NB3-ExploreHadamard.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Single Qbit H-gate"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from qiskit import(\n",
    "  QuantumCircuit,\n",
    "  execute,\n",
    "  Aer)\n",
    "from qiskit.visualization import plot_histogram\n",
    "from qiskit.visualization import plot_bloch_multivector"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "simulator_q = Aer.get_backend('qasm_simulator')\n",
    "simulator_s= Aer.get_backend('statevector_simulator')\n",
    "simulator_u = Aer.get_backend('unitary_simulator')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'\\nThe StatevectorSimulator executes a single shot of a Qiskit QuantumCircuit\\nand returns the final quantum statevector of the simulation.\\nNote that if a circuit contains measure or reset the final statevector\\nwill be a conditional statevector after simulating wave-function collapse\\nto the outcome of a measure or reset.\\nFor the Bell-state circuit this means the final statevector will be either |0> or |1>.   .\\n\\n'"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\"\"\"\n",
    "The StatevectorSimulator executes a single shot of a Qiskit QuantumCircuit\n",
    "and returns the final quantum statevector of the simulation.\n",
    "Note that if a circuit contains measure or reset the final statevector\n",
    "will be a conditional statevector after simulating wave-function collapse\n",
    "to the outcome of a measure or reset.\n",
    "For the Bell-state circuit this means the final statevector will be either |0> or |1>.   .\n",
    "\n",
    "\"\"\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "circuit = QuantumCircuit(1, 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<qiskit.circuit.instructionset.InstructionSet at 0x169658d2748>"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "circuit.h(0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 0.70710678+0.j  0.70710678+0.j]\n",
      " [ 0.70710678+0.j -0.70710678+0.j]]\n"
     ]
    }
   ],
   "source": [
    "result=execute(circuit,simulator_u).result()\n",
    "unitary=result.get_unitary(circuit)\n",
    "print (unitary)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "counts: {'1': 526, '0': 498}\n",
      "outputstate: [0.+0.j 1.+0.j]\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 233.576x144.48 with 1 Axes>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "circuit = QuantumCircuit(1, 1)\n",
    "circuit.h(0)\n",
    "circuit.measure(0,0)\n",
    "result2=execute(circuit,simulator_q).result()\n",
    "result3=execute(circuit,simulator_s).result()\n",
    "outputstate = result3.get_statevector(circuit, decimals=3)\n",
    "counts = result2.get_counts(circuit)\n",
    "print (\"counts:\",counts)\n",
    "print ('outputstate:',outputstate)\n",
    "style = {'backgroundcolor': 'lightgreen'}\n",
    "circuit.draw(output='mpl',style=style)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "outputstate: [0.707+0.j 0.707+0.j]\n"
     ]
    }
   ],
   "source": [
    "circuit = QuantumCircuit(1, 1)\n",
    "circuit.h(0)\n",
    "result3=execute(circuit,simulator_s).result()\n",
    "outputstate = result3.get_statevector(circuit, decimals=3)\n",
    "print ('outputstate:',outputstate)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Big Summary (Single Qubit)\n",
    "Always do unitary and statevector before circuit.measure().\n",
    "Below everything is done in proper order!\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Single qbit with H gate"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "outputstate:\n",
      " [0.707+0.j 0.707+0.j]\n",
      "UnitaryMatrix:\n",
      " [[ 0.70710678+0.j  0.70710678+0.j]\n",
      " [ 0.70710678+0.j -0.70710678+0.j]]\n",
      "counts:\n",
      " {'1': 505, '0': 519}\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 233.576x144.48 with 1 Axes>"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "circuit = QuantumCircuit(1, 1)\n",
    "circuit.h(0)\n",
    "#Statevector part\n",
    "result3=execute(circuit,simulator_s).result()\n",
    "outputstate = result3.get_statevector(circuit, decimals=3)\n",
    "print ('outputstate:\\n',outputstate)\n",
    "#unitary vector part\n",
    "result=execute(circuit,simulator_u).result()\n",
    "unitary=result.get_unitary(circuit)\n",
    "print ('UnitaryMatrix:\\n',unitary)\n",
    "#Now Quasm Simulator part where we need to measure\n",
    "circuit.measure(0,0)\n",
    "result2=execute(circuit,simulator_q).result()\n",
    "print (\"counts:\\n\",result2.get_counts(circuit))\n",
    "style = {'backgroundcolor': 'lightgreen'}\n",
    "circuit.draw(output='mpl',style=style)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "$\n",
    "Initial state:|0> \\\\  \n",
    "After: H= \\frac{1}{\\sqrt{2}}|0> + \\frac{1}{\\sqrt{2}}|1>\\\\  \n",
    "            H = \\frac{1}{\\sqrt{2}} \\begin{bmatrix}\n",
    "    1  & 1 \\\\\n",
    "    1 & -1\n",
    "\\end{bmatrix}\\\\ |1 > = \\begin{bmatrix}\n",
    "    1  \\\\\n",
    "    0\n",
    "\\end{bmatrix} ; |0> = \\begin{bmatrix}\n",
    "    0\\\\\n",
    "    1\n",
    "\\end{bmatrix}$\n",
    "            "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Single Qbit with Pauli-X and H gate!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "# In this case it is a matrix multiplication of H X Pauli-X!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "Manual Approch to determine Unitary Matrix: \\\n",
    "$ \n",
    "H \\otimes PauliX  =  \\frac{1}{\\sqrt{2}} \\begin{bmatrix}\n",
    "    1  &   1 \\\\\n",
    "    1  &  -1\n",
    "\\end{bmatrix}\\begin{bmatrix}\n",
    "    0  &   1 \\\\\n",
    "    1  &   0\n",
    "\\end{bmatrix}  = \\frac{1}{\\sqrt{2}}\\begin{bmatrix}\n",
    "1 & 1 \\\\\n",
    "-1 & 1\n",
    "\\end{bmatrix}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "outputstate:\n",
      " [ 0.707+0.j -0.707+0.j]\n",
      "UnitaryMatrix:\n",
      " [[ 0.70710678+0.j  0.70710678+0.j]\n",
      " [-0.70710678+0.j  0.70710678+0.j]]\n",
      "counts:\n",
      " {'1': 532, '0': 492}\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 293.776x144.48 with 1 Axes>"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "circuit = QuantumCircuit(1, 1)\n",
    "circuit.x(0)\n",
    "circuit.h(0)\n",
    "#Statevector part\n",
    "result3=execute(circuit,simulator_s).result()\n",
    "outputstate = result3.get_statevector(circuit, decimals=3)\n",
    "print ('outputstate:\\n',outputstate)\n",
    "#unitary vector part\n",
    "result=execute(circuit,simulator_u).result()\n",
    "unitary=result.get_unitary(circuit)\n",
    "print ('UnitaryMatrix:\\n',unitary)\n",
    "#Now Quasm Simulator part where we need to measure\n",
    "circuit.measure(0,0)\n",
    "result2=execute(circuit,simulator_q).result()\n",
    "print (\"counts:\\n\",result2.get_counts(circuit))\n",
    "style = {'backgroundcolor': 'lightgreen'}\n",
    "circuit.draw(output='mpl',style=style)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Two qubits with H-gate on first qubit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "#In this case first operator is H and second is Identity Matrix.\n",
    "#The product of these two gives a transformation matrix as follows:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "Manual Approch to determine Unitary Matrix: \\\n",
    "$I \\otimes H  =  \\begin{bmatrix}\n",
    "    1  &   0 \\\\\n",
    "    0  &   1\n",
    "\\end{bmatrix} \\otimes \\frac{1}{\\sqrt{2}} \\begin{bmatrix}\n",
    "    1  &   1 \\\\\n",
    "    1  &  -1\n",
    "\\end{bmatrix}  = \\frac{1}{\\sqrt{2}}\\begin{bmatrix}\n",
    "1 & 1 & 0 & 0\\\\\n",
    "1 & -1 & 0 & 0\\\\\n",
    "0 & 0 & 1 & 1 \\\\\n",
    "0 & 0 & 1 & -1\n",
    "\\end{bmatrix}$\\\\\n",
    "\n",
    "If the H-gate were on 2nd qubit, It will be:\n",
    "$H \\otimes I  = \\frac{1}{\\sqrt{2}} \\begin{bmatrix}\n",
    "    1  &   1 \\\\\n",
    "    1  &  -1\n",
    "\\end{bmatrix} \\otimes \\begin{bmatrix}\n",
    "    1  &   0 \\\\\n",
    "    0  &   1\n",
    "\\end{bmatrix}  = \\frac{1}{\\sqrt{2}}\\begin{bmatrix}\n",
    "1 & 0 & 1 & 0\\\\\n",
    "0 & 1 & 0 & 1\\\\\n",
    "1 & 0 & -1 & 0 \\\\\n",
    "0 & 1 & 0 & -1\n",
    "\\end{bmatrix}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "outputstate:\n",
      " [0.707+0.j 0.707+0.j 0.   +0.j 0.   +0.j]\n",
      "UnitaryMatrix:\n",
      " [[ 0.70710678+0.j  0.70710678+0.j  0.        +0.j  0.        +0.j]\n",
      " [ 0.70710678+0.j -0.70710678+0.j  0.        +0.j  0.        +0.j]\n",
      " [ 0.        +0.j  0.        +0.j  0.70710678+0.j  0.70710678+0.j]\n",
      " [ 0.        +0.j  0.        +0.j  0.70710678+0.j -0.70710678+0.j]]\n",
      "counts:\n",
      " {'01': 496, '00': 528}\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 276.92x204.68 with 1 Axes>"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "circuit = QuantumCircuit(2, 2)\n",
    "circuit.h(0)\n",
    "#Statevector part\n",
    "result3=execute(circuit,simulator_s).result()\n",
    "outputstate = result3.get_statevector(circuit, decimals=3)\n",
    "print ('outputstate:\\n',outputstate)\n",
    "#unitary vector part\n",
    "result=execute(circuit,simulator_u).result()\n",
    "unitary=result.get_unitary(circuit)\n",
    "print ('UnitaryMatrix:\\n',unitary)\n",
    "#Now Quasm Simulator part where we need to measure\n",
    "circuit.measure([0,1],[0,1])\n",
    "result2=execute(circuit,simulator_q).result()\n",
    "print (\"counts:\\n\",result2.get_counts(circuit))\n",
    "style = {'backgroundcolor': 'lightgreen'}\n",
    "circuit.draw(output='mpl',style=style)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Two qbits with single H-Gate for each bit"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$H_1 \\otimes H_1 = \\frac{1}{\\sqrt{2}}\\begin{bmatrix}\n",
    "    1  &  1 \\\\\n",
    "    1  & -1\n",
    "\\end{bmatrix} \\otimes \\frac{1}{\\sqrt{2}}\\begin{bmatrix}\n",
    "    1  &  1 \\\\\n",
    "    1  & -1\n",
    "\\end{bmatrix} = \\frac{1}{2} \\begin{bmatrix}\n",
    "    1  &  1  &  1  &  1 \\\\\n",
    "    1  &  -1  &  1  &  -1 \\\\\n",
    "    1  &  1  &  -1  &  -1 \\\\\n",
    "    1  &  -1  &  -1  &  1 \\\\\n",
    "\\end{bmatrix}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "outputstate:\n",
      " [0.5+0.j 0.5+0.j 0.5+0.j 0.5+0.j]\n",
      "UnitaryMatrix:\n",
      " [[ 0.5+0.j  0.5+0.j  0.5+0.j  0.5+0.j]\n",
      " [ 0.5+0.j -0.5+0.j  0.5+0.j -0.5+0.j]\n",
      " [ 0.5+0.j  0.5+0.j -0.5+0.j -0.5+0.j]\n",
      " [ 0.5+0.j -0.5+0.j -0.5+0.j  0.5+0.j]]\n",
      "counts:\n",
      " {'01': 241, '10': 267, '00': 231, '11': 285}\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 337.12x204.68 with 1 Axes>"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "circuit = QuantumCircuit(2, 2)\n",
    "circuit.h(0)\n",
    "circuit.h(1)\n",
    "#Statevector part\n",
    "result3=execute(circuit,simulator_s).result()\n",
    "outputstate = result3.get_statevector(circuit, decimals=3)\n",
    "print ('outputstate:\\n',outputstate)\n",
    "#unitary vector part\n",
    "result=execute(circuit,simulator_u).result()\n",
    "unitary=result.get_unitary(circuit)\n",
    "print ('UnitaryMatrix:\\n',unitary)\n",
    "#Now Quasm Simulator part where we need to measure\n",
    "circuit.measure([0,1],[0,1])\n",
    "result2=execute(circuit,simulator_q).result()\n",
    "print (\"counts:\\n\",result2.get_counts(circuit))\n",
    "style = {'backgroundcolor': 'lightgreen'}\n",
    "circuit.draw(output='mpl',style=style)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Basis Vectors for 2 qubits are as follows:\\\n",
    "$\n",
    "|00> = \\begin{bmatrix}\n",
    "    1  \\\\\n",
    "    0 \\\\\n",
    "    0\\\\\n",
    "    0\n",
    "\\end{bmatrix} ; |01> = \\begin{bmatrix}\n",
    "    0\\\\\n",
    "    1\\\\\n",
    "    0\\\\\n",
    "    0\n",
    "\\end{bmatrix} ; |10> = \\begin{bmatrix}\n",
    "    0  \\\\\n",
    "    0 \\\\\n",
    "    1\\\\\n",
    "    0\n",
    "\\end{bmatrix} ; |11> = \\begin{bmatrix}\n",
    "    0\\\\\n",
    "    0\\\\\n",
    "    0\\\\\n",
    "    1\n",
    "\\end{bmatrix}$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is a tensor product of two Hadamard transform. Lets apply it to |00> \n",
    "$(\\frac{1}{\\sqrt{2}}|0> + \\frac{1}{\\sqrt{2}}|1>) \\otimes (\\frac{1}{\\sqrt{2}}|0> + \\frac{1}{\\sqrt{2}}|1>) = \\frac{1}{{2}}|00> + \\frac{1}{{2}}|01>  +  \\frac{1}{{2}}|10> + \\frac{1}{{2}}|11>$\n",
    "$H_2|00>  = \\frac{1}{2} \\begin{bmatrix}\n",
    "    1  &  1  &  1  &  1 \\\\\n",
    "    1  &  -1  &  1  &  -1 \\\\\n",
    "    1  &  1  &  -1  &  -1 \\\\\n",
    "    1  &  -1  &  -1  &  1 \\\\\n",
    "\\end{bmatrix}\\begin{bmatrix} \n",
    "    1  \\\\\n",
    "    0 \\\\\n",
    "    0\\\\\n",
    "    0\n",
    "    \\end{bmatrix}\n",
    "    = \\begin{bmatrix}\n",
    "    \\frac{1}{2} \\\\\n",
    "    \\frac{1}{2} \\\\\n",
    "    \\frac{1}{2}\\\\\n",
    "    \\frac{1}{2}\n",
    "\\end{bmatrix}$\\\\\n",
    "$\n",
    "=  \\frac{1}{{2}}|00> + \\frac{1}{{2}}|01>  +  \\frac{1}{{2}}|10> + \\frac{1}{{2}}|11>$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Three Qubits with H gate on each"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "outputstate:\n",
      " [0.354+0.j 0.354+0.j 0.354+0.j 0.354+0.j 0.354+0.j 0.354+0.j 0.354+0.j\n",
      " 0.354+0.j]\n",
      "UnitaryMatrix:\n",
      " [[ 0.35355339+0.j  0.35355339+0.j  0.35355339+0.j  0.35355339+0.j\n",
      "   0.35355339+0.j  0.35355339+0.j  0.35355339+0.j  0.35355339+0.j]\n",
      " [ 0.35355339+0.j -0.35355339+0.j  0.35355339+0.j -0.35355339+0.j\n",
      "   0.35355339+0.j -0.35355339+0.j  0.35355339+0.j -0.35355339+0.j]\n",
      " [ 0.35355339+0.j  0.35355339+0.j -0.35355339+0.j -0.35355339+0.j\n",
      "   0.35355339+0.j  0.35355339+0.j -0.35355339+0.j -0.35355339+0.j]\n",
      " [ 0.35355339+0.j -0.35355339+0.j -0.35355339+0.j  0.35355339+0.j\n",
      "   0.35355339+0.j -0.35355339+0.j -0.35355339+0.j  0.35355339+0.j]\n",
      " [ 0.35355339+0.j  0.35355339+0.j  0.35355339+0.j  0.35355339+0.j\n",
      "  -0.35355339+0.j -0.35355339+0.j -0.35355339+0.j -0.35355339+0.j]\n",
      " [ 0.35355339+0.j -0.35355339+0.j  0.35355339+0.j -0.35355339+0.j\n",
      "  -0.35355339+0.j  0.35355339+0.j -0.35355339+0.j  0.35355339+0.j]\n",
      " [ 0.35355339+0.j  0.35355339+0.j -0.35355339+0.j -0.35355339+0.j\n",
      "  -0.35355339+0.j -0.35355339+0.j  0.35355339+0.j  0.35355339+0.j]\n",
      " [ 0.35355339+0.j -0.35355339+0.j -0.35355339+0.j  0.35355339+0.j\n",
      "  -0.35355339+0.j  0.35355339+0.j  0.35355339+0.j -0.35355339+0.j]]\n",
      "counts:\n",
      " {'001': 123, '110': 129, '000': 137, '101': 126, '010': 138, '100': 117, '011': 131, '111': 123}\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 397.32x264.88 with 1 Axes>"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "circuit = QuantumCircuit(3, 3)\n",
    "circuit.h(0)\n",
    "circuit.h(1)\n",
    "circuit.h(2)\n",
    "#Statevector part\n",
    "result3=execute(circuit,simulator_s).result()\n",
    "outputstate = result3.get_statevector(circuit, decimals=3)\n",
    "print ('outputstate:\\n',outputstate)\n",
    "#unitary vector part\n",
    "result=execute(circuit,simulator_u).result()\n",
    "unitary=result.get_unitary(circuit)\n",
    "print ('UnitaryMatrix:\\n',unitary)\n",
    "#Now Quasm Simulator part where we need to measure\n",
    "circuit.measure([0,1,2],[0,1,2])\n",
    "result2=execute(circuit,simulator_q).result()\n",
    "print (\"counts:\\n\",result2.get_counts(circuit))\n",
    "style = {'backgroundcolor': 'lightgreen'}\n",
    "circuit.draw(output='mpl',style=style)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "$\n",
    "H_3|000> = \\frac{1}{2\\sqrt{2}}(|000>  + |001> + |010> + |011>  +  |100> +  |101> + |110> +|111>)$  \n",
    "\n",
    "\n",
    "In Matrix form the multiplication looks like this:  \n",
    "$\n",
    "H_3|000> = \\frac{1}{2\\sqrt{2}} \\begin{bmatrix}\n",
    "    1  &   1  &  1  &   1  &  1  &   1  &  1  &   1 \\\\\n",
    "    1  &  -1  &  1  &  -1  &  1  &  -1  &  1  &  -1 \\\\\n",
    "    1  &   1  & -1  &  -1  &  1  &   1  & -1  &  -1 \\\\\n",
    "    1  &  -1  & -1  &   1  &  1  &  -1  & -1  &   1 \\\\\n",
    "    1  &   1  &  1  &   1  &  -1  & -1  &  -1  & -1 \\\\\n",
    "    1  &  -1  &  1  &  -1  &  -1  &  1  &  -1  &  1 \\\\\n",
    "    1  &   1  & -1  &  -1  &  -1  &   -1  &  1  &   1 \\\\\n",
    "    1  &  -1  & -1  &   1  &  -1  &    1  &  1  &  -1 \\\\\n",
    "\\end{bmatrix} \\begin{bmatrix} \n",
    "    1  \\\\\n",
    "    0 \\\\\n",
    "    0\\\\\n",
    "    0\\\\\n",
    "    0\\\\\n",
    "    0\\\\\n",
    "    0\\\\\n",
    "    0\n",
    "    \\end{bmatrix}\n",
    "    = \\begin{bmatrix}\n",
    "    \\frac{1}{2\\sqrt{2}} \\\\\n",
    "    \\frac{1}{2\\sqrt{2}} \\\\\n",
    "    \\frac{1}{2\\sqrt{2}}\\\\\n",
    "    \\frac{1}{2\\sqrt{2}}\\\\\n",
    "    \\frac{1}{2\\sqrt{2}} \\\\\n",
    "    \\frac{1}{2\\sqrt{2}} \\\\\n",
    "    \\frac{1}{2\\sqrt{2}}\\\\\n",
    "    \\frac{1}{2\\sqrt{2}}\n",
    "\\end{bmatrix}\n",
    "$\n",
    "$\n",
    "= \\frac{1}{2\\sqrt{2}}(|000>  + |001> + |010> + |011>  +  |100> +  |101> + |110> +|111>)\n",
    "$\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
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