QAOA_maxcut_Victor_Onofre.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import networkx as nx\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy.optimize import minimize\n",
    "from qiskit import QuantumCircuit, QuantumRegister, ClassicalRegister, execute, Aer"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Quantum Approximate Optimization Algorithm (QAOA) for the Max-cut problem\n",
    "\n",
    "### **Victor Onofre**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "style = {'backgroundcolor': 'lightyellow'} # Style of the drawing of the quantum circuit "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Part I: Max-cut problem "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Given a graph  $G = (V, E)$ where:\n",
    "\n",
    "- $V$ is the set of vertices/nodes\n",
    "- $E$ is the set of edges\n",
    "\n",
    "Each edges $e \\in E$ is a pair $\\{u,v\\}$ where $v \\in V$ are distinct"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "####  Example of a graph: \n",
    "\n",
    "$$ V = {1,2,3}$$\n",
    "$$ E = \\{\\{1,2\\}, \\{2,3\\}, \\{1,3\\} \\} $$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Graph_Example_1 = nx.Graph()\n",
    "Graph_Example_1.add_edges_from([[1,2],[2,3],[1,3]])\n",
    "nx.draw(Graph_Example_1,with_labels=True,font_weight='bold')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The goal of the max-cut problem is to:\n",
    "\n",
    "> **Have as many cut edges as possible. Where an edge is cut if its endpoints have different colors**\n",
    "\n",
    "The output is a \"2-coloring\" of $V$: Each vertex is designated a color (examples: blue or red)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The maximum cut can be formaulated as an optimization problem:\n",
    "\n",
    "$$ \\max_{s}\\frac{1}{2} \\sum_{ij \\in E}  (1-s_{i}s_{j}), \\quad s_{i} \\in \\{-1 , +1 \\}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "> Same sign: No edge is cut (no contribution to the objective function) $\\rightarrow \\frac{1}{2} (1-s_{i}s_{j}) = 0$\n",
    "\n",
    "> Different sign: An edge is cut (contribution to the objective function) $\\rightarrow \\frac{1}{2} (1-s_{i}s_{j}) = 1$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "###  Examples of solutions to the max-cut problem:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the triangular graph the solution to the max-cut problem is:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "nx.draw(Graph_Example_1,node_color = ['b','b','r'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Where we a maximum of $2$ cuts. If we assign a string to the colors in the graph we can represent this solution as: $001$. \n",
    "> Where $0$ is the node blue and $1$ the node is red"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Graph_Example_2 = nx.Graph()\n",
    "Graph_Example_2.add_edges_from([[1,2],[1,3],[4,2],[4,3]])\n",
    "nx.draw(Graph_Example_2,with_labels=True,font_weight='bold')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this example the solution to the max-cut problem is:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "nx.draw(Graph_Example_2,node_color = ['r','b','b','r'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Where we have $4$ cuts. Represented in string as: 1001"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Graph_Example_3 = nx.Graph()\n",
    "Graph_Example_3.add_edges_from([[1,4],[1,2],[2,5],[4,5],[5,3],[2,3]])\n",
    "nx.draw(Graph_Example_3,with_labels=True,font_weight='bold')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this example the solution to the max-cut problem is:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "nx.draw(Graph_Example_3,node_color = ['r','b','b','r','b'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Where, the best solution for the max-cut problem is $5$ cuts. Represented by the string: $10001$ "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Part II: Quantum Approximate Optimization Algorithm (QAOA )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We wish to maximize an objective function:\n",
    "    \n",
    "$$ C = \\sum_{k=1}^{m} c_{m}(z), \\quad  z=z_{1}z_{2}z_{3}...z_{n} \\quad z_{k} \\in \\{0,1\\}^{n} $$\n",
    "\n",
    "$c_{m} \\in \\{0,1\\}$ is a function that queries string $z$ to see if the substring satisfies certain property.\n",
    "\n",
    "The first step for the QAOA is to treat the objective fucntion $C$ as an operator\n",
    "\n",
    "$$C |z> = \\sum_{k=1}^{m} c_{k}(z)|z> = f(z)|z>$$\n",
    "\n",
    "$C$ has eigenvectors $|z>$ and eigenvalues $\\sum_{k=1}^{m}c_{k}(z) = f(z)$\n",
    "\n",
    "The largest value $f(z)$, which can denote $f(z')$ is the $C_{max}$ with corresponding eigenvector $|z'>$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "With the basis $|z>$, we can construct a general superposition state:\n",
    "\n",
    "$$|\\psi> = \\sum_{z \\in \\{0, 1\\}^{n} } a_{z} |z>$$ \n",
    "\n",
    "For $|\\psi>$ we can construct the expectation value of $C$, that is:\n",
    "\n",
    "$$<C> = < \\psi | C |\\psi > $$\n",
    "\n",
    "If $|\\psi> = |z> \\rightarrow <C> = <z|C|z> = f(z)$. Finding the $|z>$ that can maximizae $C(z)$ is corresponding to finding a state $|\\psi>$ that maximize $<C>$.\n",
    "\n",
    "So $<C>_{max} = f(z')$ only when $|\\psi> = |z'>$. This means that if we can obtain $<C>_{max}$, we are applying $|z'>$, if we measure the state $|\\psi>$ in the $|z>$ basis we will obtain $|z'>$ with probability 1. \n",
    "\n",
    "> In general, we don't known how to find such $<C>_{max}$ efficiently, we can only find a $<C>$ that is close to $<C>_{max}$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can rotate  our initial state $|s>$ to make it closer to the $|z'>$. To do this we define two types of ratations operators:\n",
    "\n",
    "$$ U(C,\\gamma) = e^{-i \\gamma C}, \\quad U(B,\\beta) = e^{-i \\beta B}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It is not guarantedd that after \n",
    "\n",
    "$$|\\psi'> = U(B, \\beta)U(C,\\gamma)|\\psi>, \\quad  U(B, \\beta)=e^{-i\\beta B}  \\quad U(C,\\gamma) = e^{-i\\gamma C}$$\n",
    "\n",
    "the new state $|\\psi'>$ is close enough to $|z'>$. A solution to this is to apply $U(B, \\beta)U(C,\\gamma)$ multiply times with different $\\beta$ and $\\gamma$ each time."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "QAOA prepares an ansatz state of the form:\n",
    "    \n",
    "$$|\\psi(\\boldsymbol{\\theta}) > = |\\psi(\\boldsymbol{\\beta,\\gamma}) > = e^{-i\\beta_{p}B} e^{-i\\gamma_{p}C}... e^{-i\\beta_{1}B} e^{-i\\gamma_{1}C} H^{\\otimes n}|0>$$    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Maxcut hamiltonian is constructed by mapping the binary variables $s_{i}$ onto the eigenvalues of $z$\n",
    "\n",
    "$$C = \\frac{1}{2} \\sum_{ij \\in E} (I - Z_{i}Z_{j})$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "B is the mixer hamiltonian:\n",
    "\n",
    "$$ B = \\sum_{i} x_{i}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Then a classical optimizer is used to vary the parameters $\\boldsymbol{\\beta}, \\boldsymbol{\\gamma}$ to maximize the function:\n",
    "\n",
    "$$f(\\boldsymbol{\\beta,\\gamma}) = <\\psi(\\boldsymbol{\\beta,\\gamma}) |C|\\psi(\\boldsymbol{\\beta,\\gamma})>$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**The quality of QAOA solution heavily depends on the quality of the parameters found by the classical optimizer**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Graph = nx.Graph()\n",
    "Graph.add_edges_from([[0,1],[0,3],[3,4],[1,4],[1,2],[4,2]])\n",
    "nx.draw(Graph,with_labels=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Construct the operator $U(B, \\beta) = exp(-i \\gamma_{p}C)$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$U(C,\\gamma)= e^{-i\\gamma_{p}C} = e^{-i\\gamma_{p}(Z_{i} \\otimes Z_{j})} $$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$|\\Psi> = a_{00}|00> + a_{01} |01> + a_{10}|10> + a_{11} |11> $$\n",
    "\n",
    "$$e^{-i\\gamma_{p}(Z_{i} \\otimes Z_{j})} |\\Psi> = a_{00}e^{-i\\gamma_{p}(Z_{i} \\otimes Z_{j})} |00> + a_{01} e^{-i\\gamma_{p}(Z_{i} \\otimes Z_{j})} |01> + a_{10}e^{-i\\gamma_{p}(Z_{i} \\otimes Z_{j})} |10> + a_{11} e^{-i\\gamma_{p}(Z_{i} \\otimes Z_{j})} |11>$$\n",
    "\n",
    "$$e^{-i\\gamma_{p}(Z_{i} \\otimes Z_{j})} |\\Psi> = a_{00}e^{-i\\gamma_{p}} |00> + a_{01} e^{i\\gamma_{p}} |01> + a_{10}e^{i\\gamma_{p}} |10> + a_{11} e^{-i\\gamma_{p}} |11>$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The operator adds a phase factor with the sign depneding on parity, in general:\n",
    "    \n",
    "$$ e^{-i\\gamma_{p}(Z_{i} \\otimes Z_{j})} |ab> =e^{-i\\gamma_{p}(-1)^{a \\oplus b}} |ab>   $$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This operator can be construct with the quantum gates:\n",
    "$$CNOT_{ij}[ I\\otimes R_{z}(\\theta) ]CNOT_{ij} $$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "N = Graph.number_of_nodes() # The number of nodes in the graph\n",
    "qc = QuantumCircuit(N,N) # Quantum circuit with N qubits and N classical register\n",
    "\n",
    "gamma = np.pi/8 # parameter gamma for the cost function (maxcut hamiltonian)\n",
    "#Apply the operator to each edge\n",
    "for i, j in Graph.edges(): \n",
    "    qc.cx(i,j)\n",
    "    qc.rz(2*gamma, j)\n",
    "    qc.cx(i,j)\n",
    "    qc.barrier()\n",
    "    \n",
    "#qc.draw(output='mpl', style=style) # Draw the quantum circuit"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Construct the operator $U(B, \\beta)=exp(-i \\beta_{p}B)$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$ B = \\sum_{i} X_{i}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$U(B, \\beta) = e^{-i\\beta_{p}B} = e^{-i\\beta_{p} \\sum_{i} X_{i}} =  \t\\prod_{i=1}^{n} e^{-i\\beta_{p} X_{i}} $$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This operator can be constructed with a rotation operator $R_{x}(\\theta) = e^{-i \\theta/2 X}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<qiskit.circuit.instructionset.InstructionSet at 0x7fe8614a1d00>"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "beta = np.pi/8 # parameter for the mixer hamiltonian\n",
    "for n in Graph.nodes():\n",
    "    qc.rx(2*beta, n)\n",
    "\n",
    "# measure the result\n",
    "qc.barrier(range(N))\n",
    "qc.measure(range(N), range(N))\n",
    "\n",
    "#qc.draw(output='mpl', style=style,fold= 35) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "def qaoa_circuit(G, theta,p):\n",
    "    r\"\"\"\n",
    "    ############################################\n",
    "    # Compute the QAOA circuit for the graph G\n",
    "    #\n",
    "    # |psi(theta) > = |psi(beta,gamma) > = e^{-i*beta_p*B} e^{-i*gamma_p*C}... e^{-i*beta_1*B} e^{-i*gamma_1*C} H^{otimes n}|0>\n",
    "    # \n",
    "    # where C is the Maxcut hamiltonian, B is the mixer hamiltonian.\n",
    "    #\n",
    "    # G: graph\n",
    "    # theta: parameters,first half is betas, second half is gammas\n",
    "    # p: number of QAOA steps\n",
    "    # return: The QAOA circuit \n",
    "    ###########################################\n",
    "    \"\"\"\n",
    "    beta = theta[:p] #Parameters beta for the mixer hamiltonian\n",
    "    gamma = theta[p:]#Parameters gamma for the maxcut hamiltonian\n",
    "    N = G.number_of_nodes()#Number of nodes of the graph G\n",
    "    qc = QuantumCircuit(N,N)# Quantum circuit wiht N qubits and N classical register\n",
    "    qc.h(range(N))# Apply the Hadamard gate to all the qubits\n",
    "    # Apply p operators\n",
    "    for k in range(p):\n",
    "        for i, j in G.edges(): #Representation of the maxcut hamiltonian\n",
    "            qc.cx(i,j)  \n",
    "            qc.rz(2*gamma[k], j)\n",
    "            qc.cx(i,j)\n",
    "            qc.barrier()\n",
    "        for n in G.nodes(): # Representation of the mixer hamiltonian\n",
    "            qc.rx(2*beta[k], n)\n",
    "    # Measurement in all the qubits\n",
    "    qc.barrier(range(N))\n",
    "    qc.measure(range(N), range(N))\n",
    "    return qc #Returns the quantum circuit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "# p is the number of QAOA alternating operators\n",
    "p = 1\n",
    "\n",
    "theta = np.array([np.pi/8,np.pi/8])\n",
    "\n",
    "circuit = qaoa_circuit(Graph, theta,p)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "# circuit.draw(output='mpl', style=style,fold= 35) # Draw the quantum circuit"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Part III: Optimization"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Qiskit uses the least significant bit in the bistring, we need to invert this string\n",
    "def invert_counts(counts):\n",
    "    r\"\"\"\n",
    "    ############################################\n",
    "    # Inverted the binary string\n",
    "    #\n",
    "    # counts: The result of running the quantum circuit\n",
    "    # return: The results with binary string inverted\n",
    "    ###########################################\n",
    "    \"\"\"\n",
    "    inv_counts = {}\n",
    "    for k, v in counts.items():\n",
    "        inv_counts[k[::-1]] = v\n",
    "    return inv_counts "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "def maxcut_objective_function(x,G):\n",
    "    r\"\"\"\n",
    "    ############################################\n",
    "    # Compute the maxcut objective function for the binary string x and graph G\n",
    "    #\n",
    "    # G: graph\n",
    "    # x: binary string\n",
    "    # return: The cost of the binary string x \n",
    "    ###########################################\n",
    "    \"\"\"\n",
    "    cut = 0\n",
    "    for i, j in G.edges():\n",
    "        if x[i] != x[j]:\n",
    "            cut -= 1# the edge is cut\n",
    "    return cut # Sum of all the edges that are cut"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "def function_to_minimize(G,p):\n",
    "    r\"\"\"\n",
    "    ############################################\n",
    "    # Define the function to minimize given the graph G and the number of parameters\n",
    "    #\n",
    "    # G: graph\n",
    "    # p: number of parameters\n",
    "    # return: The function to minimize\n",
    "    ###########################################\n",
    "    \"\"\"\n",
    "    backend = Aer.get_backend('qasm_simulator')\n",
    "    def f(theta):\n",
    "        r\"\"\"\n",
    "        ############################################\n",
    "        # Function that gives the energy for parameters theta\n",
    "        #\n",
    "        # theta: parameters\n",
    "        # return: Energy\n",
    "        ###########################################\n",
    "        \"\"\"\n",
    "        qc = qaoa_circuit(G,theta,p) # Gives the circuit of QAOA fot a graph G, parameters theta and p operators\n",
    "        counts = execute(qc, backend, seed_simulator=10).result().get_counts()# Run the circuit and get the results using the backedn \"qasm_simulator\"\n",
    "        \n",
    "        E = 0 # Initial energy\n",
    "        total_counts = 0 # Initial counts\n",
    "        #Qiskit uses the least significant bit in the bistring, we need to invert this string\n",
    "        InvertedCounts = invert_counts(counts) #Inverted the binary string\n",
    "        # meas is the binary string measure\n",
    "        # meas_count is the number of times that the binary string has been measure\n",
    "        for meas, meas_count in InvertedCounts.items():\n",
    "            objective_function = maxcut_objective_function(meas, G)#Compute the maxcut objetive function fot the binary string meas\n",
    "            E += objective_function*meas_count # Define the energy as the value of the objective functions times the counts of that measure\n",
    "            total_counts += meas_count # The total number of measures in the system\n",
    "        return E/total_counts # Returns the energy given the parameters theta\n",
    "    return f"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "      fun: -1.6103515625\n",
       " hess_inv: array([[1, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n",
       "       [0, 1, 0, 0, 0, 0, 0, 0, 0, 0],\n",
       "       [0, 0, 1, 0, 0, 0, 0, 0, 0, 0],\n",
       "       [0, 0, 0, 1, 0, 0, 0, 0, 0, 0],\n",
       "       [0, 0, 0, 0, 1, 0, 0, 0, 0, 0],\n",
       "       [0, 0, 0, 0, 0, 1, 0, 0, 0, 0],\n",
       "       [0, 0, 0, 0, 0, 0, 1, 0, 0, 0],\n",
       "       [0, 0, 0, 0, 0, 0, 0, 1, 0, 0],\n",
       "       [0, 0, 0, 0, 0, 0, 0, 0, 1, 0],\n",
       "       [0, 0, 0, 0, 0, 0, 0, 0, 0, 1]])\n",
       "      jac: array([0., 0., 0., 0., 0., 0., 0., 0., 0., 0.])\n",
       "  message: 'Optimization terminated successfully.'\n",
       "     nfev: 11\n",
       "      nit: 0\n",
       "     njev: 1\n",
       "   status: 0\n",
       "  success: True\n",
       "        x: array([-2.31112277, -0.22398937, -0.77633992, -0.24507057,  1.08540813,\n",
       "       -0.06506067, -0.18069737, -1.61171466,  0.08420666, -1.92671993])"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p = 5 # p is the number of QAOA alternating operators\n",
    "objective_function = function_to_minimize(Graph, p)\n",
    "x0=np.random.randn(10)#Initial parameters\n",
    "\n",
    "minim_solution = minimize(objective_function, x0) # Minimization of scalar function of one or more variable from scipy\n",
    "minim_solution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "optimal_theta = minim_solution['x'] # The optimal parameters to use"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "backend = Aer.get_backend('qasm_simulator')\n",
    "qc = qaoa_circuit(Graph, optimal_theta,p) # Define the quantum circuit with the optimal parameters\n",
    "counts = invert_counts(execute(qc, backend).result().get_counts()) # Get the results\n",
    "#counts"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Compute the maxcut objective function for the optimal parameters\n",
    "results = []\n",
    "for x in counts.keys():\n",
    "    results.append([maxcut_objective_function(x,Graph),x]) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Best string: 01010 with cut: 5\n"
     ]
    }
   ],
   "source": [
    "# Get the best solution given the results of the maxcut objective function\n",
    "best_cut, best_solution = min(results)\n",
    "print(f\"Best string: {best_solution} with cut: {-best_cut}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Define the colors of the nodes for the best solution\n",
    "colors = ['r' if best_solution[node] == '0' else 'b' for node in Graph]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "nx.draw(Graph,node_color = colors)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Part IV: General Case"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "def solution_max_cut(G):\n",
    "    r\"\"\"\n",
    "    ############################################\n",
    "    # Compute the solution for the maxcut problem given a graph G\n",
    "    #\n",
    "    # G: graph\n",
    "    # return:The draw of the best solution with two colors. Print the solution in the binary string form and the number of cuts \n",
    "    ###############\n",
    "    \"\"\"\n",
    "    p = 5 # p is the number of QAOA alternating operators\n",
    "    objective_function = function_to_minimize(G, p)\n",
    "    x0=np.random.randn(10)#Initial parameters\n",
    "\n",
    "    new_parameters = minimize(objective_function, x0) # Minimization of scalar function of one or more variable from scipy\n",
    "    \n",
    "    optimal_theta = new_parameters['x']# The optimal parameters to use\n",
    "    qc = qaoa_circuit(G, optimal_theta,p) # Define the quantum circuit with the optimal parameters\n",
    "    counts = invert_counts(execute(qc, backend).result().get_counts()) # Get the results\n",
    "    \n",
    "    # Compute the maxcut objective function for the optimal parameters\n",
    "    results = []\n",
    "    for x in counts.keys():\n",
    "        results.append([maxcut_objective_function(x,G),x])\n",
    "        \n",
    "    best_cut, best_solution = min(results) # Get the best solution given the results of the maxcut objective function\n",
    "    colors = ['r' if best_solution[node] == '0' else 'b' for node in G] # Define the colors of the nodes for the best solution\n",
    "    return nx.draw(G,node_color = colors),print(f\"Best string: {best_solution} with cut: {-best_cut}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Graph1 = nx.Graph()\n",
    "Graph1.add_edges_from([[0,1],[0,2],[2,1]])\n",
    "nx.draw(Graph1,with_labels=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Best string: 001 with cut: 2\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "(None, None)"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "solution_max_cut(Graph1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "graph2 = nx.random_regular_graph(3, 4, seed=1234)\n",
    "nx.draw(graph2)          #drawing the graph\n",
    "plt.show()              #plotting the graph"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Best string: 0011 with cut: 4\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "(None, None)"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "solution_max_cut(graph2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# **Solution for a random graph of 12 nodes**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "graph3 = nx.random_regular_graph(3, 12, seed=1234)\n",
    "nx.draw(graph3)          #drawing the graph\n",
    "plt.show()              #plotting the graph"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Best string: 001111000110 with cut: 14\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "(None, None)"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "solution_max_cut(graph3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## References\n",
    "\n",
    "[1] https://arxiv.org/abs/1411.4028\n",
    "\n",
    "[2] https://www.cs.umd.edu/class/fall2018/cmsc657/projects/group_16.pdf\n",
    "\n",
    "[3] https://ieeexplore.ieee.org/document/8939749\n",
    "\n",
    "[4] https://www.mustythoughts.com/quantum-approximate-optimization-algorithm-explained"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "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": "3.8.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}