Portfolio-Optimization-Qiskit.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "b595754a",
   "metadata": {},
   "source": [
    "# Portfolio Optimization using Quantum Algorithms (VQE and QAOA)\n",
    "\n",
    "Currently, quantum computing hardware is limited by the number of qubits, connectivity, and a number of other factors. However, even with the current limitations, many problems can be solved with the small-scale hardware, by simulation, or by a combination of classical and quantum techniques. Among these techniques are two extremely promising algorithms, the Variational Quantum Eigensolver (VQE) and the Quantum Approximate Optimization Algorithm (QAOA) respectively.\n",
    "\n",
    "The VQE is derived from a technique in quantum mechanics – the [Variational Method](https://en.wikipedia.org/wiki/Variational_method_(quantum_mechanics)) – and is a way of approximating the lowest energy as well as its corresponding eigenstate for a system's Hamiltonian. However, this technique is not limited to just physics or quantum chemistry. \n",
    "\n",
    "These techniques can be applied to problems in other domains, like Finance, if the problem can be cast in ways that are amenable to the logic of quantum computers.\n",
    "\n",
    "To this end, the goal of this notebook is to\n",
    "1. Solve a portfolio optimization problem using quantum algorithms.\n",
    "2. Compare the Variational Quantum Eigensolver (VQE) to the Quantum Approximate Optimization Algorithm (QAOA)."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "80b588d4",
   "metadata": {},
   "source": [
    "## The Portfolio Optimization Formulation\n",
    "\n",
    "Before getting into the details of the VQE algorithm and QAOA respectively, the portfolio optimization problem will need to be defined. \n",
    "\n",
    "The form of this problem is adapted from [Improving Variational Quantum Optimization using CVaR (Barkoutsos et al. 2019).](https://arxiv.org/abs/1907.04769), where for $n$ assets that can be chosen from:\n",
    "$$\n",
    "\\begin{aligned}\n",
    "\\max_{x \\in \\{0, 1\\}^n} \\left( \\mu^T x - q x^T \\sigma x \\right)  \\\\\n",
    "\\text{subject to: } 1^T x = B .\n",
    "\\end{aligned}\n",
    "$$\n",
    "\n",
    "In this optimization problem:\n",
    "- $x \\in \\{0, 1\\}^n$ is the vector of binary decision variables, which indicate which assets to pick ($x[i] = 1$) and which not to pick ($x[i] = 0$),\n",
    "- $\\mu \\in \\mathbb{R}^n$ is the vector of means for the daily percent returns of each asset,\n",
    "- $\\sigma \\in \\mathbb{R}^{n \\times n}$ is the covariances matrix of the daily percent returns of the assets,\n",
    "- $q > 0$ is the risk factor,\n",
    "- $B$ is the budget, i.e. the number of assets to be selected out of $n$.\n",
    "\n",
    "We assume the following simplifications:\n",
    "- the full budget $B$ has to be spent, i.e. one has to select exactly $B$ assets.\n",
    "\n",
    "In order to make this problem more easily solved on a quantum computer, we can turn this into a quadratic unconstrained binary optimization (QUBO) problem. The equality constraint above, $1^T x = B$, is thus turned into a penalty by subtracting $(1^T x - B)^2$ scaled by a penalty parameter from the objective function. \n",
    "\n",
    "With the QUBO defined, we can program it and use qiskit to apply VQE and QAOA to solve for the optimal portfolio."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "7ef895ba",
   "metadata": {},
   "outputs": [],
   "source": [
    "# %pip install --upgrade pip\n",
    "# %pip install -r requirements.txt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "f72049ab",
   "metadata": {},
   "outputs": [],
   "source": [
    "import seaborn as sn\n",
    "import matplotlib.pyplot as plt\n",
    "from qiskit.visualization import plot_histogram\n",
    "from datetime import datetime\n",
    "import numpy as np\n",
    "from itertools import permutations\n",
    "\n",
    "from qiskit_finance.data_providers import YahooDataProvider\n",
    "import json # Necessary for YahooDataProvider\n",
    "import http.client # Necessary for YahooDataProvider\n",
    "\n",
    "import pandas as pd\n",
    "import pandas_datareader as web\n",
    "\n",
    "import os\n",
    "\n",
    "from docplex.mp.model import Model\n",
    "\n",
    "from qiskit_optimization.translators import from_docplex_mp\n",
    "from qiskit_optimization.algorithms import MinimumEigenOptimizer\n",
    "from qiskit.algorithms import NumPyMinimumEigensolver\n",
    "from qiskit_optimization.converters import LinearEqualityToPenalty\n",
    "\n",
    "from qiskit.circuit.library import TwoLocal # For Ansatz\n",
    "\n",
    "from qiskit.algorithms.optimizers import COBYLA, ADAM, NELDER_MEAD, POWELL, SPSA, QNSPSA\n",
    "from qiskit.opflow import CVaRExpectation\n",
    "from qiskit.opflow import PauliExpectation\n",
    "\n",
    "from qiskit.algorithms import VQE\n",
    "from qiskit.algorithms import QAOA\n",
    "\n",
    "from qiskit import Aer"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c3b64283",
   "metadata": {},
   "source": [
    "# Loading Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "27c7cc9e",
   "metadata": {},
   "outputs": [],
   "source": [
    "dfMonthlyReturns = pd.read_csv('data/Equity-Benchmarks-Monthly-Return.csv',parse_dates=[\"Date\"],index_col=0)\n",
    "dfMonthlyReturnsRiskScaled = pd.read_csv('data/Equity-Benchmarks-Monthly-Risk-Scaled.csv',parse_dates=[\"Date\"],index_col=0)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "747264d5",
   "metadata": {},
   "source": [
    "# Assets"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "fe148455",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "We have 8 Assets:\n",
      "\n",
      "Global_Equity  \n",
      "S&P500  \n",
      "US_Midcap  \n",
      "EAFE  \n",
      "Europe  \n",
      "Japan  \n",
      "Asia_Ex-Japan  \n",
      "Emerging_Markets  \n"
     ]
    }
   ],
   "source": [
    "assets = dfMonthlyReturns.columns.to_list()\n",
    "numAssets = len(assets)\n",
    "print(\"We have \" + str(numAssets) + \" Assets:\\n\")\n",
    "[print(asset + \"  \") for asset in assets];"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "94205d32",
   "metadata": {},
   "source": [
    "# Financial Data Inputs\n",
    "\n",
    "The list of assets we want to choose from is defined in the list `assets`. The budget `B` is the number of assets that are to be chosen. The risk factor is `q`. We also define the `startDate` and `endDate` that demarcate the start and end of the data that is extracted."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "1e008b88",
   "metadata": {},
   "outputs": [],
   "source": [
    "q = 0.5 # risk apetite\n",
    "B = 5 # budget\n",
    "\n",
    "#Whole Period\n",
    "startDate=datetime(2001, 1, 31)\n",
    "endDate=datetime(2021, 12, 31)\n",
    "\n",
    "# #Pre 2008\n",
    "# startDate=datetime(2001, 1, 31)\n",
    "# endDate=datetime(2008, 6, 30)\n",
    "\n",
    "# #QE Era\n",
    "# startDate=datetime(2010, 1, 31)\n",
    "# endDate=datetime(2019, 12, 31)\n",
    "\n",
    "# #Pandemic\n",
    "# startDate=datetime(2020, 6, 30)\n",
    "# endDate=datetime(2021, 12, 31)\n",
    "\n",
    "startStr = str(startDate.date())\n",
    "endStr = str(endDate.date())\n",
    "\n",
    "backend = Aer.get_backend('statevector_simulator') # statevector_simulator, qasm_simulator, aer_simulator_statevector\n",
    "\n",
    "maxIter = 10000\n",
    "# fidelity = QNSPSA.get_fidelity(ansatz) # only for QNSPSA\n",
    "optimizer = SPSA(maxiter=500)  \n",
    "\n",
    "# Classical optimizer – COBYLA(maxiter=maxIter), ADAM(maxiter=maxIter), NELDER_MEAD(maxiter=maxIter), \n",
    "# POWELL(maxiter=maxIter), SPSA(maxiter=100), QNSPSA(fidelity,maxiter=100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "307be16c",
   "metadata": {},
   "outputs": [],
   "source": [
    "penalty = numAssets # scaling of penalty term. This can be changed at your discretion."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "7a2a58d2",
   "metadata": {},
   "outputs": [],
   "source": [
    "mu = dfMonthlyReturns[startDate:endDate].mean().to_numpy()\n",
    "sigma = dfMonthlyReturns[startDate:endDate].cov().to_numpy()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "68deb525",
   "metadata": {},
   "outputs": [],
   "source": [
    "muRisk = dfMonthlyReturnsRiskScaled[startDate:endDate].mean().to_numpy()\n",
    "sigmaRisk = dfMonthlyReturnsRiskScaled[startDate:endDate].cov().to_numpy()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "930ef0b9",
   "metadata": {},
   "source": [
    "It is good to visualize the data along the way as a sanity check, and to apply your insight on the role of the covariance matrix in portfolio optimization problems."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "32656d62",
   "metadata": {},
   "outputs": [
    {
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",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "covHeatmap = sn.heatmap(sigma,cmap=\"mako\")\n",
    "covHeatmap.set(xticklabels=assets,yticklabels=assets)\n",
    "plt.yticks(rotation='horizontal')\n",
    "plt.xticks(rotation='vertical')\n",
    "plt.title(\"Covariance of Monthly Returns\\n\"+startStr+\" to \" +endStr)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "0f232479",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "covHeatmapRisk = sn.heatmap(sigmaRisk,cmap=\"mako\")\n",
    "covHeatmapRisk.set(xticklabels=assets,yticklabels=assets)\n",
    "plt.yticks(rotation='horizontal')\n",
    "plt.xticks(rotation='vertical')\n",
    "plt.title(\"Covariance of Monthly Returns (Risk Scaled)\\n\"+startStr+\" to \" +endStr)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d37be95e",
   "metadata": {},
   "source": [
    "Better to compare these values at similar scales. \n",
    "\n",
    "For the non risk-scaled data use `vmin=0,vmax=0.004` while for the risk-scaled data use `vmin=0,vmax=0.00011`.\n",
    "\n",
    "To comapare all at the same scale, use `vmin=0,vmax=0.004`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "62ab07ed",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "covHeatmap = sn.heatmap(sigma,cmap=\"mako\",vmin=0,vmax=0.004)\n",
    "covHeatmap.set(xticklabels=assets,yticklabels=assets)\n",
    "plt.yticks(rotation='horizontal')\n",
    "plt.xticks(rotation='vertical')\n",
    "plt.title(\"Covariance of Monthly Returns\\n\"+startStr+\" to \" +endStr)\n",
    "plt.show()\n",
    "\n",
    "fig = covHeatmap.get_figure()\n",
    "fig.savefig(\"figures/CovarianceMonthlyReturns-\" + startStr + \"-to-\" + endStr + \".pdf\",bbox_inches='tight')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "b8c3347b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "covHeatmapRisk = sn.heatmap(sigmaRisk,cmap=\"mako\",vmin=0,vmax=0.00011)\n",
    "covHeatmapRisk.set(xticklabels=assets,yticklabels=assets)\n",
    "plt.yticks(rotation='horizontal')\n",
    "plt.xticks(rotation='vertical')\n",
    "plt.title(\"Covariance of Monthly Returns (Risk Scaled)\\n\"+startStr+\" to \" +endStr)\n",
    "plt.show()\n",
    "\n",
    "figRisk = covHeatmapRisk.get_figure()\n",
    "figRisk.savefig(\"figures/CovarianceMonthlyReturnsRisk-\" + startStr + \"-to-\" + endStr + \".pdf\",bbox_inches='tight')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "11623f0c",
   "metadata": {},
   "source": [
    "## QUBO Model Ising DOcplex\n",
    "\n",
    "IBM's DOcplex is a native Python modeling library for optimization. You can read more and find examples in the documentation [here](http://ibmdecisionoptimization.github.io/docplex-doc/).\n",
    "\n",
    "We will be using DOcplex to construct the quadratic program the specifications in the introduction, as it is compatible with pandas, numpy, and qiskit."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "e9f48cb1",
   "metadata": {},
   "outputs": [],
   "source": [
    "mdl = Model(\"Non-Scaled\") # You can input a string into the argument if you want to name the model.\n",
    "\n",
    "x = mdl.binary_var_list('x{}'.format(i) for i in range(numAssets)) # binary decision variables\n",
    "\n",
    "# Objective Function to be maximized\n",
    "objective = mdl.sum([mu[i]*x[i] for i in range(numAssets)])\n",
    "objective -= q * mdl.sum([sigma[i,j]*x[i]*x[j] for i in range(numAssets) for j in range(numAssets)])\n",
    "\n",
    "mdl.maximize(objective)\n",
    "mdl.add_constraint(mdl.sum(x[i] for i in range(numAssets)) == B) # Adding the budget constraint\n",
    "\n",
    "qp = from_docplex_mp(mdl) # Conversion to a quadratic program"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "abb33a2e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<QuadraticProgram: maximize -0.001021802031556314*x0^2 - 0.001875584261051034*..., 8 variables, 1 constraints, 'Non-Scaled'>"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qp"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "7914b187",
   "metadata": {},
   "outputs": [],
   "source": [
    "mdlRisk = Model(\"Risk-Scaled\") # You can input a string into the argument if you want to name the model.\n",
    "\n",
    "y = mdlRisk.binary_var_list('y{}'.format(i) for i in range(numAssets)) # binary decision variables\n",
    "\n",
    "# Objective Function to be maximized\n",
    "objectiveRisk = mdlRisk.sum([muRisk[i]*y[i] for i in range(numAssets)])\n",
    "objectiveRisk -= q * mdlRisk.sum([sigmaRisk[i,j]*y[i]*y[j] for i in range(numAssets) for j in range(numAssets)])\n",
    "\n",
    "mdlRisk.maximize(objectiveRisk)\n",
    "mdlRisk.add_constraint(mdlRisk.sum(y[i] for i in range(numAssets)) == B) # Adding the budget constraint\n",
    "\n",
    "qpRisk = from_docplex_mp(mdlRisk) # Conversion to a quadratic program"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "207bc0af",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<QuadraticProgram: maximize -4.987133837665211e-05*y0^2 - 9.594932713590086e-0..., 8 variables, 1 constraints, 'Risk-Scaled'>"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qpRisk"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "858006f9",
   "metadata": {},
   "source": [
    "## Classical Solution\n",
    "\n",
    "NOTE THAT THE DICT LABELS FOR PLOTTING ARE REVERSED FROM THE EIGENVECTOR LABELS\n",
    "\n",
    "Now we can solve the quadratic program `qp` classically as a reference before we convert the quadratic program to a QUBO and solve using the quantum algorithms."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "53e8d4e9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<MinimumEigenOptimizationResult: fval=0.012498444875498012, x0=1.0, x1=1.0, x2=1.0, x3=0.0, x4=0.0, x5=1.0, x6=1.0, x7=0.0, status=SUCCESS>"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "classicalResult = MinimumEigenOptimizer(NumPyMinimumEigensolver()).solve(qp)\n",
    "# classicalResultEigenstate = (classicalResult.min_eigen_solver_result.eigenstate._primitive.data.real).tolist()\n",
    "classicalResultEigenstate = classicalResult.min_eigen_solver_result.eigenstate.to_dict_fn().primitive\n",
    "classicalResult"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "fce76ef0",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "c:\\Users\\anish\\AppData\\Local\\Programs\\Python\\Python310\\lib\\site-packages\\qiskit\\visualization\\counts_visualization.py:303: ComplexWarning: Casting complex values to real discards the imaginary part\n",
      "  values = np.array(values, dtype=float)\n"
     ]
    }
   ],
   "source": [
    "# making the labels for plotting\n",
    "# labels = []\n",
    "# for i in range(2**numAssets):\n",
    "#     labels.append(format(i,'0'+str(numAssets)+'b'))\n",
    "# fig = plot_histogram(dict(zip(labels, classicalResultEigenstate)),figsize=(60,10))\n",
    "fig = plot_histogram(classicalResultEigenstate,figsize=(60,10))\n",
    "fig.savefig(\"figures/ClassicalEigensolver-\"+startStr+\"-\"+endStr+\".pdf\")\n",
    "# fig"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "ad3600e5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<MinimumEigenOptimizationResult: fval=0.00697634125569152, y0=1.0, y1=1.0, y2=1.0, y3=0.0, y4=0.0, y5=0.0, y6=1.0, y7=1.0, status=SUCCESS>"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "classicalResultRisk = MinimumEigenOptimizer(NumPyMinimumEigensolver()).solve(qpRisk)\n",
    "#classicalResultRiskEigenstate = (classicalResultRisk.min_eigen_solver_result.eigenstate._primitive.data.real).tolist()\n",
    "classicalResultRiskEigenstate = classicalResultRisk.min_eigen_solver_result.eigenstate.to_dict_fn().primitive\n",
    "classicalResultRisk\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "975d4900",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "c:\\Users\\anish\\AppData\\Local\\Programs\\Python\\Python310\\lib\\site-packages\\qiskit\\visualization\\counts_visualization.py:303: ComplexWarning: Casting complex values to real discards the imaginary part\n",
      "  values = np.array(values, dtype=float)\n"
     ]
    }
   ],
   "source": [
    "# making the labels for plotting\n",
    "# labels = []\n",
    "# for i in range(2**numAssets):\n",
    "#     labels.append(format(i,'0'+str(numAssets)+'b'))\n",
    "# fig = plot_histogram(dict(zip(labels, classicalResultRiskEigenstate)),figsize=(60,10))\n",
    "fig = plot_histogram(classicalResultRiskEigenstate,figsize=(60,10))\n",
    "fig.savefig(\"figures/ClassicalEigensolverRisk-\"+startStr+\"-\"+endStr+\".pdf\")\n",
    "# fig"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1ab086cc",
   "metadata": {},
   "source": [
    "A clear result."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2e7745c4",
   "metadata": {},
   "source": [
    "## Converting Quadratic Program into QUBO\n",
    "Conversion to a QUBO is quite simple, and is necessary to be put into the qiskit functions for VQE and QAOA."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "e0148053",
   "metadata": {},
   "outputs": [],
   "source": [
    "linearToPenalty = LinearEqualityToPenalty(penalty=penalty)\n",
    "qubo = linearToPenalty.convert(qp)\n",
    "quboRisk = linearToPenalty.convert(qpRisk)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "0575908f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<QuadraticProgram: maximize -8.001021802031556*x0^2 - 16.00187558426105*x0*x1 ..., 8 variables, 0 constraints, 'Non-Scaled'>"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qubo"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "1ee6be86",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<QuadraticProgram: maximize -8.000049871338376*y0^2 - 16.000095949327136*y0*y1..., 8 variables, 0 constraints, 'Risk-Scaled'>"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "quboRisk"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5e0e05a2",
   "metadata": {},
   "source": [
    "## Ansatz\n",
    "\n",
    "The choice of the Ansatz, or variational wavefuction, is extremely important to the accuracy of the results. From the variational theory, the closer the wavefunction is to the ground state, the better result will be retrieved from the algorithm. Appropriate variational forms are an active area of research, and the choice becomes more difficult when the number of qubits and gates are limited. \n",
    "\n",
    "The one used in this work is touched upon in [this paper](https://arxiv.org/pdf/2106.07619.pdf). It takes a simple form, ie a series of rotation gates followed by entanglements between the qubits. This is then repeated in several layers. The number of repetitions is a choice of the user, but generally the more layers there are, the better the variational form will be. But as a reminder, there is a practical hardware limit that needs to be considered.\n",
    "\n",
    "We'll now define and visualize this Ansatz."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "3b02350b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<pre style=\"word-wrap: normal;white-space: pre;background: #fff0;line-height: 1.1;font-family: &quot;Courier New&quot;,Courier,monospace\">     ┌──────────┐                                                ┌──────────┐»\n",
       "q_0: ┤ Rx(θ[0]) ├─■──■─────■─────■────────■────────■───────────■─┤ Rx(θ[8]) ├»\n",
       "     ├──────────┤ │  │     │     │        │        │           │ └──────────┘»\n",
       "q_1: ┤ Rx(θ[1]) ├─■──┼──■──┼──■──┼─────■──┼─────■──┼────────■──┼─────────────»\n",
       "     ├──────────┤    │  │  │  │  │     │  │     │  │        │  │             »\n",
       "q_2: ┤ Rx(θ[2]) ├────■──■──┼──┼──┼──■──┼──┼──■──┼──┼─────■──┼──┼─────────────»\n",
       "     ├──────────┤          │  │  │  │  │  │  │  │  │     │  │  │             »\n",
       "q_3: ┤ Rx(θ[3]) ├──────────■──■──┼──■──┼──┼──┼──┼──┼──■──┼──┼──┼──────■──────»\n",
       "     ├──────────┤                │     │  │  │  │  │  │  │  │  │      │      »\n",
       "q_4: ┤ Rx(θ[4]) ├────────────────■─────■──┼──■──┼──┼──■──┼──┼──┼──────┼──────»\n",
       "     ├──────────┤                         │     │  │     │  │  │      │      »\n",
       "q_5: ┤ Rx(θ[5]) ├─────────────────────────■─────■──┼─────■──┼──┼──────■──────»\n",
       "     ├──────────┤                                  │        │  │             »\n",
       "q_6: ┤ Rx(θ[6]) ├──────────────────────────────────■────────■──┼─────────────»\n",
       "     ├──────────┤                                              │             »\n",
       "q_7: ┤ Rx(θ[7]) ├──────────────────────────────────────────────■─────────────»\n",
       "     └──────────┘                                                            »\n",
       "«                                                                          »\n",
       "«q_0: ───────────────────■──────────────────■───────────────■──────────────»\n",
       "«           ┌──────────┐ │                  │               │              »\n",
       "«q_1: ────■─┤ Rx(θ[9]) ├─■──────────────────┼───────■───────┼───────■──────»\n",
       "«         │ └──────────┘      ┌───────────┐ │       │       │       │      »\n",
       "«q_2: ─■──┼─────────────────■─┤ Rx(θ[10]) ├─■───────■───────┼───────┼──────»\n",
       "«      │  │                 │ └───────────┘   ┌───────────┐ │       │      »\n",
       "«q_3: ─┼──┼──────────────■──┼───────────────■─┤ Rx(θ[11]) ├─■───────■──────»\n",
       "«      │  │              │  │               │ └───────────┘   ┌───────────┐»\n",
       "«q_4: ─┼──┼──────■───────┼──┼───────■───────┼───────────────■─┤ Rx(θ[12]) ├»\n",
       "«      │  │      │       │  │       │       │               │ └───────────┘»\n",
       "«q_5: ─┼──┼──────■───────┼──┼───────┼───────┼───────■───────┼───────■──────»\n",
       "«      │  │              │  │       │       │       │       │       │      »\n",
       "«q_6: ─■──┼──────────────■──┼───────■───────┼───────■───────┼───────┼──────»\n",
       "«         │                 │               │               │       │      »\n",
       "«q_7: ────■─────────────────■───────────────■───────────────■───────■──────»\n",
       "«                                                                          »\n",
       "«                                                          ┌───────────┐      »\n",
       "«q_0: ──────■───────────────────────■────────■───────────■─┤ Rx(θ[16]) ├──────»\n",
       "«           │                       │        │           │ └───────────┘      »\n",
       "«q_1: ──────┼────────────────────■──┼─────■──┼────────■──┼──────────────────■─»\n",
       "«           │                    │  │     │  │        │  │                  │ »\n",
       "«q_2: ──────┼────────────■───────┼──┼──■──┼──┼─────■──┼──┼───────────────■──┼─»\n",
       "«           │            │       │  │  │  │  │     │  │  │               │  │ »\n",
       "«q_3: ──────┼────────────■───────┼──┼──┼──┼──┼──■──┼──┼──┼───────■───────┼──┼─»\n",
       "«           │                    │  │  │  │  │  │  │  │  │       │       │  │ »\n",
       "«q_4: ──────■────────────────────■──┼──■──┼──┼──■──┼──┼──┼───────┼───────┼──┼─»\n",
       "«     ┌───────────┐                 │     │  │     │  │  │       │       │  │ »\n",
       "«q_5: ┤ Rx(θ[13]) ├─────────────────■─────■──┼─────■──┼──┼───────■───────┼──┼─»\n",
       "«     └───────────┘┌───────────┐             │        │  │               │  │ »\n",
       "«q_6: ──────■──────┤ Rx(θ[14]) ├─────────────■────────■──┼───────────────■──┼─»\n",
       "«           │      ├───────────┤                         │                  │ »\n",
       "«q_7: ──────■──────┤ Rx(θ[15]) ├─────────────────────────■──────────────────■─»\n",
       "«                  └───────────┘                                              »\n",
       "«                                                                     »\n",
       "«q_0: ────────────────────────────────────────────────────────────────»\n",
       "«     ┌───────────┐                                                   »\n",
       "«q_1: ┤ Rx(θ[17]) ├───────────────────────────────────────────────────»\n",
       "«     └───────────┘      ┌───────────┐                                »\n",
       "«q_2: ─────────────────■─┤ Rx(θ[18]) ├────────────────────────────────»\n",
       "«                      │ └───────────┘   ┌───────────┐                »\n",
       "«q_3: ──────────────■──┼───────────────■─┤ Rx(θ[19]) ├────────────────»\n",
       "«                   │  │               │ └───────────┘   ┌───────────┐»\n",
       "«q_4: ──────■───────┼──┼───────■───────┼───────────────■─┤ Rx(θ[20]) ├»\n",
       "«           │       │  │       │       │               │ └───────────┘»\n",
       "«q_5: ──────■───────┼──┼───────┼───────┼───────■───────┼───────■──────»\n",
       "«                   │  │       │       │       │       │       │      »\n",
       "«q_6: ──────────────■──┼───────■───────┼───────■───────┼───────┼──────»\n",
       "«                      │               │               │       │      »\n",
       "«q_7: ─────────────────■───────────────■───────────────■───────■──────»\n",
       "«                                                                     »\n",
       "«                               \n",
       "«q_0: ──────────────────────────\n",
       "«                               \n",
       "«q_1: ──────────────────────────\n",
       "«                               \n",
       "«q_2: ──────────────────────────\n",
       "«                               \n",
       "«q_3: ──────────────────────────\n",
       "«                               \n",
       "«q_4: ──────────────────────────\n",
       "«     ┌───────────┐             \n",
       "«q_5: ┤ Rx(θ[21]) ├─────────────\n",
       "«     └───────────┘┌───────────┐\n",
       "«q_6: ──────■──────┤ Rx(θ[22]) ├\n",
       "«           │      ├───────────┤\n",
       "«q_7: ──────■──────┤ Rx(θ[23]) ├\n",
       "«                  └───────────┘</pre>"
      ],
      "text/plain": [
       "     ┌──────────┐                                                ┌──────────┐»\n",
       "q_0: ┤ Rx(θ[0]) ├─■──■─────■─────■────────■────────■───────────■─┤ Rx(θ[8]) ├»\n",
       "     ├──────────┤ │  │     │     │        │        │           │ └──────────┘»\n",
       "q_1: ┤ Rx(θ[1]) ├─■──┼──■──┼──■──┼─────■──┼─────■──┼────────■──┼─────────────»\n",
       "     ├──────────┤    │  │  │  │  │     │  │     │  │        │  │             »\n",
       "q_2: ┤ Rx(θ[2]) ├────■──■──┼──┼──┼──■──┼──┼──■──┼──┼─────■──┼──┼─────────────»\n",
       "     ├──────────┤          │  │  │  │  │  │  │  │  │     │  │  │             »\n",
       "q_3: ┤ Rx(θ[3]) ├──────────■──■──┼──■──┼──┼──┼──┼──┼──■──┼──┼──┼──────■──────»\n",
       "     ├──────────┤                │     │  │  │  │  │  │  │  │  │      │      »\n",
       "q_4: ┤ Rx(θ[4]) ├────────────────■─────■──┼──■──┼──┼──■──┼──┼──┼──────┼──────»\n",
       "     ├──────────┤                         │     │  │     │  │  │      │      »\n",
       "q_5: ┤ Rx(θ[5]) ├─────────────────────────■─────■──┼─────■──┼──┼──────■──────»\n",
       "     ├──────────┤                                  │        │  │             »\n",
       "q_6: ┤ Rx(θ[6]) ├──────────────────────────────────■────────■──┼─────────────»\n",
       "     ├──────────┤                                              │             »\n",
       "q_7: ┤ Rx(θ[7]) ├──────────────────────────────────────────────■─────────────»\n",
       "     └──────────┘                                                            »\n",
       "«                                                                          »\n",
       "«q_0: ───────────────────■──────────────────■───────────────■──────────────»\n",
       "«           ┌──────────┐ │                  │               │              »\n",
       "«q_1: ────■─┤ Rx(θ[9]) ├─■──────────────────┼───────■───────┼───────■──────»\n",
       "«         │ └──────────┘      ┌───────────┐ │       │       │       │      »\n",
       "«q_2: ─■──┼─────────────────■─┤ Rx(θ[10]) ├─■───────■───────┼───────┼──────»\n",
       "«      │  │                 │ └───────────┘   ┌───────────┐ │       │      »\n",
       "«q_3: ─┼──┼──────────────■──┼───────────────■─┤ Rx(θ[11]) ├─■───────■──────»\n",
       "«      │  │              │  │               │ └───────────┘   ┌───────────┐»\n",
       "«q_4: ─┼──┼──────■───────┼──┼───────■───────┼───────────────■─┤ Rx(θ[12]) ├»\n",
       "«      │  │      │       │  │       │       │               │ └───────────┘»\n",
       "«q_5: ─┼──┼──────■───────┼──┼───────┼───────┼───────■───────┼───────■──────»\n",
       "«      │  │              │  │       │       │       │       │       │      »\n",
       "«q_6: ─■──┼──────────────■──┼───────■───────┼───────■───────┼───────┼──────»\n",
       "«         │                 │               │               │       │      »\n",
       "«q_7: ────■─────────────────■───────────────■───────────────■───────■──────»\n",
       "«                                                                          »\n",
       "«                                                          ┌───────────┐      »\n",
       "«q_0: ──────■───────────────────────■────────■───────────■─┤ Rx(θ[16]) ├──────»\n",
       "«           │                       │        │           │ └───────────┘      »\n",
       "«q_1: ──────┼────────────────────■──┼─────■──┼────────■──┼──────────────────■─»\n",
       "«           │                    │  │     │  │        │  │                  │ »\n",
       "«q_2: ──────┼────────────■───────┼──┼──■──┼──┼─────■──┼──┼───────────────■──┼─»\n",
       "«           │            │       │  │  │  │  │     │  │  │               │  │ »\n",
       "«q_3: ──────┼────────────■───────┼──┼──┼──┼──┼──■──┼──┼──┼───────■───────┼──┼─»\n",
       "«           │                    │  │  │  │  │  │  │  │  │       │       │  │ »\n",
       "«q_4: ──────■────────────────────■──┼──■──┼──┼──■──┼──┼──┼───────┼───────┼──┼─»\n",
       "«     ┌───────────┐                 │     │  │     │  │  │       │       │  │ »\n",
       "«q_5: ┤ Rx(θ[13]) ├─────────────────■─────■──┼─────■──┼──┼───────■───────┼──┼─»\n",
       "«     └───────────┘┌───────────┐             │        │  │               │  │ »\n",
       "«q_6: ──────■──────┤ Rx(θ[14]) ├─────────────■────────■──┼───────────────■──┼─»\n",
       "«           │      ├───────────┤                         │                  │ »\n",
       "«q_7: ──────■──────┤ Rx(θ[15]) ├─────────────────────────■──────────────────■─»\n",
       "«                  └───────────┘                                              »\n",
       "«                                                                     »\n",
       "«q_0: ────────────────────────────────────────────────────────────────»\n",
       "«     ┌───────────┐                                                   »\n",
       "«q_1: ┤ Rx(θ[17]) ├───────────────────────────────────────────────────»\n",
       "«     └───────────┘      ┌───────────┐                                »\n",
       "«q_2: ─────────────────■─┤ Rx(θ[18]) ├────────────────────────────────»\n",
       "«                      │ └───────────┘   ┌───────────┐                »\n",
       "«q_3: ──────────────■──┼───────────────■─┤ Rx(θ[19]) ├────────────────»\n",
       "«                   │  │               │ └───────────┘   ┌───────────┐»\n",
       "«q_4: ──────■───────┼──┼───────■───────┼───────────────■─┤ Rx(θ[20]) ├»\n",
       "«           │       │  │       │       │               │ └───────────┘»\n",
       "«q_5: ──────■───────┼──┼───────┼───────┼───────■───────┼───────■──────»\n",
       "«                   │  │       │       │       │       │       │      »\n",
       "«q_6: ──────────────■──┼───────■───────┼───────■───────┼───────┼──────»\n",
       "«                      │               │               │       │      »\n",
       "«q_7: ─────────────────■───────────────■───────────────■───────■──────»\n",
       "«                                                                     »\n",
       "«                               \n",
       "«q_0: ──────────────────────────\n",
       "«                               \n",
       "«q_1: ──────────────────────────\n",
       "«                               \n",
       "«q_2: ──────────────────────────\n",
       "«                               \n",
       "«q_3: ──────────────────────────\n",
       "«                               \n",
       "«q_4: ──────────────────────────\n",
       "«     ┌───────────┐             \n",
       "«q_5: ┤ Rx(θ[21]) ├─────────────\n",
       "«     └───────────┘┌───────────┐\n",
       "«q_6: ──────■──────┤ Rx(θ[22]) ├\n",
       "«           │      ├───────────┤\n",
       "«q_7: ──────■──────┤ Rx(θ[23]) ├\n",
       "«                  └───────────┘"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "reps = 2\n",
    "\n",
    "ansatz = TwoLocal(num_qubits=numAssets, rotation_blocks='rx', entanglement_blocks= 'cz', reps=reps, entanglement='full')\n",
    "ansatz.decompose().draw()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "456167f1",
   "metadata": {},
   "source": [
    "## Classical Optimizer Choice\n",
    "Both the VQE Algorithm and QAOA are hybrid algorithms, and thus care needs to be put into what classical optimizer is chosen. All of then availabile optimizers in qiskit may be found [here](https://qiskit.org/documentation/stubs/qiskit.algorithms.optimizers.html). \n",
    "\n",
    "If you are going to be using a Quantum ASseMbly Language (QASM) simulator, then the qiskit-recommended optimizer is SPSA, which stands for Simultaneous Perturbation Stochastic Approximation. You can read more about it [here](https://www.jhuapl.edu/SPSA/). If you want quicker results, you can test out the COBYLA and the POWELL optimizers, or a number of others."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "29969083",
   "metadata": {},
   "outputs": [],
   "source": [
    "maxIter = 10000\n",
    "# fidelity = QNSPSA.get_fidelity(ansatz) # only for QNSPSA\n",
    "optimizer = SPSA(maxiter=500)  \n",
    "\n",
    "# Classical optimizer – COBYLA(maxiter=maxIter), ADAM(maxiter=maxIter), NELDER_MEAD(maxiter=maxIter), \n",
    "# POWELL(maxiter=maxIter), SPSA(maxiter=100), QNSPSA(fidelity,maxiter=100)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "263f0983",
   "metadata": {},
   "source": [
    "## Variational Quantum Eigensolver\n",
    "\n",
    "Now that we've set up the QUBO, we can go over the VQE algorithm in greater detail. \n",
    "\n",
    "### Variational Method\n",
    "\n",
    "The goal of the Variational Method in quantum mechanics is to find the minimum eneregy (eigenvalue) of the Hamiltonian  (a matrix that captures the energetics of a system). We'll go over\n",
    "\n",
    "For some Hamiltonian $H$ there exists some true ground state wavefunction $\\left| \\psi_0 \\right\\rangle$ such that\n",
    "\n",
    "$$\n",
    "\\left\\langle \\psi_0 \\right| H \\left| \\psi_0 \\right\\rangle = \\left\\langle \\psi_0 \\right| E_0 \\left| \\psi_0 \\right\\rangle = E_0 \\left\\langle \\psi_0 \\right| \\left. \\psi_0 \\right\\rangle = E_0\n",
    "$$\n",
    "\n",
    "where $E_0$ is the ground state energy, or minimum eigenvalue of $H$. \n",
    "\n",
    "However, there are cases where we want to calculate the minimum energy, but don't know the true ground state wavefunction. However, we know that because the lowest energy corresponds to only the ground state wavefunction, and that any other wavefunction will yield an expectation value with some higher energy, ie\n",
    "\n",
    "$$\n",
    "\\left\\langle \\psi \\right| H \\left| \\psi \\right\\rangle = \\left\\langle \\psi \\right| E \\left| \\psi \\right\\rangle = E \\left\\langle \\psi \\right| \\left. \\psi \\right\\rangle = E\n",
    "\\\\\n",
    "E > E_0\n",
    "$$\n",
    "\n",
    "Now, if the wavefunction is parametrized by some parameter(s) $\\left\\lbrace\\theta_i\\right\\rbrace$, ie $\\left| \\psi \\left( \\theta \\right) \\right\\rangle$, then an optimal set of variational parameters can be found that minimizes the energy as an approximation to the true ground state energy. That is,\n",
    "\n",
    "\n",
    "$$\n",
    "E = \\left\\langle \\psi \\left( \\left\\lbrace\\theta_i\\right\\rbrace \\right) \\right| H \\left| \\psi \\left( \\left\\lbrace\\theta_i\\right\\rbrace \\right) \\right\\rangle \\geq E_0\n",
    "$$\n",
    "\n",
    "\n",
    "The VQE algorithm applies this method to allow a quantum computer prepare an Ansatz with some parameters, denoted by $\\Psi \\left\\lbrace\\theta_i\\right\\rbrace $, which is then the expectation value of the Hamiltonian that represents the problem. From here, the parameters are incrementally changed and optimized classically, and then re-input into the next iteration of the quantum circuit. This is then repeated until convergence and until the minimum energy and optimal parameters are found."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4631761e",
   "metadata": {},
   "source": [
    "### Hamiltonian\n",
    "\n",
    "It is worthwhile to see the form of the Hamiltonian that corresponds to the QUBO problem, and see what the qiskit functions will be doing."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "5128b6c8",
   "metadata": {},
   "outputs": [],
   "source": [
    "def pauliDict(H):\n",
    "    tempKey = [] \n",
    "    tempVal = [] \n",
    "    tempDict = {}\n",
    "    for i in range(len(H)):\n",
    "        tempDict[H.primitive.to_list()[i][0]] = H.primitive.to_list()[i][1]\n",
    "    return tempDict"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "5e991b62",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'IIIIIIIZ': (7.999102285620301+0j),\n",
       " 'IIIIIIZI': (8.000185504375825+0j),\n",
       " 'IIIIIZII': (8.000402701273526+0j),\n",
       " 'IIIIZIII': (7.998233555542274+0j),\n",
       " 'IIIZIIII': (7.998048050756703+0j),\n",
       " 'IIZIIIII': (7.998846265758079+0j),\n",
       " 'IZIIIIII': (7.999592097197871+0j),\n",
       " 'ZIIIIIII': (7.99930588469096+0j),\n",
       " 'IIIIIIZZ': (4.000468896065263+0j),\n",
       " 'IIIIIZIZ': (4.000525045220625+0j),\n",
       " 'IIIIIZZI': (4.000505350089167+0j),\n",
       " 'IIIIZIIZ': (4.000524850405837+0j),\n",
       " 'IIIIZIZI': (4.00045329928524+0j),\n",
       " 'IIIIZZII': (4.000516082733194+0j),\n",
       " 'IIIZIIIZ': (4.000572980689544+0j),\n",
       " 'IIIZIIZI': (4.000500502511857+0j),\n",
       " 'IIIZIZII': (4.000561571626628+0j),\n",
       " 'IIIZZIII': (4.000628448502814+0j),\n",
       " 'IIZIIIIZ': (4.000357954598115+0j),\n",
       " 'IIZIIIZI': (4.000295595228609+0j),\n",
       " 'IIZIIZII': (4.000352205919496+0j),\n",
       " 'IIZIZIII': (4.000414871777019+0j),\n",
       " 'IIZZIIII': (4.000390829562385+0j),\n",
       " 'IZIIIIIZ': (4.0005546408172075+0j),\n",
       " 'IZIIIIZI': (4.000463805917757+0j),\n",
       " 'IZIIIZII': (4.000549222659837+0j),\n",
       " 'IZIIZIII': (4.000571834917947+0j),\n",
       " 'IZIZIIII': (4.000606325396509+0j),\n",
       " 'IZZIIIII': (4.000393306086131+0j),\n",
       " 'ZIIIIIIZ': (4.000604270964159+0j),\n",
       " 'ZIIIIIZI': (4.000502492708215+0j),\n",
       " 'ZIIIIZII': (4.000597921363395+0j),\n",
       " 'ZIIIZIII': (4.000628247109814+0j),\n",
       " 'ZIIZIIII': (4.000668848280647+0j),\n",
       " 'ZIZIIIII': (4.000433115872857+0j),\n",
       " 'ZZIIIIII': (4.000869418397363+0j)}"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "H, offset = qubo.to_ising()\n",
    "pauliDict(H)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "5109110f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'IIIIIIIZ': (8.000530928340686+0j),\n",
       " 'IIIIIIZI': (8.00071996693891+0j),\n",
       " 'IIIIIZII': (8.000765219981977+0j),\n",
       " 'IIIIZIII': (8.000351397286332+0j),\n",
       " 'IIIZIIII': (8.00033137468673+0j),\n",
       " 'IIZIIIII': (8.000303088687861+0j),\n",
       " 'IZIIIIII': (8.000598879884034+0j),\n",
       " 'ZIIIIIII': (8.000576856368102+0j),\n",
       " 'IIIIIIZZ': (4.000023987331784+0j),\n",
       " 'IIIIIZIZ': (4.000023452159299+0j),\n",
       " 'IIIIIZZI': (4.0000236545429395+0j),\n",
       " 'IIIIZIIZ': (4.0000240992640945+0j),\n",
       " 'IIIIZIZI': (4.000021816027003+0j),\n",
       " 'IIIIZZII': (4.000021688365901+0j),\n",
       " 'IIIZIIIZ': (4.000023826161504+0j),\n",
       " 'IIIZIIZI': (4.0000218141843735+0j),\n",
       " 'IIIZIZII': (4.000021370487415+0j),\n",
       " 'IIIZZIII': (4.0000245907908445+0j),\n",
       " 'IIZIIIIZ': (4.000017723329263+0j),\n",
       " 'IIZIIIZI': (4.000015349652501+0j),\n",
       " 'IIZIIZII': (4.000015968711661+0j),\n",
       " 'IIZIZIII': (4.000019340371806+0j),\n",
       " 'IIZZIIII': (4.000016496044117+0j),\n",
       " 'IZIIIIIZ': (4.00002092678939+0j),\n",
       " 'IZIIIIZI': (4.000018345454848+0j),\n",
       " 'IZIIIZII': (4.000018966217036+0j),\n",
       " 'IZIIZIII': (4.000020299923284+0j),\n",
       " 'IZIZIIII': (4.000019489310733+0j),\n",
       " 'IZZIIIII': (4.000015059442349+0j),\n",
       " 'ZIIIIIIZ': (4.000021827303998+0j),\n",
       " 'ZIIIIIZI': (4.000019026414343+0j),\n",
       " 'ZIIIIZII': (4.000019771074275+0j),\n",
       " 'ZIIIZIII': (4.000021354282513+0j),\n",
       " 'ZIIZIIII': (4.000020585303429+0j),\n",
       " 'ZIZIIIII': (4.000015874668113+0j),\n",
       " 'ZZIIIIII': (4.000024282999075+0j)}"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "HRisk, offsetRisk = quboRisk.to_ising()\n",
    "pauliDict(HRisk)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c550b1b2",
   "metadata": {},
   "source": [
    "The Hamiltonian is the sum of the spin operators in the above dictionary, weighted by the corresponding coefficients. \n",
    "\n",
    "Note that this Hamiltonian takes the form of spin operators, which lends itself extremely well to quantum computers. In particular, spin operators can be directly hard-coded into quantum ciruits, and thus their expectation value can be measured."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "29ccc1f6",
   "metadata": {},
   "source": [
    "### Qiskit Implementation of VQE\n",
    "\n",
    "With the information above, one can build the circuits from scratch. However, one of the nice features of qiskit is that it has built in functions that can build them for us."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "27e0b124",
   "metadata": {},
   "outputs": [],
   "source": [
    "def getCountDictStateVecSim(vqeResult):\n",
    "    tempState = []\n",
    "    tempProb = []\n",
    "    for sample in vqeResult.samples:\n",
    "        tempProb.append(sample.probability)\n",
    "        tempStr = ''\n",
    "        for stateElement in reversed(sample.x):\n",
    "            tempStr += str(int(stateElement))\n",
    "        tempState.append(tempStr)\n",
    "    return dict(zip(tempState, tempProb))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "id": "410cd68b",
   "metadata": {},
   "outputs": [],
   "source": [
    "vqeInit = VQE(ansatz=ansatz,optimizer=optimizer, quantum_instance=backend)\n",
    "vqe = MinimumEigenOptimizer(vqeInit)\n",
    "vqeResult = vqe.solve(qubo)\n",
    "\n",
    "if backend.name() == 'qasm_simulator':\n",
    "    counts = vqeResult.min_eigen_solver_result.eigenstate\n",
    "elif backend.name() == 'statevector_simulator':\n",
    "    counts = getCountDictStateVecSim(vqeResult)\n",
    "#endif"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "id": "c8a3de41",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<MinimumEigenOptimizationResult: fval=0.012311348325738436, x0=0.0, x1=1.0, x2=1.0, x3=0.0, x4=0.0, x5=1.0, x6=1.0, x7=1.0, status=SUCCESS>"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "vqeResult"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "id": "40910df5",
   "metadata": {},
   "outputs": [],
   "source": [
    "vqeFig = plot_histogram(counts,figsize=(60,10))\n",
    "vqeFig.savefig(\"figures/VQE\"+startStr+\"-\"+endStr+\".pdf\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "id": "6bec6ec3",
   "metadata": {},
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 4320x720 with 1 Axes>"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "vqeFig"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "id": "6cb133eb",
   "metadata": {},
   "outputs": [],
   "source": [
    "## ALTERNATIVE PLOT SCHEME\n",
    "\n",
    "# samples_for_plot = {\n",
    "#     \" \".join(f\"{vqeResult.variables[i].name}={int(v)}\" for i, v in enumerate(sample.x)): sample.probability\n",
    "#     for sample in vqeResult.samples\n",
    "# }\n",
    "# plot_histogram(samples_for_plot,figsize=(60,5))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "id": "5ed2fd87",
   "metadata": {},
   "outputs": [],
   "source": [
    "vqeRiskInit = VQE(ansatz=ansatz,optimizer=optimizer, quantum_instance=backend)\n",
    "vqeRisk = MinimumEigenOptimizer(vqeRiskInit)\n",
    "vqeRiskResult = vqeRisk.solve(quboRisk)\n",
    "\n",
    "if backend.name() == 'qasm_simulator':\n",
    "    countsRisk = vqeRiskResult.min_eigen_solver_result.eigenstate\n",
    "elif backend.name() == 'statevector_simulator':\n",
    "    countsRisk = getCountDictStateVecSim(vqeRiskResult)\n",
    "#endif"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "id": "89644e94",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<MinimumEigenOptimizationResult: fval=0.006976341255722218, y0=1.0, y1=1.0, y2=1.0, y3=0.0, y4=0.0, y5=0.0, y6=1.0, y7=1.0, status=SUCCESS>"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "vqeRiskResult"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "id": "8765a9a3",
   "metadata": {},
   "outputs": [],
   "source": [
    "vqeRiskFig = plot_histogram(countsRisk,figsize=(60,10))\n",
    "vqeRiskFig.savefig(\"figures/VQERisk\"+startStr+\"-\"+endStr+\".pdf\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "id": "243fc9e4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 4320x720 with 1 Axes>"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "vqeRiskFig"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6689742b",
   "metadata": {},
   "source": [
    "Which matches the classical result."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "56e7acc9",
   "metadata": {},
   "source": [
    "## Quantum Approximation Optimization Algorithm\n",
    "\n",
    "\n",
    "The Quantum Approximate Optimization Algorithm is similar to the VQE insofar that it is also a variational algorithm, and follows the same structure of using a classical optimizer to optimize the results from the quantum circuit, until the optimal eigenstate is obtained.\n",
    "\n",
    "The form of the Ansatz is of note for this framework, and we will take care in examining it.\n",
    "\n",
    "For more information, please read [this paper](https://arxiv.org/abs/1411.4028)\n",
    "\n",
    "\n",
    "### Ansatz\n",
    "Consider a unitary $U(\\lbrace\\beta_i\\rbrace, \\lbrace\\gamma_i\\rbrace)$ with some set of variational parameters $\\lbrace\\beta_i\\rbrace, \\lbrace\\gamma_i\\rbrace$, which is used to prepare a  state $\\left| \\psi(\\lbrace\\beta_i\\rbrace, \\lbrace\\gamma_i\\rbrace) \\right\\rangle$. \n",
    "\n",
    "The unitary operator $U(\\lbrace\\beta_i\\rbrace, \\lbrace\\gamma_i\\rbrace)$ is itself a combination of unitary operators \n",
    "$U(\\lbrace\\beta_i\\rbrace) = e^{-i \\lbrace\\beta_i\\rbrace H_m}$ and $U(\\lbrace\\gamma_i\\rbrace) = e^{-i \\lbrace\\gamma_i\\rbrace H_c}$, where $H_m$ is the mixing Hamiltonian and $H_c$ is the cost Hamiltonian.\n",
    "\n",
    "The cost Hamiltonian is such that its ground state encodes the solution to the optimization problem.\n",
    "\n",
    "The state is prepared by applying these unitaries as alternating blocks of the two unitaries applied $p$ times such that \n",
    "\n",
    "$$\n",
    "\\left| \\psi(\\lbrace\\beta\\rbrace, \\lbrace\\gamma\\rbrace) \\right\\rangle = U(\\beta_1) U(\\gamma_1) \\cdots U(\\beta_p) U(\\gamma_p) \n",
    "\\left| 0\\right\\rangle\n",
    "$$\n",
    "\n",
    "\n",
    "### Qiskit Implementation of QAOA"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "id": "cdc5f774",
   "metadata": {},
   "outputs": [],
   "source": [
    "qaoaInit = QAOA(optimizer=optimizer, reps=reps, quantum_instance=backend)\n",
    "qaoa = MinimumEigenOptimizer(qaoaInit)\n",
    "qaoaResult = qaoa.solve(qubo)\n",
    "\n",
    "if backend.name() == 'qasm_simulator':\n",
    "    counts = qaoaResult.min_eigen_solver_result.eigenstate\n",
    "elif backend.name() == 'statevector_simulator':\n",
    "    counts = getCountDictStateVecSim(qaoaResult)\n",
    "#endif"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "id": "0649a932",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<MinimumEigenOptimizationResult: fval=0.0124984448754617, x0=1.0, x1=1.0, x2=1.0, x3=0.0, x4=0.0, x5=1.0, x6=1.0, x7=0.0, status=SUCCESS>"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qaoaResult"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "id": "21f7c579",
   "metadata": {},
   "outputs": [],
   "source": [
    "qaoaFig = plot_histogram(counts,figsize=(60,10))\n",
    "qaoaFig.savefig(\"figures/QAOA-\"+startStr+\"-\"+endStr+\".pdf\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "id": "1a8e65f0",
   "metadata": {},
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 4320x720 with 1 Axes>"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qaoaFig"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "id": "fdc818f0",
   "metadata": {},
   "outputs": [],
   "source": [
    "qaoaRiskInit = QAOA(optimizer=optimizer, reps=reps, quantum_instance=backend)\n",
    "qaoaRisk = MinimumEigenOptimizer(qaoaRiskInit)\n",
    "qaoaRiskResult = qaoaRisk.solve(quboRisk)\n",
    "\n",
    "if backend.name() == 'qasm_simulator':\n",
    "    countsRisk = qaoaRiskResult.min_eigen_solver_result.eigenstate\n",
    "elif backend.name() == 'statevector_simulator':\n",
    "    countsRisk = getCountDictStateVecSim(qaoaRiskResult)\n",
    "#endif"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "id": "07b3d995",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<MinimumEigenOptimizationResult: fval=0.006976341255722218, y0=1.0, y1=1.0, y2=1.0, y3=0.0, y4=0.0, y5=0.0, y6=1.0, y7=1.0, status=SUCCESS>"
      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qaoaRiskResult"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "id": "a5f0a64c",
   "metadata": {},
   "outputs": [],
   "source": [
    "qaoaRiskFig = plot_histogram(countsRisk,figsize=(60,10))\n",
    "qaoaRiskFig.savefig(\"figures/QAOARisk-\"+startStr+\"-\"+endStr+\".pdf\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "id": "49f3d10d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 4320x720 with 1 Axes>"
      ]
     },
     "execution_count": 60,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qaoaRiskFig"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "37030ad5",
   "metadata": {},
   "source": [
    "Which matches the VQE result and the classical result. However, you'll note here that the probabilities are less well-defined. I invite you to play around with the ansatz to see if you can improve the result by increasing the number of repetitions. \n",
    "\n",
    "However, with real hardware, an issue that arises is the number of operations (gates) you can actually apply. So there's often a balance that needs to be found between the number of layers and the capacity of the hardware."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "id": "3a86e19e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<MinimumEigenOptimizationResult: fval=0.012498444875498012, x0=1.0, x1=1.0, x2=1.0, x3=0.0, x4=0.0, x5=1.0, x6=1.0, x7=0.0, status=SUCCESS>"
      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "classicalResult"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "id": "b843ca7c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<MinimumEigenOptimizationResult: fval=0.012311348325738436, x0=0.0, x1=1.0, x2=1.0, x3=0.0, x4=0.0, x5=1.0, x6=1.0, x7=1.0, status=SUCCESS>"
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "vqeResult"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "id": "01cc4d6a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<MinimumEigenOptimizationResult: fval=0.0124984448754617, x0=1.0, x1=1.0, x2=1.0, x3=0.0, x4=0.0, x5=1.0, x6=1.0, x7=0.0, status=SUCCESS>"
      ]
     },
     "execution_count": 63,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qaoaResult"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "id": "7eb02ab5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<MinimumEigenOptimizationResult: fval=0.00697634125569152, y0=1.0, y1=1.0, y2=1.0, y3=0.0, y4=0.0, y5=0.0, y6=1.0, y7=1.0, status=SUCCESS>"
      ]
     },
     "execution_count": 64,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "classicalResultRisk"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "id": "6a94a9ee",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<MinimumEigenOptimizationResult: fval=0.006976341255722218, y0=1.0, y1=1.0, y2=1.0, y3=0.0, y4=0.0, y5=0.0, y6=1.0, y7=1.0, status=SUCCESS>"
      ]
     },
     "execution_count": 65,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "vqeRiskResult"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "id": "6460411c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<MinimumEigenOptimizationResult: fval=0.006976341255722218, y0=1.0, y1=1.0, y2=1.0, y3=0.0, y4=0.0, y5=0.0, y6=1.0, y7=1.0, status=SUCCESS>"
      ]
     },
     "execution_count": 66,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qaoaRiskResult"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "83a95c80",
   "metadata": {},
   "source": [
    "# Exploratory Data Visualization\n",
    "\n",
    "It's good to plot the results to see what we get, before we begin applying some weights based on other ideas."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "id": "22c563e9",
   "metadata": {},
   "outputs": [],
   "source": [
    "def getCombinations(inputVal):\n",
    "    combinations = []\n",
    "    if type(inputVal) == str:\n",
    "        for perm in set(permutations(inputVal)):\n",
    "            combinations.append(''.join(perm))\n",
    "        #endFor\n",
    "    elif type(inputVal) == list:\n",
    "        for i in range(len(inputVal)):\n",
    "            inputVal[i] = int(inputVal[i])\n",
    "        #endFor\n",
    "        for perm in set(permutations(inputVal)):\n",
    "            combinations.append(list(perm))\n",
    "        #endFor\n",
    "    else:\n",
    "        print(\"Input a string or list of ones and zeroes\")\n",
    "    return combinations\n",
    "\n",
    "def countNonZeroElemInList(inputList):\n",
    "    numNonZeroElem = 0.\n",
    "    for x in inputList:\n",
    "        if x != 0:\n",
    "            numNonZeroElem += 1\n",
    "        else:\n",
    "            numNonZeroElem += 0\n",
    "        #endIf\n",
    "    #endFor\n",
    "    return numNonZeroElem\n",
    "\n",
    "def assetTotalPortfolioGrowth(initialPortfolioValue,selectedAssets,testDF):\n",
    "    amountSplit = initialPortfolioValue/countNonZeroElemInList(selectedAssets)\n",
    "    assetGrowth = []\n",
    "    for i in range(len(selectedAssets)):\n",
    "        if selectedAssets[i] == 1:\n",
    "            tempDF = testDF.iloc[:,i]\n",
    "            amountTemp = amountSplit\n",
    "            for pctChg in tempDF:\n",
    "                amountTemp += pctChg*amountTemp\n",
    "            assetGrowth.append(amountTemp)\n",
    "        else:\n",
    "            assetGrowth.append(0.)\n",
    "        #endIf\n",
    "    #endFor\n",
    "    return assetGrowth\n",
    "\n",
    "def assetGrowthTimeSeries(initialPortfolioValue,selectedAssets,testDF):\n",
    "    amountSplit = initialPortfolioValue/countNonZeroElemInList(selectedAssets)\n",
    "    assetGrowthTS = []\n",
    "    for i in range(len(selectedAssets)):\n",
    "        if selectedAssets[i] == 1:\n",
    "            tempVec = []\n",
    "            tempDF = testDF.iloc[:,i]\n",
    "            amountTemp = amountSplit\n",
    "            for pctChg in tempDF:\n",
    "                amountTemp += pctChg*amountTemp\n",
    "                tempVec.append(amountTemp)\n",
    "            assetGrowthTS.append(tempVec)\n",
    "        else:\n",
    "            tempVec = []\n",
    "            tempDF = testDF.iloc[:,i]\n",
    "            for pctChg in tempDF:\n",
    "                tempVec.append(0.0)\n",
    "            assetGrowthTS.append(tempVec)\n",
    "        #endIf\n",
    "    #endFor\n",
    "    return assetGrowthTS\n",
    "\n",
    "def assetGrowthTimeSeriesWeighted(initialPortfolioValue,selectedAssets,testDF,weights):\n",
    "    assetGrowthTS = []\n",
    "    for i in range(len(selectedAssets)):\n",
    "        if selectedAssets[i] == 1:\n",
    "            tempVec = []\n",
    "            tempDF = testDF.iloc[:,i]\n",
    "            amountTemp = initialPortfolioValue*weights[i]\n",
    "            for pctChg in tempDF:\n",
    "                amountTemp += pctChg*amountTemp\n",
    "                tempVec.append(amountTemp)\n",
    "            assetGrowthTS.append(tempVec)\n",
    "        else:\n",
    "            tempVec = []\n",
    "            tempDF = testDF.iloc[:,i]\n",
    "            for pctChg in tempDF:\n",
    "                tempVec.append(0.0)\n",
    "            assetGrowthTS.append(tempVec)\n",
    "        #endIf\n",
    "    #endFor\n",
    "    return assetGrowthTS\n",
    "\n",
    "\n",
    "def portfolioGrowthTimeSeries(portfolioTS):\n",
    "    portfolioValueTS = []\n",
    "    for i in range(len(portfolioTS[0])):\n",
    "        tempVal = 0.0\n",
    "        for j in range(len(portfolioTS)):\n",
    "            tempVal += portfolioTS[j][i]\n",
    "        portfolioValueTS.append(tempVal)\n",
    "    return portfolioValueTS"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "id": "912e9a29",
   "metadata": {},
   "outputs": [],
   "source": [
    "assetTest = qaoaRiskResult.x.tolist() \n",
    "amountInit = 1000 "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "id": "31f4926e",
   "metadata": {},
   "outputs": [],
   "source": [
    "allAssetCombinations = getCombinations(assetTest)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "id": "2671c64d",
   "metadata": {},
   "outputs": [],
   "source": [
    "dateList = dfMonthlyReturns.index"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "id": "0a30760a",
   "metadata": {},
   "outputs": [],
   "source": [
    "# # Gives total number of chosen assets, AKA budget. More of a sanity check.\n",
    "# numAssetsChosen = countNonZeroElemInList(assetTest)\n",
    "\n",
    "# # Gives each selected asset's total final value in a list\n",
    "# finalAssetValues = assetTotalPortfolioGrowth(amountInit,assetTest,dfMonthlyReturns)\n",
    "\n",
    "# # Gives the time series of each portfolio element as a list of lists. In each list, \n",
    "# # the final element is the final value of the held asset.\n",
    "# chosenAssetsTimeSeries = assetGrowthTimeSeries(amountInit,assetTest,dfMonthlyReturns)\n",
    "\n",
    "# # Gives the time series for the total portfolio value. The final element is the final portfolio value.\n",
    "# portfolioTimeSeries = portfolioGrowthTimeSeries(chosenAssetsTimeSeries)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "id": "9b3da5ce",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure()\n",
    "ax = fig.add_subplot(1, 1, 1) \n",
    "for i in range(len(allAssetCombinations)):\n",
    "    chosenAssetsTimeSeries = assetGrowthTimeSeries(amountInit,allAssetCombinations[i],dfMonthlyReturns)\n",
    "    portfolioTimeSeries = portfolioGrowthTimeSeries(chosenAssetsTimeSeries)\n",
    "    label = ''\n",
    "    for element in allAssetCombinations[i]:\n",
    "        label+=str(element)\n",
    "    #endFor\n",
    "    ax.plot(dateList,portfolioTimeSeries,color='blue',linestyle='--',alpha=0.1,linewidth=0.5)\n",
    "#endFor\n",
    "\n",
    "winningAssetCombination = assetTest\n",
    "winningAssetTimeSeries = assetGrowthTimeSeries(amountInit,winningAssetCombination,dfMonthlyReturns)\n",
    "winningPortfolioTimeSeries = portfolioGrowthTimeSeries(winningAssetTimeSeries)\n",
    "\n",
    "label = ''\n",
    "for element in winningAssetCombination:\n",
    "    label+=str(element)\n",
    "#endFor\n",
    "ax.plot(dateList,winningPortfolioTimeSeries,label=label,color='red',alpha=1,linewidth=2)\n",
    "\n",
    "plt.xlim(startDate,endDate)\n",
    "plt.ylabel('Total Portfolio Value')\n",
    "plt.xlabel('Date')\n",
    "plt.legend()#bbox_to_anchor=(1.02, 1), loc='upper left', borderaxespad=0)\n",
    "plt.show()\n",
    "\n",
    "fig.savefig('figures/portfolio-'+label+'risk-'+str(q)+'-'+startStr+\"-\"+endStr+'.pdf',bbox_inches='tight')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "id": "3a0b1831",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure()\n",
    "ax = fig.add_subplot(1, 1, 1) \n",
    "for i in range(len(allAssetCombinations)):\n",
    "    chosenAssetsTimeSeries = assetGrowthTimeSeries(amountInit,allAssetCombinations[i],dfMonthlyReturns)\n",
    "    portfolioTimeSeries = portfolioGrowthTimeSeries(chosenAssetsTimeSeries)\n",
    "    label = ''\n",
    "    for element in allAssetCombinations[i]:\n",
    "        label+=str(element)\n",
    "    #endFor\n",
    "    ax.plot(dateList,portfolioTimeSeries,color='blue',linestyle='--',alpha=0.1,linewidth=0.5)\n",
    "#endFor\n",
    "\n",
    "winningAssetCombination = assetTest\n",
    "winningAssetTimeSeries = assetGrowthTimeSeries(amountInit,winningAssetCombination,dfMonthlyReturns)\n",
    "winningPortfolioTimeSeries = portfolioGrowthTimeSeries(winningAssetTimeSeries)\n",
    "\n",
    "label = ''\n",
    "for element in winningAssetCombination:\n",
    "    label+=str(element)\n",
    "#endFor\n",
    "\n",
    "label += ' equally weighted'\n",
    "ax.plot(dateList,winningPortfolioTimeSeries,label=label,color='red',alpha=1,linewidth=2)\n",
    "\n",
    "portfolioWeights = [0.223214286,0.233800935,0.2042007,0.0,0.0,0.0,0.172583826,0.165250236]\n",
    "weightedWinningAssetTimeSeries = assetGrowthTimeSeriesWeighted(amountInit,assetTest,dfMonthlyReturns,portfolioWeights)\n",
    "weightedWinningPortfolioTimeSeries = portfolioGrowthTimeSeries(weightedWinningAssetTimeSeries)\n",
    "\n",
    "label = ''\n",
    "for element in winningAssetCombination:\n",
    "    label+=str(element)\n",
    "#endFor\n",
    "\n",
    "label += ' risk-parity weighted'\n",
    "\n",
    "ax.plot(dateList,weightedWinningPortfolioTimeSeries,label=label,color='purple',alpha=1,linewidth=2)\n",
    "\n",
    "plt.xlim(startDate,endDate)\n",
    "plt.ylabel('Total Portfolio Value')\n",
    "plt.xlabel('Date')\n",
    "plt.legend()#bbox_to_anchor=(1.02, 1), loc='upper left', borderaxespad=0)\n",
    "plt.show()\n",
    "\n",
    "fig.savefig('figures/weighted-comparison-portfolio-'+label+'risk-'+str(q)+'-'+startStr+\"-\"+endStr+'.pdf',bbox_inches='tight')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "id": "5604df11",
   "metadata": {},
   "outputs": [],
   "source": [
    "from qiskit import QuantumCircuit, assemble, Aer\n",
    "from math import pi, sqrt\n",
    "from qiskit.visualization import plot_bloch_multivector, plot_histogram, plot_bloch_vector\n",
    "sim = Aer.get_backend('aer_simulator')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "id": "5baf0ba6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<pre style=\"word-wrap: normal;white-space: pre;background: #fff0;line-height: 1.1;font-family: &quot;Courier New&quot;,Courier,monospace\">   \n",
       "q: \n",
       "   </pre>"
      ],
      "text/plain": [
       "   \n",
       "q: \n",
       "   "
      ]
     },
     "execution_count": 75,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qc = QuantumCircuit(1)\n",
    "\n",
    "qc.draw()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "id": "d0a7e161",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 288x288 with 1 Axes>"
      ]
     },
     "execution_count": 76,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qc.save_statevector()\n",
    "qobj = assemble(qc)\n",
    "state = sim.run(qobj).result().get_statevector()\n",
    "plot_bloch_multivector(state)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "id": "17ee38d7",
   "metadata": {},
   "outputs": [],
   "source": [
    "qc = QuantumCircuit(1)\n",
    "qc.draw()\n",
    "qc.save_statevector()\n",
    "qobj = assemble(qc)\n",
    "state = sim.run(qobj).result().get_statevector()\n",
    "fig=plot_bloch_multivector(state)\n",
    "fig.savefig('figures/bloch-no-rotate.pdf', bbox_inches='tight')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "id": "a5d1672a",
   "metadata": {},
   "outputs": [],
   "source": [
    "qc = QuantumCircuit(1)\n",
    "qc.rx(theta=pi/2,qubit=0)\n",
    "qc.draw()\n",
    "qc.save_statevector()\n",
    "qobj = assemble(qc)\n",
    "state = sim.run(qobj).result().get_statevector()\n",
    "fig=plot_bloch_multivector(state)\n",
    "fig.savefig('figures/bloch-pi-over-two-x-rotate.pdf', bbox_inches='tight')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "109ea4e1",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3.10.5 64-bit",
   "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": "6fb996f9db7db23e4f714c035d08cc8b5f45c750693f36fb368a56f4d1be34c1"
   }
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}