_qubits)\n", "transpiled = transpile(basket_option, basis_gates=[\"u\", \"cx\"])\n", "print(\"circuit width:\", transpiled.width())\n", "print(\"circuit depth:\", transpiled.depth())" ] }, { "cell_type": "code", "execution_count": 12, "id": "c19dba7c-abe3-473b-af93-93547dad626d", "metadata": {}, "outputs": [], "source": [ "#\n", "# Note: The pub is encapsulated inside a [] in the call to the run method below.\n", "#\n", "\n", "basket_option_measure = basket_option.measure_all(inplace=False)\n", "sampler = Sampler(backend = qr_backend)\n", "job = sampler.run([basket_option_measure])" ] }, { "cell_type": "code", "execution_count": 13, "id": "6f1406d3-02ed-4bbb-8ae7-c511bb94aff0", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Exact Operator Value: 0.5127\n", "Mapped Operator value: 1.1321\n", "Exact Expected Payoff: 0.4870\n" ] } ], "source": [ "# Quasi distribution is not supported in SamplerV2\n", "# Here is a workaround\n", "from qiskit.result import QuasiDistribution\n", "result = job.result()\n", "pub_result = result[0]\n", "counts = pub_result.data.meas.get_counts()\n", "shots = 0\n", "for key, val in counts.items():\n", " shots += val\n", "quasi_dist = QuasiDistribution({outcome: freq / shots for outcome, freq in counts.items()})\n", "\n", "# evaluate the result\n", "value = 0\n", "probabilities = quasi_dist.binary_probabilities()\n", "for i, prob in probabilities.items():\n", " if prob > 1e-4 and i[-num_state_qubits:][0] == \"1\":\n", " value += prob\n", "\n", "\n", "# map value to original range\n", "mapped_value = (\n", " basket_objective.post_processing(value) / (2**num_uncertainty_qubits - 1) * (high_ - low_)\n", ")\n", "print(\"Exact Operator Value: %.4f\" % value)\n", "print(\"Mapped Operator value: %.4f\" % mapped_value)\n", "print(\"Exact Expected Payoff: %.4f\" % exact_value)" ] }, { "cell_type": "code", "execution_count": 14, "id": "36fe75d8-eb04-4fea-acdc-c5db9d532f34", "metadata": {}, "outputs": [], "source": [ "# Example output:\n", "\n", "# Exact Operator Value: 0.4678\n", "# Mapped Operator value: 0.8888\n", "# Exact Expected Payoff: 0.4870" ] }, { "cell_type": "code", "execution_count": 15, "id": "7157e4f0-defd-4ea7-81cb-6a919ff6684e", "metadata": {}, "outputs": [], "source": [ "# set target precision and confidence level\n", "epsilon = 0.01\n", "alpha = 0.05\n", "\n", "problem = EstimationProblem(\n", " state_preparation=basket_option,\n", " objective_qubits=[objective_index],\n", " post_processing=basket_objective.post_processing,\n", ")\n", "# construct amplitude estimation\n", "ae = IterativeAmplitudeEstimation(\n", " epsilon_target=epsilon, alpha=alpha, sampler=Sampler(backend = qr_backend, options={\"shots\": 100, \"seed\": 75})\n", ")" ] }, { "cell_type": "code", "execution_count": 16, "id": "d114af47-6e2c-4ddb-869b-395c171ee5a6", "metadata": {}, "outputs": [], "source": [ "result = ae.estimate(problem)" ] }, { "cell_type": "code", "execution_count": 17, "id": "031d2bce-10bb-486a-8057-31daf4a41df5", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Exact value: \t0.4870\n", "Estimated value: \t1.0218\n", "Confidence interval:\t[1.0089, 1.0346]\n" ] } ], "source": [ "conf_int = (\n", " np.array(result.confidence_interval_processed)\n", " / (2**num_uncertainty_qubits - 1)\n", " * (high_ - low_)\n", ")\n", "print(\"Exact value: \\t%.4f\" % exact_value)\n", "print(\n", " \"Estimated value: \\t%.4f\"\n", " % (result.estimation_processed / (2**num_uncertainty_qubits - 1) * (high_ - low_))\n", ")\n", "print(\"Confidence interval:\\t[%.4f, %.4f]\" % tuple(conf_int))" ] }, { "cell_type": "code", "execution_count": 18, "id": "6e30ac96-4c06-43de-8be7-17b7d8effab4", "metadata": {}, "outputs": [], "source": [ "# Example output:\n", "\n", "# Exact value: \t0.4870\n", "# Estimated value: \t1.0976\n", "# Confidence interval:\t[1.0698, 1.1254]" ] }, { "cell_type": "code", "execution_count": 19, "id": "fdb8fbb3-b35b-452f-88a4-7ad533bbbd9e", "metadata": {}, "outputs": [ { "data": { "text/html": [ "

Version Information

SoftwareVersion
qiskit2.2.1
qiskit_algorithms0.4.0
qiskit_ibm_runtime0.40.1
qiskit_aer0.17.1
qiskit_finance0.4.1
System information
Python version3.12.9
OSWindows
Thu Oct 16 11:19:11 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
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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" ] } ], "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 }