QuantumWalk.ipynb

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   "source": [
    "# Quantum walk search algorithm\n"
   ]
  },
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    "$$\\newcommand{\\ket}[1]{\\left|{#1}\\right\\rangle}$$\n",
    "$$\\newcommand{\\bra}[1]{\\left\\langle{#1}\\right|}$$\n",
    "$$\\newcommand{\\braket}[2]{\\left\\langle{#1}\\middle|{#2}\\right\\rangle}$$\n"
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   "source": [
    "import numpy as np\n",
    "import networkx as nx\n",
    "from networkx import hypercube_graph\n",
    "from networkx.drawing.nx_agraph import graphviz_layout\n",
    "import matplotlib.pyplot as plt\n",
    "from typing import Callable\n",
    "from qiskit import QuantumCircuit, Aer, QuantumRegister, ClassicalRegister, transpile\n",
    "from qiskit.quantum_info import Operator\n",
    "from qiskit.tools.visualization import plot_histogram, plot_bloch_vector\n",
    "from qiskit_aer import AerSimulator\n",
    "from numpy import pi\n"
   ]
  },
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   "source": [
    "## Base quantum computing concepts\n",
    "\n",
    "The physics of quantum computing is marvelous, but very complex.\n",
    "\n",
    "> If you think you understand quantum mechanics, you don't understand quantum mechanics.\n",
    ">\n",
    "> - Richard Feynman\n"
   ]
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   "source": [
    "### Hilbert space\n",
    "\n",
    "Luckily, it is possible to abstract the inner working of a quantum computer using some mathematical abstractions.\n",
    "The state of a quantum computer can be represented as a vector in a Hilbert space.\n",
    "The Hilbert space $\\mathcal{H}$ is a vector space with an inner product, and the inner product is defined as follows:\n",
    "\n",
    "$$\n",
    "\\langle \\psi | \\phi \\rangle = \\sum_{i=1}^n \\bar{\\psi_i} \\phi_i\n",
    "$$\n",
    "\n",
    "where $\\psi$ and $\\phi$ are two vectors in the Hilbert space, and $\\bar{\\psi}_i$ is the complex conjugate of $\\psi_i$.\n",
    "\n",
    "It is also possible to define the norm of a vector in the Hilbert space by using the inner product:\n",
    "\n",
    "$$\n",
    "\\| \\psi \\| = \\sqrt{\\langle \\psi | \\psi \\rangle}\n",
    "$$\n"
   ]
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   "source": [
    "### Superposition\n",
    "\n",
    "One of the peculiar properties of a quantum system is its ability to be in a superposition of states.\n",
    "Mathematically, this means that a quantum state can be represented as a linear combination of other states:\n",
    "\n",
    "$$\n",
    "\\ket{\\psi_1}, \\ket{\\psi_2} \\in \\mathcal{H} \\implies \\ket{\\psi} = \\alpha \\ket{\\psi_1} + \\beta \\ket{\\psi_2}, \\ket{\\psi} \\in \\mathcal{H} \\\\\n",
    "\\forall \\alpha, \\beta \\in \\mathbb{C}\n",
    "$$\n"
   ]
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   "source": [
    "### Linear operators\n",
    "\n",
    "Operating over the state of a quantum system means applying a linear operator to the state vector.\n",
    "Linear operators over a $d$-dimensional Hilbert space may be represented as a $d \\times d$ matrix.\n",
    "They all follow the common mathematical rules associated with matrices.  \n",
    "In particular, given an operator $A$, it satisfies the linearity condition:\n",
    "\n",
    "$$\n",
    "A(\\alpha \\ket{\\psi_1} + \\beta \\ket{\\psi_2}) = \\alpha A(\\ket{\\psi_1}) + \\beta A(\\ket{\\psi_2}) \\\\\n",
    "\\forall \\alpha, \\beta \\in \\mathbb{C}, \\forall \\ket{\\psi_1}, \\ket{\\psi_2} \\in \\mathcal{H}\n",
    "$$\n"
   ]
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   "source": [
    "### Normal unitary operators\n",
    "\n",
    "A normal unitary operator is a linear operator that satisfies the following conditions:\n",
    "\n",
    "$$\n",
    "A^\\dagger A = I \\\\\n",
    "AA^\\dagger = I \\\\\n",
    "$$\n",
    "\n",
    "where $A^\\dagger$ is the complex conjugate of $A$ and $I$ is the identity matrix.\n",
    "\n",
    "The reason why normal unitary operators are so important is because of their useful properties:\n",
    "\n",
    "- the rows and columns of a normal unitary operator are orthonormal vectors\n",
    "- they preserve the inner product and, by extension, the norm of the state vector\n",
    "  - $\\braket{\\psi_1 A}{A \\psi_2} = \\bra{\\psi_1} A^\\dagger A \\ket{\\psi_2} = \\braket{\\psi_1}{\\psi_2}$\n"
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   "source": [
    "### Tensor product\n",
    "\n",
    "The tensor product is a mathematical operation that allows to join two systems together.\n",
    "Given two matrices $A$ and $B$, their tensor product is defined as follows:\n",
    "\n",
    "$$\n",
    "A \\otimes B = \\begin{bmatrix} a_{11} B & a_{12} B & \\dots & a_{1n} B \\\\ a_{21} B & a_{22} B & \\dots & a_{2n} B \\\\ \\vdots & \\vdots & \\ddots & \\vdots \\\\ a_{m1} B & a_{m2} B & \\dots & a_{mn} B \\end{bmatrix}\n",
    "$$\n"
   ]
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    "Similarly, given two vectors $\\ket{\\psi}$ and $\\ket{\\phi}$, their tensor product is defined as follows:\n"
   ]
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    "$$\n",
    "\\ket{\\psi} \\otimes \\ket{\\phi} = \\begin{bmatrix} \\psi_1 \\\\ \\psi_2 \\\\ \\vdots \\\\ \\psi_n \\end{bmatrix} \\otimes \\begin{bmatrix} \\phi_1 \\\\ \\phi_2 \\\\ \\vdots \\\\ \\phi_m \\end{bmatrix} = \\begin{bmatrix} \\psi_1 \\phi_1 \\\\ \\psi_1 \\phi_2 \\\\ \\vdots \\\\ \\psi_1 \\phi_m \\\\ \\psi_2 \\phi_1 \\\\ \\psi_2 \\phi_2 \\\\ \\vdots \\\\ \\psi_2 \\phi_m \\\\ \\vdots \\\\ \\psi_n \\phi_1 \\\\ \\psi_n \\phi_2 \\\\ \\vdots \\\\ \\psi_n \\phi_m \\end{bmatrix}\n",
    "$$\n"
   ]
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   "source": [
    "## Common operators\n",
    "\n",
    "When dealing with quantum computing, there are some operators that are used very often.\n"
   ]
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    "### Pauli's operators\n",
    "\n",
    "Four of the most common operators are:\n",
    "\n",
    "- the identity operator, which does not change the state of the system\n",
    "- the Pauli-X operator, which flips the state of the qubit\n",
    "- the Pauli-Y operator, which rotates the state of the qubit by $\\pi/2$\n",
    "- the Pauli-Z operator, which flips the sign of the state of the qubit\n"
   ]
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   "source": [
    "In their matrix representation, they become:\n",
    "\n",
    "$$\n",
    "I = \\begin{bmatrix} 1 & 0 \\\\ 0 & 1 \\end{bmatrix} \\\\\n",
    "X = \\begin{bmatrix} 0 & 1 \\\\ 1 & 0 \\end{bmatrix} \\\\\n",
    "Y = \\begin{bmatrix} 0 & -i \\\\ i & 0 \\end{bmatrix} \\\\\n",
    "Z = \\begin{bmatrix} 1 & 0 \\\\ 0 & -1 \\end{bmatrix}\n",
    "$$\n"
   ]
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   "source": [
    "### Hadamard operator\n",
    "\n",
    "The Hadamard operator is a normal unitary operator that maps the state $\\ket{0}$ to $\\ket{+}$ and $\\ket{1}$ to $\\ket{-}$, where $\\ket{+}$ and $\\ket{-}$ are the Hadamard basis states.\n",
    "\n",
    "$$\n",
    "\\ket{+} = \\frac{1}{\\sqrt{2}} \\begin{bmatrix} 1 \\\\ 1 \\end{bmatrix} \\\\\n",
    "\\ket{-} = \\frac{1}{\\sqrt{2}} \\begin{bmatrix} 1 \\\\ -1 \\end{bmatrix} \\\\\n",
    "\\\\\n",
    "H = \\frac{1}{\\sqrt{2}} \\begin{bmatrix} 1 & 1 \\\\ 1 & -1 \\end{bmatrix} \\\\\n",
    "$$\n",
    "\n",
    "The Hadamard operator is very useful because it allows to create superpositions of states.\n",
    "When in a $\\ket{-}$ or $\\ket{+}$ state, measuring the qubit will collapse to either $0$ or $1$ with a probability of exactly $\\frac{1}{2}$.\n",
    "It can be seen as a perfectly balanced coin.\n"
   ]
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    "### Phase operator\n",
    "\n",
    "The phase operator is able to rotate the state of the qubit by $\\pi/2$ around the Z axis.\n",
    "\n",
    "$$\n",
    "S = \\begin{bmatrix} 1 & 0 \\\\ 0 & i \\end{bmatrix} \\\\\n",
    "$$\n"
   ]
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   "source": [
    "## Quantum computation\n"
   ]
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    "### Qubit\n",
    "\n",
    "The fundamental unit of quantum computation is the qubit.\n",
    "It can be seen as the quantum equivalent of a classical bit, albeit with very different properties.\n",
    "A qubit $\\ket{\\psi}$ is defined as the superposition of two states:\n",
    "\n",
    "$$\n",
    "\\ket{0} = \\begin{bmatrix} 1 \\\\ 0 \\end{bmatrix} \\\\\n",
    "\\ket{1} = \\begin{bmatrix} 0 \\\\ 1 \\end{bmatrix} \\\\\n",
    "\\ket{\\psi} = \\alpha \\ket{0} + \\beta \\ket{1} \\\\\n",
    "\\alpha, \\beta \\in \\mathbb{C}\n",
    "$$\n"
   ]
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    "Another way to represent qubits is by using the Bloch sphere.  \n",
    "The Bloch sphere is a three-dimensional representation of the qubit state.\n",
    "Operators such as the Pauli-X, Pauli-Y and Pauli-Z operators can be used to rotate the qubit around the Bloch sphere.\n",
    "We can simplify the notation of a qubit using the angles $\\theta$ and $\\phi$, defined from the $\\ket{0}$ and the x point, respectively:\n",
    "\n",
    "$$\n",
    "\\ket{\\psi} = \\cos \\frac{\\theta}{2} \\ket{0} + e^{i \\phi} \\sin \\frac{\\theta}{2} \\ket{1} \\\\\n",
    "$$\n",
    "\n",
    "Notice that such a vector is a unit vector: $\\cos^2{\\frac{\\theta}{2}} + \\sin^2 {\\frac{\\theta}{2}} = 1$.\n"
   ]
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   "source": [
    "This is the the qubit $\\ket{+}$ on the Bloch sphere.\n"
   ]
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",
      "text/plain": [
       "<Figure size 500x500 with 1 Axes>"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "coords = [1, np.pi / 2, 0]  # [Radius, Theta, Phi]\n",
    "plot_bloch_vector(coords, coord_type=\"spherical\")\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### Quantum gates\n",
    "\n",
    "When seen in the context of quantum computing, the operators we have seen so far are called quantum gates.\n",
    "They are usually represented by a square that applies the operator to the qubit.\n",
    "\n",
    "Starting from a state $\\ket{\\psi_0} = \\ket{0} \\otimes \\ket{0}$, the quantum circuit shown produces a final $\\ket{\\psi_f} = (H \\otimes I)(X \\otimes Y)(H \\otimes X)\\ket{\\psi_0}$.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "hide_input": true,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAWAAAACuCAYAAAAI9Nc8AAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjYuMiwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy8o6BhiAAAACXBIWXMAAA9hAAAPYQGoP6dpAAAV+UlEQVR4nO3df3RU5Z3H8fedCQlGqA1pERJ+hCaGkBA5kWz5URYCSxpa8UhpbUDGJf4qa9dNFUyWH56zns0eJELQPZ5dWX4oJtKKtbFiBEkVeqiNqEhYRBYjnAYSSKIswYMSMszcu3/kJEtIQgmZzCOTz+sc/3Ce5975zuXOZ54897kzluM4DiIiEnQu0wWIiPRVCmAREUMUwCIihiiARUQMUQCLiBiiABYRMUQBLCJiiAJYRMQQBbCIiCEKYBERQxTAIiKGKIBFRAxRAIuIGKIAFhExRAEsImKIAlhExBAFsIiIIQpgERFDFMAiIoYogEVEDFEAi4gYogAWETFEASwiYogCWETEEAWwiIghCmAREUMUwCIihiiARUQMUQCLiBiiABYRMUQBLCJiiAJYRMQQBbCIiCEKYBERQxTAIiKGKIBFRAxRAIuIGBJmugAJLY4DXr/pKron3A2WFbj9OY7Defv6OgiRLjdWgA6CzoGrpwCWgPL64Z+3mq6iewqzISKA74Tztp+oXX8I3A6DoHFGJje6A3MQdA5cPU1BiIgYogAWETFEASwiYogCWETEEAWwiIghCmAREUMUwCIihiiARUQMUQCLiBiiABYRMUQB3Euqq6uxLIuMjAzTpYjIN5QC2KDy8nJmzZpFdHQ0kZGRpKam8uSTT+L1ek2XJiJBoAA2pKioiKysLHbu3MnAgQMZPXo0R44cYfny5WRkZNDU1GS6RBHpZQpgAz744APy8vKwLIsXXniB6upqKisrOXLkCAkJCbz33nssW7bMdJki0ssUwAYUFBTgOA733nsvOTk5bY/Hx8ezadMmAJ577jk+//zzDttWVFTwxRdfBKtUY2oP/5F/91h8uG1Vl33+8/4BvPpvGcErKsj8z2/m4g9/jP1WeaftvqUruPijO3A+OxrkyoKjL5wDIR/Ap0+f5rHHHiM+Pp7+/fszfPhwlixZQlNTEx6PB8uy2LhxY9DqOXfuHOXlLW+oBx98sEP71KlTSUxMxOv1sm3btg7t69evJzY2ljlz5vDaa69pvjiEue5ZAKPi8K9bj3PZh7H/jTdx9lfimp+NdUuCoQqlp0I6gA8ePMjYsWMpKiqioaGB5ORkvF4va9euxePx8OmnnwIwbty4oNVUWVmJ1+slIiKC9PT0TvtMmTIFgL1793Zou+2224iIiOD1119n7ty5xMTEkJuby0cffdSrdUvwWf36EZa3BLxe/GuexnEcAJy6OuwNmyAhHtfd8wxXKT0RsgF8+vRpZs+eTUNDA/n5+dTX17N//34aGhooKCigtLSUAwcO4HK5GDt2bNDqqqqqAmDkyJGEhXX+Ffzx8fHt+l4qNzeXhoYGSkpKyMzMpLGxkWeffZb09HRSU1NZs2YN9fX1vfcCJKishHhc87NxDvw39rYyHNvGv3ot+H2E5S3G6uIckutDyAZwbm4uNTU1LF68mMLCQgYMGNDWtmLFCpKSkvD5fCQmJnLDDTcEra7GxkYAoqKiuuzT2tba93KRkZF4PB7Ky8upqanhqaeeIjU1lUOHDpGXl8ewYcO4/fbbeeWVV2hubg78iwgin/c8TedOd/pfX+G6ex4kJGBvfB77ufU4hz7B5VmANWqU6dKCIpTPgZD8+Dx8+DBbt25l8ODBFBQUdGi3LIvx48dz5MiRDtMPf/nLX/jVr37F7t27CQsL44477uDpp58mOjo6ILVduHABgPDw8C77REREAFzVUrSYmBjy8vLIy8ujsrKSkpISfv3rX7N9+3a2b99OVFQU2dnZPPLII4wePTogryGYPvh9AR/8vuO/YV9iud2E5S3G93Au9uvbsEYn4vr5z0yXFTShfA6EZABv2bIF27bxeDxERkZ22qc15C4N4HPnzjF9+nQGDRrEb37zG5qamsjPz2f27Nn8+c9/xuXq+R8M/fv3B7jixbPWUWt3R+ZpaWmkpaWxevVqdu7cyYoVKzhw4ADr1q3j5ptv5oknnujW/tLT07s9neHudwM/+bfPurXNlaRMu5/ESZ3Pc24ruiMgz5F4yy34LwZu3bUTHg7/9R8B2x8AN0ZCv35w0Yf1N+lYbndAd594SyJWgC7o9rVzYMiQIezbt++atg3JAH7nnXcAmD59epd9amtrgfYBvH79ek6ePMmePXsYMWIEALGxsfzgBz9g27ZtzJkzp8e1/bXphUvbrjRN0ZW6ujq2bNlCcXExH3/8MdAy2m59Pd1RX1/PyZMnu7VNWETnH3jX6qabExgxdmanbS5XYELoVN0pfM3nA7IvAPpH0C9we8NxHPxFz4D3Iowcgb31t7gypmJdw79pV07VnYILgZmu0jlw9UIygI8fPw5AXFxcp+3Nzc28//77QPsALisrY8qUKe3CavLkycTFxfHGG28EJIATExPbavT5fJ1eiDt27Fi7vn/N+fPnKS0tpaSkhLfffhvbtoGWEWxOTg7z589n0KBB3a51yJAh3d7G3S948+mBEjM0JuAj4ECu1LbfKMOpPIDr7z24pk3F99DD+Fevxf1MUcBGwjFDYwI6Ar7e9OQcuJb3SauQDOCvv/4a+P/51su99NJLfPnll0RHRxMbG9v2+OHDh7nrrrs69E9OTubw4cMBqS0tLY3w8HCam5vZt28fEydO7NDn3XffBWDChAld7se2bXbv3k1xcTGlpaV89dVXQMucsMfjYeHChSQnJ/eo1mv5s6rZB/+8tUdPG3RVn31GRADfCV/7fUTt+kNA9uWcqsPe+ALWLQkta37dblwL78HesAn7t7/DPe/nAXmeqs+quNEdmIOgc+DqheQqiNZPpM4CpKampu0231tvvbVdW2NjI9/+9rc7bBMVFcWZM2cCUtvAgQPJzMwEYMOGDR3a9+zZQ1VVFeHh4dx5550d2quqqli6dCkjR45k5syZFBcX4/P5yM7OZseOHZw4cYLCwsIeh6+Y59g2/jVrwe/HnbekbbTr+ulPsJLHYJdswTl+wnCV0hMhGcAzZ7bMF61cubLdWtq9e/cyY8YMzp49C3R+A4ZlWR0ea10AHyiPP/542/dAvPjii22PHzt2jPvvvx+ARYsWMXjw4A7brly5ksLCQmpra5k0aRLr1q2jvr6el19+mVmzZuEO8MUZMcf+3WstS84WerDiRrY9brlcuB97FFwu/GvW4vj9BquUngjJAF66dClRUVHU1NSQkpJCamoqCQkJTJo0iTFjxrTdaXZ5AEdFRXV6cezs2bPXNIfalYkTJ7Jq1SocxyEnJ4e4uDjS0tJISkri6NGjTJgwgVWrOr//ffjw4SxfvpyqqioqKipYtGgRN910U8Bqk28G58QJ7BdLsMYk4frp3A7t1rBhuBbeg/NpFfYrrxqoUALBcgI9vPuG+OSTT8jPz2fPnj1YlkVKSgoPPPAA9913H7GxsdTV1bF//37S0tLatsnIyMDlcrFr1652+xo1ahTTp0/n+eefv+rnr66uZtSoUUybNo0//vGPnfbZuXMnRUVFfPjhh1y4cIHvfe97LFiwgCVLlrQtk7veXI/zf4XZfGPngIOlcUZmn54DDvQ5cLVC8iIcQEpKCm+++WaHx8+cOUNdXR1hYWEd5klnz57N8uXLqampYfjw4UDLtEV1dTV33BGY9YaXysrKIisrK+D7FZHrQ0hOQVxJ69rYpKSkDqPMX/ziFwwdOpQ5c+ZQVlbGq6++yt133833v//9Ti+IiYj0RJ8N4M4uwH3rW99i165dDB06lHnz5vHAAw8wefJkysrKAnIXnIjIpUJ2CqIrVwpgaPkmsrKysmCWJCJ9VJ8b1rUG8OVrgEVEgq3PjYArKiqC8jxxcXEBXz8sIqGlz42ARUS+KRTAIiKGKIBFRAxRAIuIGKIAFhExRAEsImKIAlhExBAFsIiIIQpgERFDQvb7gMUMxwHvdfYDDeFu6OSHUK6Z4zict6+vgxDpcnf6azDXQufA1VMAi4gYoikIERFDFMAiIoYogEVEDFEAi4gYogAWETFEASwiYogCWETEEAWwiIghCmAREUMUwCIihiiARUQMUQCLiBiiABYRMUQBLCJiiAJYRMQQBbCIiCEKYBERQ8JMFyChpa//HA/oGMjVUwBLQJ23/UTt+oPpMrqlcUYmN7oD91bQMZCrpSkIERFDFMAiIoYogEVEDFEAi4gYogAWETFEASwiYogCWETEEAWwiIghCmAREUMUwCIihiiAe0l1dTWWZZGRkWG6FBH5hlIAG1ReXs6sWbOIjo4mMjKS1NRUnnzySbxer+nSRCQIFMCGFBUVkZWVxc6dOxk4cCCjR4/myJEjLF++nIyMDJqamkyXKCK9TAFswAcffEBeXh6WZfHCCy9QXV1NZWUlR44cISEhgffee49ly5aZLlNEepkC2ICCggIcx+Hee+8lJyen7fH4+Hg2bdoEwHPPPcfnn3/eYduKigq++OKLYJVqlP/5zVz84Y+x3yrvtN23dAUXf3QHzmdHg1xZcPj+5V+5OGs29qFPOm23D/8PF2fNxvcv/xrkyiRQQj6AT58+zWOPPUZ8fDz9+/dn+PDhLFmyhKamJjweD5ZlsXHjxqDVc+7cOcrLWwLlwQcf7NA+depUEhMT8Xq9bNu2rUP7+vXriY2NZc6cObz22mshPV/sumcBjIrDv249zmUfRv433sTZX4lrfjbWLQmGKuxd7kf+CQYOwL9mLU7ThXZtTnMz/jVrYeAA3I/kGqpQeiqkA/jgwYOMHTuWoqIiGhoaSE5Oxuv1snbtWjweD59++ikA48aNC1pNlZWVeL1eIiIiSE9P77TPlClTANi7d2+Htttuu42IiAhef/115s6dS0xMDLm5uXz00Ue9WrcJVr9+hOUtAa8X/5qncRwHAKeuDnvDJkiIx3X3PMNV9h4rKgp37sNwqg5746Z2bfbzm6H2JO5f/RNW1LeN1Cc9F7IBfPr0aWbPnk1DQwP5+fnU19ezf/9+GhoaKCgooLS0lAMHDuByuRg7dmzQ6qqqqgJg5MiRhIV1/gsE8fHx7fpeKjc3l4aGBkpKSsjMzKSxsZFnn32W9PR0UlNTWbNmDfX19b33AoLMSojHNT8b58B/Y28rw7Ft/KvXgt9HWN5irC6OYahw/e0UrBnTscu2Y++vBMA++DH277dh/d10XFN+YLhC6YmQDeDc3FxqampYvHgxhYWFDBgwoK1txYoVJCUl4fP5SExM5IYbbghaXY2NjQBERUV12ae1rbXv5SIjI/F4PJSXl1NTU8NTTz1Famoqhw4dIi8vj2HDhnH77bfzyiuv0NzcHPgXEWSuu+dBQgL2xuexn1uPc+gTXJ4FWKNGmS4tKNwPPwTRg/AXPYPzv/+Lf83TED0I9z8+ZLo06aGQDODDhw+zdetWBg8eTEFBQYd2y7IYP3480H76oba2ltzcXCZPnkxkZCSWZVFdXR3Q2i5caJnLCw8P77JPREQEwFUtRYuJiSEvL4+DBw+yf/9+Hn30Ub7zne+wfft2srOzGTp0KA899FDbdMv1yHK7CctbDLYf+/VtWKMTcf38Z6bLChprwADcix+FL77A9w//CPX1uBc/inXJoEKuTyH599uWLVuwbRuPx0NkZGSnfVpD7tIAPnr0KFu3bmX8+PFMmzaNt956K+C19e/fH+CKF89aR63dHZmnpaWRlpbG6tWr2blzJytWrODAgQOsW7eOm2++mSeeeKJb+0tPT+/2dIYTHg7/9R/d2uaq3BgJ/frBRR/W36Rjud0B23XiLYlYAbyY2RvHwJV+G/aPZuHseAvXj3+EK/22gO4/0MegLxkyZAj79u27pm1DMoDfeecdAKZPn95ln9raWqB9AE+dOpWGhgYANm/e3CsB/NemFy5tu9I0RVfq6urYsmULxcXFfPzxx0DLaHvEiBHd3ld9fT0nT57s3kb9I+jX7We6Msdx8Bc9A96LMHIE9tbf4sqYinUNr6kzp+pOwYUATtX0wjEAcKWMwb/jLazkpIDvO+DHQK5KSAbw8ePHAYiLi+u0vbm5mffffx9oH8AuV+/PyCQmJgItNfp8vk4vxB07dqxd37/m/PnzlJaWUlJSwttvv41t20DLCDYnJ4f58+czaNCgbtc6ZMiQbm/jhIcT6FXK9htlOJUHcP29B9e0qfgeehj/6rW4nykKyEg4ZmhMwEfA19tK7UAfg77kWt4nrUIygL/++mvg/+dbL/fSSy/x5ZdfEh0dTWxsbDBLIy0tjfDwcJqbm9m3bx8TJ07s0Ofdd98FYMKECV3ux7Ztdu/eTXFxMaWlpXz11VdAy5ywx+Nh4cKFJCcn96jWa/mz6mu/j6hdf+jR817KOVWHvfEFrFsSWtb8ut24Ft6DvWET9m9/h3vez3v8HFWfVXGjO3BvhUAfg2AI9DGQqxOSF+FaP5E6C5Campq223xvvfXWoNYFMHDgQDIzMwHYsGFDh/Y9e/ZQVVVFeHg4d955Z4f2qqoqli5dysiRI5k5cybFxcX4fD6ys7PZsWMHJ06coLCwsMfh+03g2HbLzQZ+P+68JW2jXddPf4KVPAa7ZAvO8ROGqxS5diEZwDNnzgRg5cqV7dbS7t27lxkzZnD27FkguDdgXOrxxx9v+x6IF198se3xY8eOcf/99wOwaNEiBg8e3GHblStXUlhYSG1tLZMmTWLdunXU19fz8ssvM2vWLNwBvDhlmv2711qWnC30YMWNbHvccrlwP/YouFwtd4n5/QarFLl2IRnAS5cuJSoqipqaGlJSUkhNTSUhIYFJkyYxZsyYtjvNTAXwxIkTWbVqFY7jkJOTQ1xcHGlpaSQlJXH06FEmTJjAqlWrOt12+PDhLF++nKqqKioqKli0aBE33XRTkF9B73NOnMB+sQRrTBKun87t0G4NG4Zr4T04n1Zhv/KqgQpFei4kJ31GjBjBn/70J/Lz89mzZw/Hjx8nJSWFZcuWcd9997XN+5oKYID8/HzGjRtHUVERH374IQ0NDSQmJrJgwQKWLFnStkzucp2taw5F1ogR9Cv7/RX7uH82F/fPOoZzqHL9MBPXDzNNlyEBFJIBDJCSksKbb77Z4fEzZ85QV1dHWFiY8XnSrKwssrKyjNYgIuaEbAB3pXVtbFJSUqejzFdfbflztvUC3o4dO/jud79LXFxcl1+eIyJyLfpsAHc1/XDXXXe1+/9f/vKXACxcuJDNmzf3am0i0rcogC/T+pWHIiK9LSRXQVxJawCbWAMsInKpPjcCrqioCMrzxMXFaTQtIlfU50bAIiLfFApgERFDFMAiIoYogEVEDFEAi4gYogAWETFEASwiYogCWETEEAWwiIghlqPbtSSAHMfhvH19/UJFpMuNZVkB25+OgVwtBbCIiCGaghARMUQBLCJiiAJYRMQQBbCIiCEKYBERQxTAIiKGKIBFRAxRAIuIGKIAFhExRAEsImKIAlhExBAFsIiIIQpgERFDFMAiIoYogEVEDFEAi4gYogAWETFEASwiYogCWETEEAWwiIghCmAREUMUwCIihiiARUQMUQCLiBiiABYRMeT/AKAeLCPpvb4WAAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 431.799x200.667 with 1 Axes>"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qc = QuantumCircuit(2)\n",
    "qc.h(0)\n",
    "qc.x(1)\n",
    "qc.x(0)\n",
    "qc.y(1)\n",
    "qc.h(0)\n",
    "qc.draw(\"mpl\", initial_state=True)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### Controlled gates\n",
    "\n",
    "Another important building block of quantum circuits are controlled gates.\n",
    "They are gates that are applied to a qubit only if the controlling qubits are in a specific state, usually $\\ket{1}$.\n",
    "The controlled-NOT gate is the most common controlled gate, and the corresponding matrix is:\n",
    "\n",
    "$$\n",
    "CNOT = \\begin{bmatrix} 1 & 0 & 0 & 0 \\\\ 0 & 1 & 0 & 0 \\\\ 0 & 0 & 0 & 1 \\\\ 0 & 0 & 1 & 0 \\end{bmatrix}\n",
    "$$\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "hide_input": true,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 431.799x200.667 with 1 Axes>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qc = QuantumCircuit(2)\n",
    "qc.x(0)\n",
    "qc.cx(0, 1)\n",
    "qc.x(0)\n",
    "qc.draw(\"mpl\", initial_state=True)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### Quantum algorithms\n",
    "\n",
    "As seen before, it is possible to apply some unitary operators to a qubit, altering the state of the system.\n",
    "Then, a quantum algorithm can be seen as a sequence of unitary operators applied to an initial state, in order to solve a problem.\n",
    "\n",
    "$$\n",
    "\\ket{\\psi_n} = U_n U_{n-1} \\dots U_1 \\ket{\\psi_0}\n",
    "$$\n",
    "\n",
    "Finally, the result of the algorithm can be obtained by measuring the qubits.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Classical Markov chains\n",
    "\n",
    "A Markov chain can be seen as a set of nodes, linked to each other by a probability distribution.  \n",
    "The transition between a node and the following is random and depends only on the probability of the outgoing links of the current node.  \n",
    "This property is called **Markovian property**.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Markov chain can be further classified as **discrete** or **continuous**, depending the times steps.\n",
    "Only **discrete** Markov chains are considered in this presentation.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### Transition matrix\n",
    "\n",
    "The transition matrix is a square matrix, with the number of rows and columns equal to the number of nodes.  \n",
    "It is used to describe the probability of transition between nodes.\n",
    "\n",
    "The probability distribution after $t$ steps (or at time $t$) can be obtained by multiplying the transition matrix by itself $t$ times: $P^t$.\n",
    "\n",
    "An example of a transition matrix could be\n",
    "\n",
    "$$\n",
    "P = \\begin{pmatrix}\n",
    "0.1 & 0.4 & 0.4 & 0.1 \\\\\n",
    "0.2 & 0.3 & 0.2 & 0.0 \\\\\n",
    "0.6 & 0.2 & 0.1 & 0.1 \\\\\n",
    "0.1 & 0.1 & 0.3 & 0.8 \\\\\n",
    "\\end{pmatrix}\n",
    "$$\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "cell_style": "split",
    "hide_input": true,
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pos = {1: [0.75, 1.0], 2: [0.75, 0.15], 3: [0.5, -0.5], 4: [1.0, -0.5]}\n",
    "U = [\n",
    "    [0.1, 0.2, 0.6, 0.1],\n",
    "    [0.4, 0.3, 0.2, 0.1],\n",
    "    [0.4, 0.2, 0.1, 0.3],\n",
    "    [0.1, 0.0, 0.1, 0.8],\n",
    "]\n",
    "\n",
    "G = nx.DiGraph(directed=True)\n",
    "for i in range(1, 5):\n",
    "    G.add_node(i)\n",
    "    for j in range(1, 5):\n",
    "        G.add_edge(i, j, weight=U[i - 1][j - 1])\n",
    "\n",
    "nx.draw(G, pos=pos, with_labels=True)\n",
    "nx.draw_networkx_edge_labels(\n",
    "    G, pos=pos, edge_labels=nx.get_edge_attributes(G, \"weight\")\n",
    ")\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Quantum walk\n",
    "\n",
    "Quantum walks are the equivalent to a classical Markov chain.  \n",
    "Due to superposition, a quantum walk can take all possible path simultaneously until the measurement makes the system collapse.  \n",
    "States can be manipulated so that some of them will cancel out, leaving only the desired one.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "There are two main models used to implement a quantum walk: **coined walk** and **Szegedy walk**.\n",
    "The two models can be equivalent under certain conditions.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### Coined walk\n",
    "\n",
    "A coined walk can be exemplified by a walk over the integer's line.\n",
    "The walker's position is represented with an integer  \n",
    "A coin is used to decide where to move next, left or right.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The walker is located at: x = -12\n"
     ]
    }
   ],
   "source": [
    "n_steps = 50  # Number of steps the walker will take\n",
    "pr = 0.5  # Probability of the walker stepping to the right\n",
    "initial_position = 0  # Initial position of our walker\n",
    "\n",
    "\n",
    "def random_walk(pr: float, n_steps: int, initial_pos: int) -> int:\n",
    "    \"\"\"Run a random walk with N steps and a probability of stepping to the right of pr.\n",
    "\n",
    "    Args:\n",
    "        pr: probability of stepping to the right\n",
    "        N: number of steps\n",
    "        i: initial position\n",
    "\n",
    "    Returns:\n",
    "        The final position of the walker\n",
    "    \"\"\"\n",
    "    position = initial_pos\n",
    "\n",
    "    for _ in range(n_steps):\n",
    "        coin_flip = list(\n",
    "            np.random.choice(2, 1, p=[1 - pr, pr])\n",
    "        )  # Flips our weighted coin\n",
    "        position += 2 * coin_flip[0] - 1  # Moves the walker according to the coin flip\n",
    "\n",
    "    return position\n",
    "\n",
    "\n",
    "print(f\"The walker is located at: x = {random_walk(pr, n_steps, initial_position)}\")\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Once plotted, the distribution of such a walk creates the following distribution:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "cell_style": "split",
    "hide_input": true,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def dist(n_runs: int, n_steps: int):\n",
    "    \"\"\"Plot the distribution of the random walk.\n",
    "\n",
    "    Args:\n",
    "        runs: number of runs\n",
    "        N: number of steps\n",
    "    \"\"\"\n",
    "    positions = range(-1 * n_steps, n_steps + 1)\n",
    "    instances = [0 for _ in range(-1 * n_steps, n_steps + 1)]\n",
    "\n",
    "    for _ in range(n_runs):\n",
    "        result = random_walk(pr, n_steps, initial_position)\n",
    "        instances[positions.index(result)] += 1\n",
    "\n",
    "    plt.bar(positions, [n / n_runs for n in instances])\n",
    "    plt.show()\n",
    "\n",
    "\n",
    "dist(10000, n_steps)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Quantum coin walk\n",
    "\n",
    "The coin walk algorithm can be translated in a pretty straightforward way to a quantum walk.\n",
    "The position of the walker is encoded in a $n$ dimensional space, with $2^n$ possible positions.\n",
    "The resulting Hilbert space is $\\mathcal{H}_p$, defined as $\\mathcal{H}_p = \\{\\ket{j} : j = 0, \\dots, n - 1 \\}$.\n",
    "\n",
    "To simulate the flip of a coin, we need to define an additional 2-dimensional space, $\\mathcal{H}_c$, defined as $\\mathcal{H}_c = \\{\\ket{i} : i = \\downarrow, \\uparrow \\}$.\n",
    "\n",
    "The space of all possible states of the system is obtained by combining the two components $\\mathcal{H} = \\mathcal{H_c} \\otimes \\mathcal{H_p}$.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "#### Coin operator\n",
    "\n",
    "While the coin can be represented with many different operators, the most common ones are:\n",
    "\n",
    "$$\n",
    "\\text{Hadamard gate} \\quad H = \\frac{1}{\\sqrt{2}} \\begin{bmatrix}\n",
    "1 & 1 \\\\\n",
    "1 & -1 \\\\\n",
    "\\end{bmatrix} \\\\\n",
    "\\ \\\\\n",
    "\\ \\\\\n",
    "\\text{Grover gate} \\quad G = \\begin{bmatrix}\n",
    "\\frac{2}{n} - 1 & \\frac{2}{n} & \\dots & \\frac{2}{n} \\\\\n",
    "\\frac{2}{n} & \\frac{2}{n} - 1 & \\dots & \\frac{2}{n} \\\\\n",
    "\\vdots & \\vdots & \\ddots & \\vdots \\\\\n",
    "\\frac{2}{n} & \\frac{2}{n} & \\dots & \\frac{2}{n} - 1 \\\\\n",
    "\\end{bmatrix}\n",
    "$$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "cell_style": "center",
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "While the Hadamard gate produces a uniform distribution, the Grover gate can be used to produce a skewed distribution.\n",
    "In the example above, applying the Grover gate to a state $\\ket{000}$ produces this kind of probability distribution:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "cell_style": "center",
    "hide_input": true,
    "scrolled": false,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Number of qubits\n",
    "n = 3\n",
    "# Initial state\n",
    "initial_state = np.array([1] + [0] * (2**n - 1))\n",
    "assert initial_state.size == 2**n\n",
    "\n",
    "# Hadamard gate\n",
    "hadamard_gate_base = 1 / np.sqrt(2) * np.array([[1, 1], [1, -1]])\n",
    "hadamard_gate = hadamard_gate_base\n",
    "for i in range(n - 1):\n",
    "    hadamard_gate = np.kron(hadamard_gate, hadamard_gate_base)\n",
    "\n",
    "# Grover's gate\n",
    "grover_gate = np.full((2**n, 2**n), 1 / 2 ** (n - 1)) - np.eye(2**n)\n",
    "\n",
    "# Apply gates\n",
    "hadamard_res = np.dot(initial_state, hadamard_gate)\n",
    "hadamard_res = np.square(hadamard_res)\n",
    "grover_res = np.dot(initial_state, grover_gate)\n",
    "grover_res = np.square(grover_res)\n",
    "\n",
    "# Plot results\n",
    "fig, axes = plt.subplots(2)\n",
    "plt.suptitle(\"Hadamard vs Grover gates (|000>)\")\n",
    "for ax, res in zip(axes, [hadamard_res, grover_res]):\n",
    "    ax.set_ylabel(\"Probability\")\n",
    "    ax.set_ylim(0, 1)\n",
    "    ax.bar(tuple(bin(i)[2:].zfill(n) for i in range(res.size)), res)\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "#### Shift operator\n",
    "\n",
    "The shift operator is able to move the walker to its next position.\n",
    "If the coin is in state $\\ket{\\downarrow}$, that corresponds to the $\\ket{0}$ qubit, the walker moves to the left. Otherwise, if the coin is in the $\\ket{\\uparrow}$ state, or $\\ket{1}$ qubit, it moves to the right.\n",
    "\n",
    "$$\n",
    "S(\\ket{\\downarrow} \\otimes \\ket{j}) = \\ket{\\downarrow} \\otimes \\ket{j-1} \\\\\n",
    "S(\\ket{\\uparrow} \\otimes \\ket{j}) = \\ket{\\uparrow} \\otimes \\ket{j+1}\n",
    "$$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Notice how the shift operator does not alter the state of the coin.\n",
    "An operator with such properties can be build with the following construction:\n",
    "\n",
    "$$\n",
    "S = \\ket{\\uparrow}\\bra{\\uparrow} \\otimes \\sum_j \\ket{j + 1}\\bra{j} + \\ket{\\downarrow}\\bra{\\downarrow} \\otimes \\sum_j \\ket{j - 1}\\bra{j} \\\\\n",
    "$$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "#### Example use of the shift operator\n",
    "\n",
    "Starting from the state $\\ket{\\uparrow}\\ket{2}$, the shift operator will produce the following states:\n",
    "\n",
    "$$\n",
    "\\begin{array}{ll}\n",
    "S(\\ket{\\uparrow} \\otimes \\ket{2}) &= (\\ket{\\uparrow}\\bra{\\uparrow} \\otimes \\sum_j \\ket{j + 1}\\bra{j} + \\ket{\\downarrow}\\bra{\\downarrow} \\otimes \\sum_j \\ket{j - 1}\\bra{j})(\\ket{\\uparrow} \\otimes \\ket{0}) \\\\\n",
    "&= \\ket{\\uparrow}\\braket{\\uparrow}{\\uparrow} \\otimes \\sum_j \\ket{j + 1}\\braket{j}{2} + \\\\\n",
    "&\\quad \\ket{\\downarrow}\\braket{\\downarrow | \\downarrow} \\otimes \\sum_j \\ket{j - 1}\\braket{j}{2} \\\\\n",
    "&= \\ket{\\uparrow} \\otimes \\sum_j \\ket{j + 1}\\braket{j}{2} + \\ket{\\downarrow}0 \\otimes \\sum_j \\ket{j - 1}\\braket{j}{2} \\\\\n",
    "&= \\ket{\\uparrow} \\otimes \\ket{3} + 0 \\otimes \\ket{1} \\\\\n",
    "&= \\ket{\\uparrow} \\otimes \\ket{3}\n",
    "\\end{array}\n",
    "$$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "#### Quantum walk operator\n",
    "\n",
    "Putting everything together, the quantum walk operator is the composition of the coin operator and the shift operator:\n",
    "\n",
    "$$\n",
    "U = S(C \\otimes I)\n",
    "$$\n",
    "\n",
    "where $S$ is the shift operator and $C$ is the chosen coin operator.\n",
    "The identity operator is added to the coin operator to keep the walker state unchanged.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "The same logic used for the classical Markov chain can be applied here.\n",
    "It is possible to obtain an operator able to compute $k$ steps at once by multiplying the operator by itself $k$ times: $U^k$.\n",
    "\n",
    "If $\\ket{\\psi(0)}$ is the initial state of the system, the state after $t$ steps can be calculated as $\\ket{\\psi(t)} = U^t\\ket{\\psi(0)}$\n",
    "\n",
    "Coined quantum walks are most suited for graphs where all nodes have the same number of neighbors.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "#### Coined walk example\n",
    "\n",
    "Assume that the starting position of the walker is $\\ket{0}$, and an Hadamard gate is used as the coin operator, starting in a state $\\ket{\\downarrow}$.\n",
    "The probability distribution of the first step can be calculated as:\n",
    "\n",
    "$$\n",
    "\\begin{array}{ll}\n",
    "\\ket{\\psi(1)} &= U\\ket{\\psi(0)} \\\\\n",
    "&= S(C \\otimes I)\\ket{\\psi(0)} \\\\\n",
    "&= S(H \\otimes I)(\\ket{\\downarrow} \\otimes \\ket{0}) \\\\\n",
    "&= S(\\frac{1}{\\sqrt{2}}(\\ket{\\downarrow} + \\ket{\\uparrow}) \\otimes \\ket{0}) \\\\\n",
    "&= (\\ket{\\uparrow}\\bra{\\uparrow} \\otimes \\sum_j \\ket{j + 1}\\bra{j})(\\frac{1}{\\sqrt{2}}(\\ket{\\downarrow} + \\ket{\\uparrow}) \\otimes \\ket{0}) + \\\\\n",
    "&\\quad (\\ket{\\downarrow}\\bra{\\downarrow} \\otimes \\sum_j \\ket{j - 1}\\bra{j}) (\\frac{1}{\\sqrt{2}}(\\ket{\\downarrow} + \\ket{\\uparrow}) \\otimes \\ket{0}) \\\\\n",
    "&= \\frac{1}{\\sqrt{2}}\\ket{\\uparrow} \\otimes \\ket{1} + \\frac{1}{\\sqrt{2}}\\ket{\\downarrow} \\otimes \\ket{-1} \\\\\n",
    "&= \\frac{1}{\\sqrt{2}}(\\ket{\\uparrow} \\otimes \\ket{1} + \\ket{\\downarrow} \\otimes \\ket{-1}) \\\\\n",
    "\\end{array}\n",
    "$$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Quantum coined walk implementation\n",
    "\n",
    "The implementation of the quantum coined walk will be done using the [Qiskit](https://qiskit.org/) simulator.  \n",
    "The code is inspired by the one found in the [Qiskit's Quantum Walk Search Algorithm](https://qiskit.org/textbook/ch-algorithms/quantum-walk-search-algorithm.html#2.A-Coined-quantum-walks-) and [Google's Quantum walk](https://quantumai.google/cirq/experiments/quantum_walks) examples.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### Quantum registers\n",
    "\n",
    "A circuit implementing a quantum coined needs:\n",
    "\n",
    "- a qubit to represent the coin\n",
    "  - $\\ket{0} \\iff \\downarrow$, $\\ket{1} \\iff \\uparrow$\n",
    "- $n$ qubits to represent the walker position\n",
    "  - with $n$ qubits, the number of possible positions is $2^n$\n",
    "  - the numbers are represented in binary form, with the most significant bit at the top\n",
    "- $n$ classical bits to store the measurement of the walker position\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "hide_input": true,
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 247.617x535.111 with 1 Axes>"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "n_walker_qubits = 4  # The number of qubits used to represent the position of the walker\n",
    "\n",
    "\n",
    "def coined_walk_circuit(\n",
    "    n_walker_qubits: int,\n",
    ") -> tuple[QuantumCircuit, QuantumRegister, QuantumRegister, ClassicalRegister]:\n",
    "    \"\"\"Create a quantum circuit for the quantum walk.\n",
    "\n",
    "    Args:\n",
    "        n_walker_qubits: number of qubits used to represent the position of the walker\n",
    "\n",
    "    Returns:\n",
    "        a tuple containing the circuit, the walker qubits, the coin qubits and the classical register to store the output\n",
    "    \"\"\"\n",
    "    walker_r = QuantumRegister(n_walker_qubits, name=\"w\")\n",
    "    coin_r = QuantumRegister(1, name=\"c\")  # The coin requires only one qubit\n",
    "    classic_r = ClassicalRegister(n_walker_qubits, name=\"output\")\n",
    "    qc = QuantumCircuit(walker_r, coin_r, classic_r)\n",
    "    return qc, walker_r, coin_r, classic_r\n",
    "\n",
    "\n",
    "qc, _, _, _ = coined_walk_circuit(n_walker_qubits)\n",
    "qc.draw(output=\"mpl\", initial_state=True)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### Initial state of the circuit\n",
    "\n",
    "The initial state of the circuit can be chosen arbitrarily.\n",
    "The coin state can be either $\\ket{0}$ or $\\ket{1}$, and the walker position can be any number between $0$ and $2^n - 1$, although it convenient to choose the value closest to the middle: $2^{n-1}$.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "cell_style": "split",
    "hide_input": true,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 373.034x535.111 with 1 Axes>"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "initial_position = 2 ** (\n",
    "    n_walker_qubits - 1\n",
    ")  # The initial position of the walker is the middle of all possible positions\n",
    "initial_coin_value = 1  # The initial value of the coin is 0\n",
    "\n",
    "\n",
    "def initialize_coined_walk_circuit(\n",
    "    qc: QuantumCircuit,\n",
    "    walker_r: QuantumRegister,\n",
    "    coin_r: QuantumRegister,\n",
    "    initial_position: int,\n",
    "    initial_coin_value: int,\n",
    ") -> QuantumCircuit:\n",
    "    \"\"\"Initialize the circuit with the initial position of the walker and the initial value of the coin.\n",
    "\n",
    "    Args:\n",
    "        qc: the quantum circuit\n",
    "        walker_r: the quantum register containing the walker's position qubits\n",
    "        coin_r: the quantum register containing the coin qubit\n",
    "        initial_position: the initial position of the walker\n",
    "        initial_coin_value: the initial value of the coin\n",
    "\n",
    "    Returns:\n",
    "        the initialized quantum circuit\n",
    "    \"\"\"\n",
    "    if initial_coin_value == 1:\n",
    "        qc.x(coin_r)\n",
    "    for i in range(n_walker_qubits):\n",
    "        if initial_position & (1 << i):\n",
    "            qc.x(walker_r[n_walker_qubits - i - 1])\n",
    "    qc.barrier()\n",
    "    return qc\n",
    "\n",
    "\n",
    "qc, walker_r, coin_r, _ = coined_walk_circuit(n_walker_qubits)\n",
    "qc = initialize_coined_walk_circuit(\n",
    "    qc, walker_r, coin_r, initial_position, initial_coin_value\n",
    ")\n",
    "qc.draw(output=\"mpl\", initial_state=True)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### Operators\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "cell_style": "split",
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "#### Coin operator\n",
    "\n",
    "For the coin operator, the simplest choice is to use the Hadamard gate.\n",
    "When applied to the coin qubit, it will be put in a state of superposition.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "cell_style": "split",
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "#### Shift operator\n",
    "\n",
    "The shift operator has to be able to either increment or decrement the walker position, depending on the state of the coin.\n",
    "This can be achieved by using an addition operator, controlled by the coin state.  \n",
    "Since all operators are unitary, once an addition operator $A$ is found, building a corresponding subtraction operator is trivial.\n",
    "\n",
    "$$\n",
    "A : \\mathcal{H} \\to \\mathcal{H} : A\\ket{j} = \\ket{j + 1} \\\\\n",
    "\\exists A^\\dagger \\in \\mathcal{H} : A^\\dagger A = I \\\\\n",
    "A^\\dagger A \\ket{j} = A^\\dagger \\ket{j + 1} \\implies \\ket{j} = A^\\dagger \\ket{j + 1} \\implies A^\\dagger \\ket{k} = \\ket{k - 1} \\\\\n",
    "$$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "#### Quantum walk operator\n",
    "\n",
    "The quantum walk operator is the composition of the coin operator and the shift operator:\n",
    "\n",
    "$$\n",
    "U = S(C \\otimes I)\n",
    "$$\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "hide_input": true,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
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      "text/plain": [
       "<Figure size 1627.2x535.111 with 1 Axes>"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def coined_walk_step(\n",
    "    qc: QuantumCircuit, walker_r: QuantumRegister, coin_r: QuantumRegister\n",
    ") -> QuantumCircuit:\n",
    "    \"\"\"Single step of the quantum walk.\n",
    "\n",
    "    Args:\n",
    "        qc: quantum circuit\n",
    "        walker_r: the quantum register containing the walker's position qubits\n",
    "        coin_r: the quantum register containing the coin qubit\n",
    "\n",
    "    Returns:\n",
    "        quantum circuit with an added walk step\n",
    "    \"\"\"\n",
    "\n",
    "    # \"Flip\" the coin vector\n",
    "    qc.h(coin_r)\n",
    "\n",
    "    # Implement the Addition Operator\n",
    "    for i in reversed(range(len(walker_r))):\n",
    "        # Qubits with less significant bits than the current one\n",
    "        controls = [walker_r[v] for v in range(len(walker_r) - 1, i, -1)]\n",
    "        controls.append(coin_r)  # The coin qubit is also used as a control\n",
    "        qc.mcx(controls, walker_r[i])  # Multi-controlled X gate\n",
    "        if i != 0:\n",
    "            qc.x(walker_r[i])  # Flip the qubit\n",
    "\n",
    "    # Switch the coin vector\n",
    "    qc.x(coin_r)\n",
    "\n",
    "    # Implement the Subtraction Operator\n",
    "    for i in range(len(walker_r)):\n",
    "        if i != 0:\n",
    "            qc.x(walker_r[i])  # Reverse the flip\n",
    "        # Qubits with less significant bits than the current one\n",
    "        controls = [walker_r[v] for v in range(len(walker_r) - 1, i, -1)]\n",
    "        controls.append(coin_r)  # The coin qubit is also used as a control\n",
    "        qc.mcx(controls, walker_r[i])  # Multi-controlled X gate\n",
    "\n",
    "    # Revert the switch of the coin vector\n",
    "    qc.x(coin_r)\n",
    "\n",
    "    return qc\n",
    "\n",
    "\n",
    "qc, walker_r, coin_r, _ = coined_walk_circuit(n_walker_qubits)\n",
    "qc = coined_walk_step(qc, walker_r, coin_r)\n",
    "qc.draw(output=\"mpl\", initial_state=True)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### Circuit\n",
    "\n",
    "With all the operators defined, the circuit can be built by iterating the single step operator as many times as needed.\n",
    "Finally, the walker position is measured and the result is stored in the classical bits.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Mind that we could just take one step at a time and collapse the state of the circuit by measuring it.\n",
    "This would be equivalent to a classical random walk, and would not take advantage of the quantum properties of the system.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "hide_input": true,
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1627.2x535.111 with 1 Axes>"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "n_steps = 5  # The number of steps of the quantum walk\n",
    "\n",
    "\n",
    "def coined_walk(\n",
    "    n_walker_qubits: int,\n",
    "    n_steps: int,\n",
    "    initial_position: int,\n",
    "    initial_coin_value: int,\n",
    "    init_func: Callable,\n",
    ") -> QuantumCircuit:\n",
    "    \"\"\"Create a quantum circuit for the quantum walk.\n",
    "\n",
    "    Args:\n",
    "        n_walker_qubits: number of qubits used to represent the position of the walker\n",
    "        n_steps: number of steps of the quantum walk\n",
    "        initial_position: initial position of the walker\n",
    "        initial_coin_value: initial value of the coin\n",
    "        init_func: function used to initialize the circuit\n",
    "\n",
    "    Returns:\n",
    "        quantum circuit for the quantum walk\n",
    "    \"\"\"\n",
    "    qc, walker_r, coin_r, classic_r = coined_walk_circuit(n_walker_qubits)\n",
    "    qc = init_func(qc, walker_r, coin_r, initial_position, initial_coin_value)\n",
    "    for i in range(n_steps):\n",
    "        step_gate = coined_walk_step(QuantumCircuit(walker_r, coin_r), walker_r, coin_r)\n",
    "        qc.append(step_gate.to_gate(label=f\"Step #{i + 1}\"), walker_r[:] + coin_r[:])\n",
    "    qc.barrier()\n",
    "    qc.measure(walker_r, reversed(classic_r))\n",
    "    return qc\n",
    "\n",
    "\n",
    "qc = coined_walk(\n",
    "    n_walker_qubits,\n",
    "    n_steps,\n",
    "    initial_position,\n",
    "    initial_coin_value,\n",
    "    initialize_coined_walk_circuit,\n",
    ")\n",
    "qc.draw(output=\"mpl\", initial_state=True)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Results of the simulation\n",
    "\n",
    "To get an idea of the behavior of the circuit, it is useful to plot multiple results obtained by running the Qiskit simulator.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "cell_style": "center",
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### Skewed results\n",
    "\n",
    "Contrary to the classical random walk, this circuit results are clearly skewed towards one side of the graph.\n",
    "Inverting the initial coin state will result in a flipped graph.\n",
    "\n",
    "The reason for this behavior originates from the repeated application of the Hadamard gate.\n",
    "Depending on the starting state of the coin, $\\ket{\\downarrow}$ or $\\ket{\\uparrow}$, a bias will be introduced in the results.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "cell_style": "split",
    "hide_input": true,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 700x500 with 1 Axes>"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "n_walker_qubits = 6  # The number of qubits used to represent the position of the walker\n",
    "n_steps = 30  # The number of steps of the quantum walk\n",
    "initial_position = 2 ** (\n",
    "    n_walker_qubits - 1\n",
    ")  # The initial position of the walker is the middle of all possible positions\n",
    "initial_coin_value = 0  # The initial value of the coin is 0\n",
    "n_runs = 5000  # The number of runs of the quantum circuit\n",
    "\n",
    "qc = coined_walk(\n",
    "    n_walker_qubits,\n",
    "    n_steps,\n",
    "    initial_position,\n",
    "    initial_coin_value,\n",
    "    initialize_coined_walk_circuit,\n",
    ")\n",
    "\n",
    "\n",
    "def plot_results(qc: QuantumCircuit, n_runs: int, title: str):\n",
    "    \"\"\"Plot the results of the quantum walk.\n",
    "\n",
    "    Args:\n",
    "        qc: quantum circuit for the quantum walk\n",
    "        n_runs: number of runs of the quantum circuit\n",
    "\n",
    "    Returns:\n",
    "        histogram of the results of the quantum walk\n",
    "    \"\"\"\n",
    "    simulator: AerSimulator = Aer.get_backend(\"aer_simulator\")\n",
    "    transpiled_qc = transpile(qc, simulator)\n",
    "    results = simulator.run(transpiled_qc, shots=n_runs).result()\n",
    "    counts = results.get_counts(transpiled_qc)\n",
    "    counts = {int(k, 2): v for k, v in counts.items()}\n",
    "    return plot_histogram(counts, title=title)\n",
    "\n",
    "\n",
    "plot_results(qc, n_runs, \"Quantum Coined Walk\")\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### Math behind the skewed results\n",
    "\n",
    "Starting from the initial state $\\ket{\\psi(0)} = \\ket{\\downarrow} \\otimes \\ket{0}$, the first iteration of the operator will result in the state $\\ket{\\psi(1)} = \\frac{1}{\\sqrt{2}}(\\ket{\\uparrow} \\otimes \\ket{1} + \\ket{\\downarrow} \\otimes \\ket{-1})$.\n",
    "Going through the same process, the state after $t$ iterations will be:\n",
    "\n",
    "$$\n",
    "\\begin{array}{ll}\n",
    "\\ket{\\psi(0)} &= \\ket{\\downarrow} \\otimes \\ket{0} \\\\\n",
    "\\ket{\\psi(1)} &= \\frac{1}{\\sqrt{2}}(\\ket{\\uparrow} \\otimes \\ket{1} + \\ket{\\downarrow} \\otimes \\ket{-1}) \\\\\n",
    "\\ket{\\psi(2)} &= \\frac{1}{2}(-\\ket{\\uparrow} \\otimes \\ket{-2} + (\\ket{\\downarrow} + \\ket{\\uparrow})\\ket{0} + \\ket{\\downarrow} \\otimes \\ket{2}) \\\\\n",
    "\\ket{\\psi(3)} &= \\frac{1}{2\\sqrt{2}}(\\ket{\\uparrow}\\ket{-3} - \\ket{\\downarrow}\\ket{-1} + (2\\ket{\\downarrow} + \\ket{\\uparrow})\\ket{1} - \\ket{\\downarrow}\\ket{3}) \\\\\n",
    "\\end{array}\n",
    "$$\n",
    "\n",
    "This few iterations are enough to see that the state is not balanced: the probability of finding the walker in the position $\\ket{1}$ are $\\left(\\frac{2 + 1}{2\\sqrt{2}}\\right)^2 = \\frac{5}{8}$, as opposed to $\\frac{1}{8}$ for all other positions.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "cell_style": "center",
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### Balanced coin\n",
    "\n",
    "To avoid this bias, why may use another coin, or ensure that the starting state of the coin is equal to $\\frac{1}{\\sqrt{2}}(\\ket{\\downarrow} + i \\ket{\\uparrow})$.\n",
    "This can be achieved by applying a Hadamard gate followed by an $S$ gate to the coin qubit before starting the walk.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "cell_style": "center",
    "hide_input": true,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 456.645x702.333 with 1 Axes>"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def initialize_balance_coined_walk_circuit(\n",
    "    qc: QuantumCircuit,\n",
    "    walker_r: QuantumRegister,\n",
    "    coin_r: QuantumRegister,\n",
    "    initial_position: int,\n",
    "    initial_coin_value: int,\n",
    ") -> QuantumCircuit:\n",
    "    \"\"\"Initialize the circuit with the initial position of the walker and the initial value of the coin.\n",
    "    Set the coin qubit to |+> and apply the S gate to it to make sure that the coin operator keeps being balanced.\n",
    "\n",
    "    Args:\n",
    "        qc: the quantum circuit\n",
    "        walker_r: the quantum register containing the walker's position qubits\n",
    "        coin_r: the quantum register containing the coin qubit\n",
    "        initial_position: the initial position of the walker\n",
    "        initial_coin_value: the initial value of the coin\n",
    "\n",
    "    Returns:\n",
    "        the initialized quantum circuit\n",
    "    \"\"\"\n",
    "    if initial_coin_value == 1:\n",
    "        qc.x(coin_r)\n",
    "    qc.h(coin_r)\n",
    "    qc.s(coin_r)\n",
    "    for i in range(n_walker_qubits):\n",
    "        if initial_position & (1 << i):\n",
    "            qc.x(walker_r[n_walker_qubits - i - 1])\n",
    "    qc.barrier()\n",
    "    return qc\n",
    "\n",
    "\n",
    "qc, walker_r, coin_r, _ = coined_walk_circuit(n_walker_qubits)\n",
    "qc = initialize_balance_coined_walk_circuit(\n",
    "    qc, walker_r, coin_r, initial_position, initial_coin_value\n",
    ")\n",
    "qc.draw(output=\"mpl\", initial_state=True)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "cell_style": "center",
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### Balanced coin results\n",
    "\n",
    "Having the coin in this starting state produces results that are more evenly distributed across the graph.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "cell_style": "split",
    "hide_input": true,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 700x500 with 1 Axes>"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "n_walker_qubits = 6  # The number of qubits used to represent the position of the walker\n",
    "n_steps = 30  # The number of steps of the quantum walk\n",
    "initial_position = 2 ** (\n",
    "    n_walker_qubits - 1\n",
    ")  # The initial position of the walker is the middle of all possible positions\n",
    "initial_coin_value = 0  # The initial value of the coin is 0\n",
    "n_runs = 5000  # The number of runs of the quantum circuit\n",
    "\n",
    "qc = coined_walk(\n",
    "    n_walker_qubits,\n",
    "    n_steps,\n",
    "    initial_position,\n",
    "    initial_coin_value,\n",
    "    initialize_balance_coined_walk_circuit,\n",
    ")\n",
    "\n",
    "plot_results(qc, n_runs, \"Balanced Quantum Coined Walk\")\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Conclusion\n",
    "\n",
    "When compared to the classical random walk, it becomes clear that the quantum coined walk results lack the Gaussian properties of the classical random walk.\n",
    "The statistical analysis of its behavior becomes more difficult.\n",
    "\n",
    "On the other hand, in can be proven that the standard deviation of the distribution, its width, is $t$, when the classical counterpart has a standard deviation of $\\sqrt{t}$.\n",
    "The quantum walk travel much further than a classical walk with the same number of steps.  \n",
    "This allows certain problems to be solved more efficiently with a quantum approach, such as Grover's search algorithm.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Quantum walk on a hypercube\n",
    "\n",
    "The quantum random walk can be used to walk on the vertices of a hypercube.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### Hypercube\n",
    "\n",
    "A hypercube with degree $n$ is a graph with $2^n$ vertices, where each vertex is connected to all the other vertices that differ by a single bit.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "> _Example_\n",
    ">\n",
    "> A 4-dimesional hypercube has $2^4 = 16$ nodes.  \n",
    "> The neighbors of the node $\\ket{0101}$ are $\\ket{1101}$, $\\ket{0001}$, $\\ket{0111}$ and $\\ket{0110}$.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "hide_input": true,
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n = 3  # Number of qubits\n",
    "\n",
    "G = hypercube_graph(n)  # Create hypercube graph\n",
    "# Draw graph\n",
    "nx.draw(\n",
    "    G,\n",
    "    with_labels=True,\n",
    "    pos=graphviz_layout(G, prog=\"dot\"),\n",
    "    node_color=\"#dddddd\",\n",
    "    node_size=2500,\n",
    ")\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### State of the quantum walk circuit\n",
    "\n",
    "The state of the system needs to account for coin space, $\\mathcal{H}_c = \\mathcal{H}^n$, and walker space, $\\mathcal{H}_p = \\mathcal{H}^{2^n}$.\n",
    "The two spaces are then combined to form the state of the system, $\\mathcal{H} = \\mathcal{H}_c \\otimes \\mathcal{H}_p$.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "It is possible to define $\\mathcal{H}$ as $\\{\\ket{a} \\otimes \\ket{v}: 0 \\le a \\lt n, v \\in \\{(00 \\dots 00)_2, (00\\dots 01)_2, \\dots, (11 \\dots 11)\\}\\}$.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "The value of $a$ decides where the walker should move next, inverting the value of the bit at position $a$ of $v$.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "> _Example_\n",
    ">\n",
    "> The state $\\ket{a} \\otimes \\ket{v} = \\ket{2} \\otimes \\ket{0101}$.\n",
    "> The walker will move to the node $\\ket{0111}$, since the bit at position 2 is inverted.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### Quantum registers\n",
    "\n",
    "A circuit implementing a quantum coined needs:\n",
    "\n",
    "- $n$ qubits to represent the coin\n",
    "  - the coin will yield one of the $2^n$ possible outcomes, indicating which qubit to invert\n",
    "- $2^n$ qubits to represent the walker position\n",
    "  - the numbers are represented in binary form, with the most significant bit at the top\n",
    "- $2^n$ classical bits to store the measurement of the walker position\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "hide_input": true,
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 247.617x618.722 with 1 Axes>"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "n = 2  # Dimension of the hypercube\n",
    "\n",
    "\n",
    "def graph_walk_circuit(\n",
    "    n: int,\n",
    ") -> tuple[QuantumCircuit, QuantumRegister, QuantumRegister, ClassicalRegister]:\n",
    "    \"\"\"Create a quantum circuit for the graph walk.\n",
    "\n",
    "    Args:\n",
    "        n: number of qubits used to represent the position of the walker\n",
    "\n",
    "    Returns:\n",
    "        quantum circuit for the graph walk, walker register, coin register, and output register\n",
    "    \"\"\"\n",
    "    walker_r = QuantumRegister(2**n, name=\"w\")\n",
    "    coin_r = QuantumRegister(n, name=\"c\")\n",
    "    classic_r = ClassicalRegister(2**n, name=\"output\")\n",
    "    qc = QuantumCircuit(walker_r, coin_r, classic_r)\n",
    "    return qc, walker_r, coin_r, classic_r\n",
    "\n",
    "\n",
    "qc, _, _, _ = graph_walk_circuit(n)\n",
    "qc.draw(output=\"mpl\", initial_state=True)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### Operators\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hide_input": true,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "#### Coin operator\n",
    "\n",
    "In this case, the coin operator is the Grover coin, $C$.\n",
    "It is defined as:\n",
    "\n",
    "$$\n",
    "C = \\begin{bmatrix}\n",
    "\\frac{2}{n} - 1& \\frac{2}{n} & \\dots & \\frac{2}{n} \\\\\n",
    "\\frac{2}{n} & \\frac{2}{n} - 1& \\dots &  \\frac{2}{n} \\\\\n",
    "\\vdots & \\vdots & \\ddots & \\vdots \\\\\n",
    "\\frac{2}{n} & \\frac{2}{n} & \\dots & \\frac{2}{n} - 1\n",
    "\\end{bmatrix}\n",
    "$$\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "hide_input": true,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 429.395x200.667 with 1 Axes>"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "n = 2  # Dimension of the hypercube\n",
    "\n",
    "def grover_coin(coin_r: QuantumRegister) -> Operator:\n",
    "    matrix_size = 2 ** len(coin_r)\n",
    "    grover_matrix = np.full((matrix_size, matrix_size), 2 / matrix_size) - np.eye(\n",
    "        matrix_size\n",
    "    )\n",
    "    return Operator(grover_matrix)\n",
    "\n",
    "\n",
    "coin_r = QuantumRegister(n, name=\"c\")\n",
    "qc = QuantumCircuit(coin_r)\n",
    "gc = grover_coin(coin_r)\n",
    "qc.unitary(gc, coin_r[:], label=\"Grover Coin\")\n",
    "qc.draw(output=\"mpl\", initial_state=True)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "#### Shift operator\n",
    "\n",
    "Let $e_a$ be the vector with a single 1 at position $a$ and 0s everywhere else.\n",
    "The shift operator $S$ is defined as:\n",
    "\n",
    "$$\n",
    "S(\\ket{a} \\otimes \\ket{v}) = \\ket{a} \\otimes \\ket{v \\oplus e_a}\n",
    "$$\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "hide_input": true,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 855.46x535.111 with 1 Axes>"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "n = 2  # Dimension of the hypercube\n",
    "\n",
    "\n",
    "def shift_operator(\n",
    "    walker_r: QuantumRegister, coin_r: QuantumRegister\n",
    ") -> QuantumCircuit:\n",
    "    \"\"\"Create a quantum circuit for the shift operator.\n",
    "\n",
    "    Args:\n",
    "        walker_r: the quantum register containing the walker's position qubits\n",
    "        coin_r: the quantum register containing the coin qubit\n",
    "\n",
    "    Returns:\n",
    "        quantum circuit for the shift operator\n",
    "    \"\"\"\n",
    "    qc = QuantumCircuit(walker_r, coin_r)\n",
    "    for i in reversed(range(len(walker_r))):\n",
    "        qc.mcx(coin_r, walker_r[i])\n",
    "        qc.x(coin_r[-1])\n",
    "        for j in range(1, len(coin_r)):\n",
    "            if i & ((1 << j) - 1) == 0:\n",
    "                qc.x(coin_r[-(j + 1)])\n",
    "    return qc\n",
    "\n",
    "\n",
    "qc, walker_r, coin_r, _ = graph_walk_circuit(n)\n",
    "qc = shift_operator(walker_r, coin_r)\n",
    "qc.draw(output=\"mpl\", initial_state=True)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "#### Quantum walk operator\n",
    "\n",
    "The quantum walk operator is the composition of the coin operator and the shift operator:\n",
    "\n",
    "$$\n",
    "U = S(C \\otimes I)\n",
    "$$\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "hide_input": true,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1106.29x535.111 with 1 Axes>"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "n = 2  # Dimension of the hypercube\n",
    "\n",
    "\n",
    "def graph_walk_step(\n",
    "    walker_r: QuantumRegister, coin_r: QuantumRegister\n",
    ") -> QuantumCircuit:\n",
    "    \"\"\"Create a quantum circuit for one step of the graph walk.\n",
    "\n",
    "    Args:\n",
    "        walker_r: the quantum register containing the walker's position qubits\n",
    "        coin_r: the quantum register containing the coin qubit\n",
    "\n",
    "    Returns:\n",
    "        quantum circuit for one step of the graph walk\n",
    "    \"\"\"\n",
    "    shift = shift_operator(walker_r, coin_r)\n",
    "    gc = grover_coin(coin_r)\n",
    "    walk_step = QuantumCircuit(walker_r, coin_r)\n",
    "    walk_step.unitary(gc, coin_r, label=\"Grover Coin\")\n",
    "    walk_step.compose(shift, inplace=True)\n",
    "    return walk_step\n",
    "\n",
    "\n",
    "walk_step = graph_walk_step(walker_r, coin_r)\n",
    "walk_step.draw(output=\"mpl\", initial_state=True)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### Circuit\n",
    "\n",
    "With all the operators defined, the circuit can be built by iterating the single step operator as many times as needed.\n",
    "Finally, the walker position is measured and the result is stored in the classical bits.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "hide_input": true,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1125.53x618.722 with 1 Axes>"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "n = 2  # Dimension of the hypercube\n",
    "n_steps = 3  # Number of steps of the quantum walk\n",
    "\n",
    "\n",
    "def graph_walk(\n",
    "    n: int,\n",
    "    n_steps: int,\n",
    ") -> QuantumCircuit:\n",
    "    \"\"\"Create a quantum circuit for the quantum walk over a graph.\n",
    "\n",
    "    Args:\n",
    "        n: dimension of the hypercube\n",
    "        n_steps: number of steps of the quantum walk\n",
    "        initial_position: initial position of the walker\n",
    "        initial_coin_value: initial value of the coin\n",
    "\n",
    "    Returns:\n",
    "        quantum circuit for the quantum walk over a graph\n",
    "    \"\"\"\n",
    "    qc, walker_r, coin_r, classic_r = graph_walk_circuit(n)\n",
    "    for i in range(n_steps):\n",
    "        step_gate = graph_walk_step(walker_r, coin_r).to_gate(label=f\"Step #{i + 1}\")\n",
    "        qc.append(step_gate, walker_r[:] + coin_r[:])\n",
    "    qc.barrier()\n",
    "    qc.measure(walker_r, reversed(classic_r))\n",
    "    return qc\n",
    "\n",
    "\n",
    "qc = graph_walk(n, n_steps)\n",
    "qc.draw(output=\"mpl\", initial_state=True)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Results of the simulation\n",
    "\n",
    "The selection of the coin operator determines the behavior of the quantum walk.\n",
    "The Grover coin is used to produce a biased walk."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "hide_input": true,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 700x500 with 1 Axes>"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "n = 2  # Dimension of the hypercube\n",
    "n_steps = 30  # Number of steps of the quantum walk\n",
    "n_runs = 5000  # Number of runs of the quantum circuit\n",
    "\n",
    "qc = graph_walk(n, n_steps)\n",
    "plot_results(qc, n_runs, \"Quantum Walk on a Hypercube\")\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
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   "source": [
    "### Conclusion\n",
    "\n",
    "A radom walk on a hypercube could be used to simulate efficiently network routing.\n",
    "A hypercube structure is particularly suited for this task in a distributed environment, since deleting an edge will have a minimal impact on the network."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## References\n",
    "\n",
    "- [Quantum Walk Search Algorithm](https://qiskit.org/textbook/ch-algorithms/quantum-walk-search-algorithm.html)\n",
    "- [An Insight Into: Quantum Random Walks](https://bayesianbrad.github.io/assets/publications/2014_thesis/paper.pdf)\n",
    "- [Quantum Walks and Search Algorithms](http://ndl.ethernet.edu.et/bitstream/123456789/73178/1/277.pdf)\n",
    "- [Quantum Walk](https://quantumai.google/cirq/experiments/quantum_walks)\n"
   ]
  }
 ],
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