aula2_sbf.ipynb

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   "source": [
    "### Computação Quântica com Qiskit\n",
    "\n",
    "##### Jonas Maziero\n",
    "\n",
    "<table>\n",
    "<td> Universidade Federal de Santa Maria <br>\n",
    "Centro de Ciências Naturais e Exatas <br>\n",
    "Departamento de Física <br>\n",
    "https://sites.google.com/site/jonasmaziero <br>\n",
    "jonas.maziero@ufsm.br \n",
    "    </td>\n",
    "    <td><img src='ufsm.jpg' width='250'></td>\n",
    "    <td><img src='inpe_ufsm.jpg' width='550'></td>\n",
    "</table>\n",
    "<table>\n",
    "    <td>Suporte Financeiro:</td>\n",
    "    <td><img src='cnpq.png' width='200'></td>\n",
    "    <td><img src='inct-iq.png' width='330'></td>\n",
    "    <td><img src='capes.png' width='100'></td>\n",
    "    <td><img src='fapergs.png' width='150'></td>\n",
    "    <td><img src='ufsm.jpg' width='75'></td>\n",
    "    </table>"
   ]
  },
  {
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   "source": [
    "## Aula 2\n",
    "\n",
    "- Postulados da Mecânica Quântica; \n",
    "- Transformações unitárias importantes; \n",
    "- Medidas em uma base qualquer; \n",
    "- Tomografia de estados quânticos."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c030bf1c",
   "metadata": {
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   },
   "source": [
    "# Mecânica Quântica"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "292f9863",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
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   "source": [
    "## Postulados da Mecânica Quântica\n",
    "\n",
    "### Postulado dos Estados\n",
    "$$|\\psi\\rangle\\in\\mathcal{H} \\text{ com } ||\\psi||=1$$\n",
    "Um qubit - Base computacional:\n",
    "$$|0\\rangle = \\begin{bmatrix} 1 \\\\ 0 \\end{bmatrix}, |1\\rangle = \\begin{bmatrix} 0 \\\\ 1 \\end{bmatrix}$$\n",
    "Estado geral ($c_{j}\\in\\mathbb{C}$ para $j=0,1$ com $|c_0|^2 + |c_1|^2 =1$):\n",
    "$$|\\psi\\rangle = \\begin{bmatrix} c_{0} \\\\ c_{1} \\end{bmatrix} = c_{0}\\begin{bmatrix} 1 \\\\ 0 \\end{bmatrix}+c_{1}\\begin{bmatrix} 0 \\\\ 1 \\end{bmatrix} = c_{0}|0\\rangle+c_{1}|1\\rangle$$"
   ]
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  {
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   "id": "a57c0cbd",
   "metadata": {
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   "source": [
    "#### Sistemas compostos\n",
    "Graus de liberdade $s=1,2,\\cdots,n$:\n",
    "$$|\\Psi\\rangle \\in \\mathcal{H} = \\mathcal{H}_{1}\\otimes\\mathcal{H}_{2}\\otimes\\cdots\\otimes\\mathcal{H}_{n} \\text{ com } ||\\Psi||=1.$$\n",
    "\n",
    "$$\\text{Produto tensorial: }A\\otimes B := \\begin{bmatrix} A_{11}B & A_{12}B & \\cdots \\\\\n",
    "                    A_{21}B & A_{22}B & \\cdots \\\\\n",
    "                    \\vdots & \\vdots & \\ddots\\end{bmatrix}.$$                    \n",
    "\n",
    "$$\\text{Ex. }|01\\rangle = \\begin{bmatrix} 1 \\\\ 0 \\end{bmatrix}\\otimes\\begin{bmatrix} 0 \\\\ 1 \\end{bmatrix} = \\begin{bmatrix} 0 \\\\ 1 \\\\ 0 \\\\ 0\\end{bmatrix},\\ |00\\rangle=\\begin{bmatrix} 1 \\\\ 0 \\\\ 0 \\\\ 0\\end{bmatrix},\\ |10\\rangle=\\begin{bmatrix} 0 \\\\ 0 \\\\ 1 \\\\ 0\\end{bmatrix},\\ |11\\rangle=\\begin{bmatrix} 0 \\\\ 0 \\\\ 0 \\\\ 1\\end{bmatrix}$$\n",
    "Notação: $|\\psi\\rangle\\otimes|\\phi\\rangle = |\\psi\\rangle|\\phi\\rangle = |\\psi\\phi\\rangle$"
   ]
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   "id": "02382328",
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   "source": [
    "#### Estados emaranhados\n",
    "\n",
    "Definição de emaranhamento: $|\\Psi\\rangle_{AB} \\ne |\\psi\\rangle_A\\otimes|\\phi\\rangle_B$ <br>\n",
    "\n",
    "Base de Bell:\n",
    "\\begin{align}\n",
    "& |\\Phi_\\pm\\rangle = \\frac{1}{\\sqrt{2}}\\big(|00\\rangle\\pm|11\\rangle\\big) = \\frac{1}{\\sqrt{2}}\\begin{bmatrix} 1 \\\\ 0 \\\\ 0 \\\\ \\pm1\\end{bmatrix},\\\\\n",
    "& |\\Psi_\\pm\\rangle = \\frac{1}{\\sqrt{2}}\\big(|01\\rangle\\pm|10\\rangle\\big) = \\frac{1}{\\sqrt{2}}\\begin{bmatrix} 0 \\\\ 1 \\\\ \\pm1 \\\\ 0\\end{bmatrix}.\n",
    "\\end{align}"
   ]
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   "id": "4763d859",
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   "source": [
    "### Postulado das medidas\n",
    "\n",
    "Observáveis:\n",
    "$$O\\in L(\\mathcal{H}) \\text{, } O=O^{\\dagger}=\\sum_{j}o_j|o_j\\rangle\\langle o_j|$$\n",
    "Regra de Born:\n",
    "$$Pr(o_j|\\psi)=|\\langle o_j|\\psi\\rangle|^{2}$$\n",
    "$\\text{ Repetibilidade: }|\\psi\\rangle\\xrightarrow[]{o_j}|o_j\\rangle = (|o_j\\rangle\\langle o_j|\\psi\\rangle)/|||o_j\\rangle\\langle o_j|\\psi\\rangle||.$\n",
    "\n",
    "Exemplo:\n",
    "$$\\text{Prepara }|\\psi\\rangle = c_0|0\\rangle+c_1|1\\rangle \\xrightarrow{\\text{Mede}\\ \\{|0\\rangle,|1\\rangle\\}}\\begin{cases}\\text{obtém }|0\\rangle \\text{ com prob. }|c_0|^2 \\\\ \\text{obtém }|1\\rangle \\text{ com prob. }|c_1|^2\\end{cases}$$"
   ]
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   "id": "ab1bb858",
   "metadata": {
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   "source": [
    "#### Postulado da dinâmica\n",
    "$$|\\psi_{t}\\rangle=U_{t}|\\psi_{0}\\rangle \\text{ com } i\\hbar\\partial_{t}U_{t}=H_{t}U_{t} \\text{ e } UU^\\dagger = U^\\dagger U = I$$\n",
    "\n",
    "Exemplos - __matrizes de Pauli__:\n",
    "$$Z=\\begin{bmatrix}1&0\\\\0&-1\\end{bmatrix}\\ \\therefore Z|0\\rangle=|0\\rangle,\\ Z|1\\rangle=-|1\\rangle$$\n",
    "$$X=\\begin{bmatrix}0&1\\\\1&0\\end{bmatrix}=NOT\\ \\therefore X|0\\rangle=|1\\rangle,\\ X|1\\rangle=|0\\rangle$$\n",
    "$$Y=\\begin{bmatrix}0&-i\\\\i&0\\end{bmatrix}\\ \\therefore Y|0\\rangle=i|1\\rangle,\\ Y|1\\rangle=-i|0\\rangle$$\n",
    "Autoverores: $|\\pm\\rangle=(|0\\rangle\\pm|1\\rangle)/\\sqrt{2}$ pra $X$ e $|\\oplus\\rangle=(|0\\rangle+i|1\\rangle)/\\sqrt{2}$ e $|\\ominus\\rangle=(|0\\rangle-i|1\\rangle)/\\sqrt{2}$ pra $Y$"
   ]
  },
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   "cell_type": "markdown",
   "id": "69604d2e",
   "metadata": {
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   "source": [
    "__Problema__: Verifique que a matriz de Pauli $Z$ faz o papel da NOT quando atua na base $\\{|+\\rangle,|-\\rangle\\}$.\n",
    "\n",
    "__Problema__: Verifique que $Y = iXZ.$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1d70d229",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "#### Usando o Sympy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 196,
   "id": "23c91018",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}0 & 1\\\\1 & 0\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "⎡0  1⎤\n",
       "⎢    ⎥\n",
       "⎣1  0⎦"
      ]
     },
     "execution_count": 196,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sympy import Matrix\n",
    "X = Matrix([[0,1],[1,0]]); X"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 197,
   "id": "912e5419",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}0 & - 1.0 i\\\\1.0 i & 0\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "⎡  0    -1.0⋅ⅈ⎤\n",
       "⎢             ⎥\n",
       "⎣1.0⋅ⅈ    0   ⎦"
      ]
     },
     "execution_count": 197,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Y = Matrix([[0,-1j],[1j,0]]); Y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 198,
   "id": "f6d76397",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}1 & 0\\\\0 & -1\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "⎡1  0 ⎤\n",
       "⎢     ⎥\n",
       "⎣0  -1⎦"
      ]
     },
     "execution_count": 198,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Z = Matrix([[1,0],[0,-1]]); Z"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1ae0400a",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "##### Autovalores e autovetores"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 199,
   "id": "75894d20",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\left\\{ -1 : 1, \\  1 : 1\\right\\}$"
      ],
      "text/plain": [
       "{-1: 1, 1: 1}"
      ]
     },
     "execution_count": 199,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X.eigenvals()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 200,
   "id": "eda36440",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[ \\left( -1, \\  1, \\  \\left[ \\left[\\begin{matrix}-1\\\\1\\end{matrix}\\right]\\right]\\right), \\  \\left( 1, \\  1, \\  \\left[ \\left[\\begin{matrix}1\\\\1\\end{matrix}\\right]\\right]\\right)\\right]$"
      ],
      "text/plain": [
       "⎡⎛       ⎡⎡-1⎤⎤⎞  ⎛      ⎡⎡1⎤⎤⎞⎤\n",
       "⎢⎜-1, 1, ⎢⎢  ⎥⎥⎟, ⎜1, 1, ⎢⎢ ⎥⎥⎟⎥\n",
       "⎣⎝       ⎣⎣1 ⎦⎦⎠  ⎝      ⎣⎣1⎦⎦⎠⎦"
      ]
     },
     "execution_count": 200,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X.eigenvects()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 201,
   "id": "9dc1f753",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[ \\left( -1.0, \\  1, \\  \\left[ \\left[\\begin{matrix}-0.707106781186548\\\\0.707106781186548 i\\end{matrix}\\right]\\right]\\right), \\  \\left( 1.0, \\  1, \\  \\left[ \\left[\\begin{matrix}0.707106781186548 i\\\\-0.707106781186548\\end{matrix}\\right]\\right]\\right)\\right]$"
      ],
      "text/plain": [
       "⎡⎛         ⎡⎡-0.707106781186548 ⎤⎤⎞  ⎛        ⎡⎡0.707106781186548⋅ⅈ⎤⎤⎞⎤\n",
       "⎢⎜-1.0, 1, ⎢⎢                   ⎥⎥⎟, ⎜1.0, 1, ⎢⎢                   ⎥⎥⎟⎥\n",
       "⎣⎝         ⎣⎣0.707106781186548⋅ⅈ⎦⎦⎠  ⎝        ⎣⎣-0.707106781186548 ⎦⎦⎠⎦"
      ]
     },
     "execution_count": 201,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Y.eigenvects()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 202,
   "id": "40e346a9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[ \\left( -1, \\  1, \\  \\left[ \\left[\\begin{matrix}0\\\\1\\end{matrix}\\right]\\right]\\right), \\  \\left( 1, \\  1, \\  \\left[ \\left[\\begin{matrix}1\\\\0\\end{matrix}\\right]\\right]\\right)\\right]$"
      ],
      "text/plain": [
       "⎡⎛       ⎡⎡0⎤⎤⎞  ⎛      ⎡⎡1⎤⎤⎞⎤\n",
       "⎢⎜-1, 1, ⎢⎢ ⎥⎥⎟, ⎜1, 1, ⎢⎢ ⎥⎥⎟⎥\n",
       "⎣⎝       ⎣⎣1⎦⎦⎠  ⎝      ⎣⎣0⎦⎦⎠⎦"
      ]
     },
     "execution_count": 202,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Z.eigenvects()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a4571953",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Preparando estados da base computacional\n",
    "\n",
    "Lembrando \n",
    "\\begin{align}\n",
    "I|0\\rangle=|0\\rangle, \\\\\n",
    "X|0\\rangle=|1\\rangle.\n",
    "\\end{align}\n",
    "Portanto\n",
    "\\begin{align}\n",
    "(I\\otimes I)|00\\rangle = |00\\rangle, \\\\\n",
    "(I\\otimes X)|00\\rangle = |01\\rangle, \\\\\n",
    "(X\\otimes I)|00\\rangle = |10\\rangle, \\\\\n",
    "(X\\otimes X)|00\\rangle = |11\\rangle.\n",
    "\\end{align}"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "29fd2a7f",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "#### Ação na base computacional usando Sympy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 203,
   "id": "821f8cd6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left( \\left[\\begin{matrix}1\\\\0\\end{matrix}\\right], \\  \\left[\\begin{matrix}0\\\\1\\end{matrix}\\right]\\right)$"
      ],
      "text/plain": [
       "⎛⎡1⎤  ⎡0⎤⎞\n",
       "⎜⎢ ⎥, ⎢ ⎥⎟\n",
       "⎝⎣0⎦  ⎣1⎦⎠"
      ]
     },
     "execution_count": 203,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sympy import Matrix\n",
    "X = Matrix([[0,1],[1,0]])\n",
    "ket0 = Matrix([[1],[0]]); ket1 = Matrix([[0],[1]]); ket0, ket1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 204,
   "id": "835f74a5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left( \\left[\\begin{matrix}0\\\\1\\end{matrix}\\right], \\  \\left[\\begin{matrix}1\\\\0\\end{matrix}\\right]\\right)$"
      ],
      "text/plain": [
       "⎛⎡0⎤  ⎡1⎤⎞\n",
       "⎜⎢ ⎥, ⎢ ⎥⎟\n",
       "⎝⎣1⎦  ⎣0⎦⎠"
      ]
     },
     "execution_count": 204,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X*ket0, X*ket1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 205,
   "id": "f3a978b7",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left( \\left[\\begin{matrix}0\\\\1.0 i\\end{matrix}\\right], \\  \\left[\\begin{matrix}- 1.0 i\\\\0\\end{matrix}\\right], \\  \\left[\\begin{matrix}1\\\\0\\end{matrix}\\right], \\  \\left[\\begin{matrix}0\\\\-1\\end{matrix}\\right]\\right)$"
      ],
      "text/plain": [
       "⎛⎡  0  ⎤  ⎡-1.0⋅ⅈ⎤  ⎡1⎤  ⎡0 ⎤⎞\n",
       "⎜⎢     ⎥, ⎢      ⎥, ⎢ ⎥, ⎢  ⎥⎟\n",
       "⎝⎣1.0⋅ⅈ⎦  ⎣  0   ⎦  ⎣0⎦  ⎣-1⎦⎠"
      ]
     },
     "execution_count": 205,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Y*ket0, Y*ket1, Z*ket0, Z*ket1"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "489c397c",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "#### Estados da base computacional"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 206,
   "id": "d0b7632c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left( \\left[\\begin{matrix}1\\\\0\\\\0\\\\0\\end{matrix}\\right], \\  \\left[\\begin{matrix}0\\\\1\\\\0\\\\0\\end{matrix}\\right], \\  \\left[\\begin{matrix}0\\\\0\\\\1\\\\0\\end{matrix}\\right], \\  \\left[\\begin{matrix}0\\\\0\\\\0\\\\1\\end{matrix}\\right]\\right)$"
      ],
      "text/plain": [
       "⎛⎡1⎤  ⎡0⎤  ⎡0⎤  ⎡0⎤⎞\n",
       "⎜⎢ ⎥  ⎢ ⎥  ⎢ ⎥  ⎢ ⎥⎟\n",
       "⎜⎢0⎥  ⎢1⎥  ⎢0⎥  ⎢0⎥⎟\n",
       "⎜⎢ ⎥, ⎢ ⎥, ⎢ ⎥, ⎢ ⎥⎟\n",
       "⎜⎢0⎥  ⎢0⎥  ⎢1⎥  ⎢0⎥⎟\n",
       "⎜⎢ ⎥  ⎢ ⎥  ⎢ ⎥  ⎢ ⎥⎟\n",
       "⎝⎣0⎦  ⎣0⎦  ⎣0⎦  ⎣1⎦⎠"
      ]
     },
     "execution_count": 206,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sympy.physics.quantum import TensorProduct as tp\n",
    "ket00 = tp(ket0,ket0); ket01 = tp(ket0,ket1); ket10 = tp(ket1,ket0); ket11 = tp(ket1,ket1); ket00, ket01, ket10, ket11"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 207,
   "id": "1d2a48a6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left( \\left[\\begin{matrix}0 & 1 & 0 & 0\\\\1 & 0 & 0 & 0\\\\0 & 0 & 0 & 1\\\\0 & 0 & 1 & 0\\end{matrix}\\right], \\  \\left[\\begin{matrix}1\\\\0\\\\0\\\\0\\end{matrix}\\right], \\  \\left[\\begin{matrix}0\\\\1\\\\0\\\\0\\end{matrix}\\right], \\  \\left[\\begin{matrix}0\\\\0\\\\1\\\\0\\end{matrix}\\right], \\  \\left[\\begin{matrix}0\\\\0\\\\0\\\\1\\end{matrix}\\right]\\right)$"
      ],
      "text/plain": [
       "⎛⎡0  1  0  0⎤  ⎡1⎤  ⎡0⎤  ⎡0⎤  ⎡0⎤⎞\n",
       "⎜⎢          ⎥  ⎢ ⎥  ⎢ ⎥  ⎢ ⎥  ⎢ ⎥⎟\n",
       "⎜⎢1  0  0  0⎥  ⎢0⎥  ⎢1⎥  ⎢0⎥  ⎢0⎥⎟\n",
       "⎜⎢          ⎥, ⎢ ⎥, ⎢ ⎥, ⎢ ⎥, ⎢ ⎥⎟\n",
       "⎜⎢0  0  0  1⎥  ⎢0⎥  ⎢0⎥  ⎢1⎥  ⎢0⎥⎟\n",
       "⎜⎢          ⎥  ⎢ ⎥  ⎢ ⎥  ⎢ ⎥  ⎢ ⎥⎟\n",
       "⎝⎣0  0  1  0⎦  ⎣0⎦  ⎣0⎦  ⎣0⎦  ⎣1⎦⎠"
      ]
     },
     "execution_count": 207,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tp(eye(2),X), tp(eye(2),eye(2))*ket00, tp(eye(2),X)*ket00, tp(X,eye(2))*ket00, tp(X,X)*ket00"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9df453df",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Prepara o estado $|00\\rangle$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 255,
   "id": "0a7bb4f1",
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Statevector([1.+0.j, 0.+0.j, 0.+0.j, 0.+0.j],\n",
      "            dims=(2, 2))\n"
     ]
    }
   ],
   "source": [
    "from qiskit import QuantumCircuit\n",
    "import qiskit\n",
    "from qiskit.quantum_info import Statevector\n",
    "qc = QuantumCircuit(2) # prepara o estado |00>\n",
    "qc.draw('mpl')\n",
    "state = Statevector(qc)\n",
    "state"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "70a723d5",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Prepara o estado $|01\\rangle$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 257,
   "id": "6c38e0aa",
   "metadata": {
    "scrolled": true,
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Statevector([0.+0.j, 0.+0.j, 1.+0.j, 0.+0.j],\n",
      "            dims=(2, 2))\n"
     ]
    }
   ],
   "source": [
    "qc = QuantumCircuit(2)\n",
    "qc.x(1) # estado |01>\n",
    "qc.draw('mpl')\n",
    "state = Statevector(qc); state"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "460fbdfa",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "\n",
    "__Problema__: Prepare o estado $|10\\rangle$ a partir do estado $|00\\rangle$, e mostre o circuito quântico utilizado.\n",
    "\n",
    "__Problema__: Prepare o estado $|11\\rangle$ a partir do estado $|00\\rangle$, e mostre vetor de estado obtido."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0cd7e158",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "$$\\text{Porta Hadamard: }H=\\frac{1}{\\sqrt{2}}\\begin{bmatrix}1&1\\\\1&-1\\end{bmatrix}\\ \\therefore H|0\\rangle=|+\\rangle,\\ H|1\\rangle=|-\\rangle$$\n",
    "\n",
    "$$\\text{Porta Ctrl-NOT: }C_{X}^{A\\rightarrow B} = |0\\rangle\\langle 0|\\otimes\\mathbb{I} + |1\\rangle\\langle 1|\\otimes X\\ \\therefore\\ C_{X}^{A\\rightarrow B}|j\\rangle|k\\rangle=|j\\rangle|j\\oplus k\\rangle$$\n",
    "\n",
    "__Base computacional $\\rightarrow$ Base de Bell__\n",
    "$$|\\psi_1\\rangle = (H\\otimes\\mathbb{I})|00\\rangle = |+\\rangle\\otimes|0\\rangle = 2^{-1/2}(|00\\rangle+|10\\rangle) $$\n",
    "Aplica a CNOT com o qubit coerente como controle\n",
    "\\begin{align}\n",
    "|\\Phi_+\\rangle & = C_{X}^{A\\rightarrow B}|\\psi_1\\rangle = 2^{-1/2}(|00\\rangle + |11\\rangle).\n",
    "\\end{align}\n",
    "Outros estados da base de Bell ($U=C_{X}^{A\\rightarrow B}(H\\otimes I)$):\n",
    "$$U|10\\rangle=|\\Phi_-\\rangle,\\ U|01\\rangle=|\\Psi_+\\rangle,\\ U|11\\rangle=|\\Psi_-\\rangle$$\n",
    "__Base de Bell $\\rightarrow$ base computacional__ ($U^\\dagger=(H\\otimes I)C_{X}^{A\\rightarrow B}$)\n",
    "$$|00\\rangle = U^\\dagger|\\Phi_+\\rangle,\\ |01\\rangle = U^\\dagger|\\Psi_+\\rangle,\\ |10\\rangle = U^\\dagger|\\Psi_-\\rangle,\\ |11\\rangle = U^\\dagger|\\Phi_-\\rangle.$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0307d4ba",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "#### Projetores e Matrix da CNOT em Sympy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 210,
   "id": "5bec5689",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left( \\left[\\begin{matrix}1 & 0\\\\0 & 0\\end{matrix}\\right], \\  \\left[\\begin{matrix}0 & 0\\\\0 & 1\\end{matrix}\\right]\\right)$"
      ],
      "text/plain": [
       "⎛⎡1  0⎤  ⎡0  0⎤⎞\n",
       "⎜⎢    ⎥, ⎢    ⎥⎟\n",
       "⎝⎣0  0⎦  ⎣0  1⎦⎠"
      ]
     },
     "execution_count": 210,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sympy.physics.quantum.dagger import Dagger\n",
    "P0 = ket0*Dagger(ket0); P1 = ket1*Dagger(ket1); P0,P1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 211,
   "id": "2f4f26d8",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left( \\left[\\begin{matrix}1 & 0 & 0 & 0\\\\0 & 1 & 0 & 0\\\\0 & 0 & 0 & 1\\\\0 & 0 & 1 & 0\\end{matrix}\\right], \\  \\left[\\begin{matrix}1 & 0 & 0 & 0\\\\0 & 0 & 0 & 1\\\\0 & 0 & 1 & 0\\\\0 & 1 & 0 & 0\\end{matrix}\\right]\\right)$"
      ],
      "text/plain": [
       "⎛⎡1  0  0  0⎤  ⎡1  0  0  0⎤⎞\n",
       "⎜⎢          ⎥  ⎢          ⎥⎟\n",
       "⎜⎢0  1  0  0⎥  ⎢0  0  0  1⎥⎟\n",
       "⎜⎢          ⎥, ⎢          ⎥⎟\n",
       "⎜⎢0  0  0  1⎥  ⎢0  0  1  0⎥⎟\n",
       "⎜⎢          ⎥  ⎢          ⎥⎟\n",
       "⎝⎣0  0  1  0⎦  ⎣0  1  0  0⎦⎠"
      ]
     },
     "execution_count": 211,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "CNOTab = tp(P0,eye(2)) + tp(P1,X); CNOTba = tp(eye(2),P0) + tp(X,P1); CNOTab,CNOTba"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "85fcf6a1",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "#### $|00\\rangle\\rightarrow|\\Phi_+\\rangle$ com Sympy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 212,
   "id": "647cbb92",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}\\frac{\\sqrt{2}}{2} & \\frac{\\sqrt{2}}{2}\\\\\\frac{\\sqrt{2}}{2} & - \\frac{\\sqrt{2}}{2}\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "⎡√2   √2 ⎤\n",
       "⎢──   ── ⎥\n",
       "⎢2    2  ⎥\n",
       "⎢        ⎥\n",
       "⎢√2  -√2 ⎥\n",
       "⎢──  ────⎥\n",
       "⎣2    2  ⎦"
      ]
     },
     "execution_count": 212,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "H = Matrix([[1,1],[1,-1]])/sqrt(2); H"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 213,
   "id": "28312a9d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left( \\left[\\begin{matrix}\\frac{\\sqrt{2}}{2}\\\\0\\\\0\\\\\\frac{\\sqrt{2}}{2}\\end{matrix}\\right], \\  \\left[\\begin{matrix}\\frac{\\sqrt{2}}{2}\\\\0\\\\0\\\\- \\frac{\\sqrt{2}}{2}\\end{matrix}\\right]\\right)$"
      ],
      "text/plain": [
       "⎛⎡√2⎤  ⎡ √2 ⎤⎞\n",
       "⎜⎢──⎥  ⎢ ── ⎥⎟\n",
       "⎜⎢2 ⎥  ⎢ 2  ⎥⎟\n",
       "⎜⎢  ⎥  ⎢    ⎥⎟\n",
       "⎜⎢0 ⎥  ⎢ 0  ⎥⎟\n",
       "⎜⎢  ⎥, ⎢    ⎥⎟\n",
       "⎜⎢0 ⎥  ⎢ 0  ⎥⎟\n",
       "⎜⎢  ⎥  ⎢    ⎥⎟\n",
       "⎜⎢√2⎥  ⎢-√2 ⎥⎟\n",
       "⎜⎢──⎥  ⎢────⎥⎟\n",
       "⎝⎣2 ⎦  ⎣ 2  ⎦⎠"
      ]
     },
     "execution_count": 213,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Phip = CNOTab*tp(H,eye(2))*ket00; Phim = CNOTab*tp(H,eye(2))*ket10; Phip,Phim"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a0029a9c",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "__Problema__: Use o Sympy para obter os estados da base de Bell $|\\Psi_+\\rangle,|\\Psi_-\\rangle$ a partir dos estados da base computacional $|01\\rangle,|11\\rangle$."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2694cdbf",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Preparação dos estados da base de Bell a partir de $|00\\rangle$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "173742bb",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Prepara o estado $|\\Phi_+\\rangle$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 214,
   "id": "6f42d4ae",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 287.294x200.667 with 1 Axes>"
      ]
     },
     "execution_count": 214,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from qiskit import QuantumCircuit\n",
    "qc = QuantumCircuit(2)\n",
    "qc.h(0)\n",
    "qc.cx(0,1)\n",
    "qc.draw('mpl')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 215,
   "id": "e38b596c",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Statevector([0.70710678+0.j, 0.        +0.j, 0.        +0.j,\n",
      "             0.70710678+0.j],\n",
      "            dims=(2, 2))\n"
     ]
    }
   ],
   "source": [
    "from qiskit.quantum_info import Statevector\n",
    "state = Statevector(qc); state # |Phi+>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "167c1de3",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Prepara o estado $|\\Psi_-\\rangle$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 216,
   "id": "a3aff8cd",
   "metadata": {
    "scrolled": false,
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 370.906x200.667 with 1 Axes>"
      ]
     },
     "execution_count": 216,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from qiskit import QuantumCircuit\n",
    "qc = QuantumCircuit(2)\n",
    "qc.x([0,1])\n",
    "qc.h(0)\n",
    "qc.cx(0,1)\n",
    "qc.draw('mpl')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 217,
   "id": "52328122",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Statevector([ 0.        +0.j, -0.70710678+0.j,  0.70710678+0.j,\n",
      "              0.        +0.j],\n",
      "            dims=(2, 2))\n"
     ]
    }
   ],
   "source": [
    "from qiskit.quantum_info import Statevector\n",
    "state = Statevector(qc); state # |Psi->"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1702d736",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "__Problema:__ Prepare o estado de Bell $|\\Phi_-\\rangle$ a partir do estado $|00\\rangle$, e mostre o circuito quântico utilizado.\n",
    "\n",
    "__Problema:__ Prepare o estado de Bell $|\\Psi_+\\rangle$ a partir do estado $|00\\rangle$, e mostre o vetor de estado obtido."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "28a1b44e",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "#### Indo da base de Bell $\\{|\\Phi_+\\rangle,|\\Psi_+\\rangle,|\\Phi_-\\rangle,|\\Psi_-\\rangle\\}$ para a base computacional $\\{|00\\rangle,|01\\rangle,|10\\rangle,|11\\rangle\\}$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "50fd7697",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "$|\\Phi_+\\rangle\\rightarrow|00\\rangle$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 218,
   "id": "baf81a66",
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 538.128x200.667 with 1 Axes>"
      ]
     },
     "execution_count": 218,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from qiskit import QuantumCircuit\n",
    "qc = QuantumCircuit(2)\n",
    "qc.h(0); qc.cx(0,1) # prepara |Phi+>\n",
    "qc.barrier()\n",
    "qc.cx(0,1)\n",
    "qc.h(0)\n",
    "qc.draw('mpl')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 219,
   "id": "de820e2b",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Statevector([1.+0.j, 0.+0.j, 0.+0.j, 0.+0.j],\n",
      "            dims=(2, 2))\n"
     ]
    }
   ],
   "source": [
    "from qiskit.quantum_info import Statevector\n",
    "state = Statevector(qc); state # estado |00>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "eab29f59",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "$|\\Psi_-\\rangle\\rightarrow|11\\rangle$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 220,
   "id": "0511220c",
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 621.739x200.667 with 1 Axes>"
      ]
     },
     "execution_count": 220,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from qiskit import QuantumCircuit\n",
    "qc = QuantumCircuit(2)\n",
    "qc.x([0,1]); qc.h(0); qc.cx(0,1) # prepara |Psi->\n",
    "qc.barrier()\n",
    "qc.cx(0,1)\n",
    "qc.h(0)\n",
    "qc.draw('mpl')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 221,
   "id": "360158c7",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Statevector([0.+0.j, 0.+0.j, 0.+0.j, 1.+0.j],\n",
      "            dims=(2, 2))\n"
     ]
    }
   ],
   "source": [
    "from qiskit.quantum_info import Statevector\n",
    "state = Statevector(qc); state # estado |11>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7a02a64d",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "__Problema__: Obtenha o estado $|01\\rangle$ a partir do estado $|\\Psi_+\\rangle$, e mostre o circuito quântico utilizado.\n",
    "\n",
    "__Problema__: Obtenha o estado $|10\\rangle$ a partir do estado $|\\Phi_-\\rangle$, e mostre o vetor de estado obtido."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "601dc219",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "#### Medidas em uma base qualquer\n",
    "$$|b_{j_0 \\cdots j_n}\\rangle = U |j_0 \\cdots j_n\\rangle$$ a partir de medidas na base $|j_0 \\cdots j_n\\rangle$:\n",
    "\\begin{align}\n",
    "Pr(b_{j_0 \\cdots j_n}|\\psi) & = |\\langle b_{j_0 \\cdots j_n}|\\psi\\rangle|^2 \\\\\n",
    "& = |\\langle j_0 \\cdots j_n|U^\\dagger|\\psi\\rangle|^2 \\\\\n",
    "& \\equiv |\\langle j_0 \\cdots j_n|\\psi'\\rangle|^2 \\\\\n",
    "& = Pr(j_0 \\cdots j_n|\\psi')\n",
    "\\end{align}\n",
    "em que\n",
    "$$|\\psi'\\rangle := U^\\dagger|\\psi\\rangle.$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f1821ca9",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "__Medidas na base__ de auovetores de $X$,\n",
    "$$\\{|+\\rangle,|-\\rangle\\} = \\{H|0\\rangle,H|1\\rangle\\},$$\n",
    "de um qubit\n",
    "$$Pr(+|\\psi) = Pr(0|\\psi')$$\n",
    "$$Pr(-|\\psi)=Pr(1|\\psi'),$$\n",
    "com $$|\\psi'\\rangle=H^\\dagger|\\psi\\rangle=H|\\psi\\rangle.$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "df933b4c",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "#### Autovalores e autovetores com o Sympy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 222,
   "id": "349b8c04",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}0 & 1\\\\1 & 0\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "⎡0  1⎤\n",
       "⎢    ⎥\n",
       "⎣1  0⎦"
      ]
     },
     "execution_count": 222,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sympy import Matrix\n",
    "X = Matrix([[0,1],[1,0]]); X"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 223,
   "id": "20a2c5fa",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[ \\left( -1, \\  1, \\  \\left[ \\left[\\begin{matrix}-1\\\\1\\end{matrix}\\right]\\right]\\right), \\  \\left( 1, \\  1, \\  \\left[ \\left[\\begin{matrix}1\\\\1\\end{matrix}\\right]\\right]\\right)\\right]$"
      ],
      "text/plain": [
       "⎡⎛       ⎡⎡-1⎤⎤⎞  ⎛      ⎡⎡1⎤⎤⎞⎤\n",
       "⎢⎜-1, 1, ⎢⎢  ⎥⎥⎟, ⎜1, 1, ⎢⎢ ⎥⎥⎟⎥\n",
       "⎣⎝       ⎣⎣1 ⎦⎦⎠  ⎝      ⎣⎣1⎦⎦⎠⎦"
      ]
     },
     "execution_count": 223,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "init_printing(use_unicode=True) # pra visualização ficar melhor\n",
    "X.eigenvects()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fd51c2a3",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "#### Medida de $Z$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 224,
   "id": "9a34a7b9",
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Statevector([0.70710678+0.j, 0.70710678+0.j],\n",
      "            dims=(2,))\n"
     ]
    }
   ],
   "source": [
    "from qiskit import QuantumCircuit\n",
    "qc = QuantumCircuit(1,1)\n",
    "qc.h(0)\n",
    "from qiskit.quantum_info import Statevector\n",
    "state = Statevector(qc)\n",
    "state"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 225,
   "id": "24b30a1d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 269.064x200.667 with 1 Axes>"
      ]
     },
     "execution_count": 225,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qc.measure(0,0)\n",
    "qc.draw('mpl')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 226,
   "id": "ec6d81a9",
   "metadata": {
    "scrolled": true,
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 700x500 with 1 Axes>"
      ]
     },
     "execution_count": 226,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from qiskit import Aer, execute\n",
    "simulator = Aer.get_backend('qasm_simulator')\n",
    "nshots = 2**13 # 8192 \n",
    "job = execute(qc, backend=simulator, shots=nshots)\n",
    "from qiskit.tools.visualization import plot_histogram\n",
    "plot_histogram(job.result().get_counts())"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9f63bdf5",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Medida de $X$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 227,
   "id": "8c43cf04",
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 436.286x200.667 with 1 Axes>"
      ]
     },
     "execution_count": 227,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from qiskit import QuantumCircuit\n",
    "qc = QuantumCircuit(1,1)\n",
    "qc.h(0)\n",
    "qc.barrier()\n",
    "qc.h(0)\n",
    "qc.measure(0,0)\n",
    "qc.draw('mpl')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 228,
   "id": "0b65d6cf",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 700x500 with 1 Axes>"
      ]
     },
     "execution_count": 228,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from qiskit import Aer, execute\n",
    "simulator = Aer.get_backend('qasm_simulator')\n",
    "nshots = 2**13 # 8192 \n",
    "job = execute(qc, backend=simulator, shots=nshots)\n",
    "from qiskit.tools.visualization import plot_histogram\n",
    "plot_histogram(job.result().get_counts())"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d6131a1a",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "$$\\text{ Porta } S = \\begin{bmatrix}1&0\\\\0&i\\end{bmatrix}\\ \\therefore\\ S^{\\dagger} = \\begin{bmatrix}1&0\\\\0&-i\\end{bmatrix}\\ \\therefore\\ S|0\\rangle=|0\\rangle, S|1\\rangle=i|1\\rangle = e^{i\\pi/2}|1\\rangle$$\n",
    "\n",
    "$$\\text{ Porta de fase: } P(\\theta) = \\begin{bmatrix}1&0\\\\0&e^{i\\theta}\\end{bmatrix}\\ \\therefore\\ P(\\theta)|0\\rangle=|0\\rangle, P(\\theta)|1\\rangle = e^{i\\theta}|1\\rangle$$\n",
    "\n",
    "__Medidas na base de autoveres de $Y$__, $\\{|\\oplus\\rangle,|\\ominus\\rangle\\}$,\n",
    "\\begin{align}\n",
    "& S|+\\rangle = (|0\\rangle+i|1\\rangle)/\\sqrt{2} = |\\oplus\\rangle = SH|0\\rangle \\\\\n",
    "& S|-\\rangle = (|0\\rangle-i|1\\rangle)/\\sqrt{2} = |\\ominus\\rangle = SH|1\\rangle.\n",
    "\\end{align}\n",
    "Assim\n",
    "\\begin{align}\n",
    "& Pr(\\oplus|\\psi) = Pr(0|\\psi'),\\ Pr(\\ominus|\\psi)=Pr(1|\\psi')\n",
    "\\end{align}\n",
    "com \n",
    "$$|\\psi'\\rangle = (SH)^\\dagger|\\psi\\rangle = HS^{\\dagger}|\\psi\\rangle.$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3a7a41a8",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Medida de $Y$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 229,
   "id": "3d0a74cd",
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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AhjOjgoICqNVq2NvbQ6PRIDg4WLJtH045hfoG09d4dDqdYY1INcQRdra2Ug2NBhmdTgedXi/cz5CL8xBseGG5SY+V3czos88+AwBERUVJGiIAqG9oRl1DoyTbampukWQ7RHIhuxgVFhYCAGbOnCn5tl2cTV9s5qyIBoP+/I7ILkZ1dXUAAHd3d8m3ber0EwA+y7yAy5rrCPT3QdzqKAlHRSQPsouRq6srAKCmpkbybZu6ZvTgrOju9/eQ8OExqYdGJASuGT0gJCQEp06dQm5uruTblmLNiGtFRN2TXYyWL1+OvXv3IiMjA0VFRQgK6vkUemOZcjzMtSIaTPqzZiS7l/YBYNWqVfjkk08QEBCAtLQ0hIWFGW67e/cukpKSsHv3brOMhWtFRH0jyxjV1dUhOjoaX331FQDAz8/PcAa2Vqs12xnYPNuaqO9k+d40V1dXZGVlISkpCeHh4aivr8fVq1dhb2+PyMhIpKammmUcPNuaqO9kOTMSRdbX+bjwj6t4ccUixojoIRijAdZyvxWOSgdLD4NIeIwREQlBlmtGRGR9GCMiEgJjRERCYIyISAiMEREJgTEiIiEwRkQkBMaIiITAGBGREBgjIhICY0REQmCMiEgIjBERCYExIiIhMEZEJATGiIiEwBgRkRAYIyISAmNEREJgjIhICIwREQmBMSIiITBGRCQExoiIhMAYEZEQGCMiEgJjRERCYIyISAiMEREJgTEiIiEwRkQkBMaIiITAGBGREBgjIhICY0REQmCMiEgIjBERCYExIiIhMEZEJIT/BwvfbN1GI8XpAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 352.675x200.667 with 1 Axes>"
      ]
     },
     "execution_count": 229,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from qiskit import QuantumCircuit\n",
    "qc = QuantumCircuit(1,1)\n",
    "qc.sdg(0)\n",
    "qc.h(0)\n",
    "qc.measure(0,0)\n",
    "qc.draw('mpl')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 230,
   "id": "98832ee9",
   "metadata": {
    "scrolled": true,
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 700x500 with 1 Axes>"
      ]
     },
     "execution_count": 230,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from qiskit import execute, Aer\n",
    "simulator = Aer.get_backend('qasm_simulator')\n",
    "nshots = 2**13\n",
    "job = execute(qc, backend=simulator, shots=nshots)\n",
    "from qiskit.tools.visualization import plot_histogram\n",
    "plot_histogram(job.result().get_counts())"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3b96d57a",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "__Observável geral__ de um sistema de 2 níveis\n",
    "$$\\sigma_n = \\hat{n}\\cdot\\vec{\\sigma} = \\begin{bmatrix}\n",
    "\\cos\\theta & e^{-i\\phi}\\sin\\theta \\\\ e^{i\\phi}\\sin\\theta & -\\cos\\theta \\\\ \\end{bmatrix}$$\n",
    "aplica\n",
    "$$|\\psi'\\rangle = (U(\\theta,\\phi,\\pi-\\phi))^{\\dagger}|\\psi\\rangle = U(\\theta,\\phi,\\pi-\\phi)|\\psi\\rangle$$\n",
    "Porta de __rotação geral de 1 qubit__\n",
    "$$U(\\theta,\\phi,\\lambda) = \\begin{bmatrix} \\cos(\\theta/2) & -e^{i\\lambda}\\sin(\\theta/2) \\\\ e^{i\\phi}\\sin(\\theta/2) & e^{i(\\phi+\\lambda)}\\cos(\\theta/2) \\end{bmatrix}$$\n",
    "Assim, e.g.,\n",
    "\\begin{align}\n",
    "& U(\\theta,\\phi,\\pi-\\phi)|0\\rangle = \\cos(\\theta/2)|0\\rangle + e^{i\\phi}\\sin(\\theta/2)|1\\rangle = |n_+\\rangle, \\\\\n",
    "& U(\\theta,\\phi,\\pi-\\phi)|1\\rangle = e^{-i\\phi}\\sin(\\theta/2)|0\\rangle - \\cos(\\theta/2)|1\\rangle = |n_-\\rangle.\n",
    "    \\end{align}\n",
    "E $$Pr(n_+|\\psi)=Pr(0|\\psi'),\\ Pr(n_-|\\psi)=Pr(1|\\psi').$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3aa6d19e",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "#### Usando Sympy com símbolos agora:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 231,
   "id": "0039f48c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\left( \\theta, \\  \\phi, \\  \\lambda\\right)$"
      ],
      "text/plain": [
       "(θ, φ, λ)"
      ]
     },
     "execution_count": 231,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sympy import symbols\n",
    "th, ph, lb = symbols('theta phi lambda'); th, ph, lb"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 232,
   "id": "a8b508ec",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}\\cos{\\left(\\theta \\right)} & e^{- 1.0 i \\phi} \\sin{\\left(\\theta \\right)}\\\\e^{1.0 i \\phi} \\sin{\\left(\\theta \\right)} & - \\cos{\\left(\\theta \\right)}\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "⎡                  -1.0⋅ⅈ⋅φ       ⎤\n",
       "⎢    cos(θ)       ℯ        ⋅sin(θ)⎥\n",
       "⎢                                 ⎥\n",
       "⎢ 1.0⋅ⅈ⋅φ                         ⎥\n",
       "⎣ℯ       ⋅sin(θ)      -cos(θ)     ⎦"
      ]
     },
     "execution_count": 232,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sn = Matrix([[cos(th),exp(-1j*ph)*sin(th)],[exp(1j*ph)*sin(th),-cos(th)]]); sn"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 233,
   "id": "1ea2e926",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[ \\left( -1.0, \\  1, \\  \\left[ \\left[\\begin{matrix}- \\frac{\\sin{\\left(\\theta \\right)}}{e^{i \\phi} \\cos{\\left(\\theta \\right)} + e^{i \\phi}}\\\\1.0\\end{matrix}\\right]\\right]\\right), \\  \\left( 1.0, \\  1, \\  \\left[ \\left[\\begin{matrix}- \\frac{\\sin{\\left(\\theta \\right)}}{e^{i \\phi} \\cos{\\left(\\theta \\right)} - e^{i \\phi}}\\\\1.0\\end{matrix}\\right]\\right]\\right)\\right]$"
      ],
      "text/plain": [
       "⎡⎛         ⎡⎡     -sin(θ)      ⎤⎤⎞  ⎛        ⎡⎡     -sin(θ)      ⎤⎤⎞⎤\n",
       "⎢⎜         ⎢⎢──────────────────⎥⎥⎟  ⎜        ⎢⎢──────────────────⎥⎥⎟⎥\n",
       "⎢⎜         ⎢⎢ ⅈ⋅φ           ⅈ⋅φ⎥⎥⎟  ⎜        ⎢⎢ ⅈ⋅φ           ⅈ⋅φ⎥⎥⎟⎥\n",
       "⎢⎜-1.0, 1, ⎢⎢ℯ   ⋅cos(θ) + ℯ   ⎥⎥⎟, ⎜1.0, 1, ⎢⎢ℯ   ⋅cos(θ) - ℯ   ⎥⎥⎟⎥\n",
       "⎢⎜         ⎢⎢                  ⎥⎥⎟  ⎜        ⎢⎢                  ⎥⎥⎟⎥\n",
       "⎣⎝         ⎣⎣       1.0        ⎦⎦⎠  ⎝        ⎣⎣       1.0        ⎦⎦⎠⎦"
      ]
     },
     "execution_count": 233,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sn.eigenvects()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "da53a44f",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "__Exemplo__: Medida de\n",
    "\\begin{align}\n",
    "\\hat{n}\\cdot\\vec{\\sigma} & = \\sin\\theta\\cos\\phi X + \\sin\\theta\\sin\\phi Y + \\cos\\theta Z \\\\\n",
    "& = \\frac{1}{\\sqrt{2}}(Z-X). \n",
    "\\end{align}\n",
    "Assim\n",
    "$$\\theta = -\\frac{\\pi}{4},\\ \\phi = 0.$$\n",
    "\n",
    "_Teoria_: \n",
    "$$Pr(n_+|0) = |\\langle n_+|0\\rangle|^2 = \\big|\\big(\\cos(\\theta/2)\\langle 0|+e^{-i\\phi}\\sin(\\theta/2)\\langle 1|\\big)|0\\rangle\\big|^2 = \\cos^2(\\theta/2).$$\n",
    "Para $\\theta = -\\pi/4$ temos $Pr(n_+|0) = \\cos^2(-\\pi/8) \\approx 0.85$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "0eaa6232",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.8535533905932737"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import math\n",
    "math.cos(math.pi/8)**2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "52b55d9b",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 269.064x200.667 with 1 Axes>"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from qiskit import QuantumCircuit\n",
    "qc = QuantumCircuit(1,1)\n",
    "import math\n",
    "th = -math.pi/4\n",
    "ph = 0\n",
    "lb = math.pi - ph\n",
    "qc.u(th,ph,lb, 0) # porta parametrizada\n",
    "qc.measure(0,0)\n",
    "qc.draw('mpl')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "e20d7223",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 700x500 with 1 Axes>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from qiskit import Aer, execute\n",
    "simulator = Aer.get_backend('qasm_simulator')\n",
    "nshots = 2**13\n",
    "job = execute(qc, backend = simulator, shots=nshots)\n",
    "from qiskit.tools.visualization import plot_histogram\n",
    "plot_histogram(job.result().get_counts())"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c2be863d",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Tomografia de estados\n",
    "\n",
    "__Postulado dos estados:__ $\\rho:\\mathcal{H}\\rightarrow\\mathcal{H}$ com $\\rho\\ge 0$ e $Tr(\\rho)=1$ <br>\n",
    "__Postulado das medidas:__ $Pr(o_j|\\rho) = Tr(\\rho|o_j\\rangle\\langle o_j|)$.\n",
    "\n",
    "$*$ Estados de __1 qubit:__\n",
    "$$\\rho = (1/2)\\big(I + \\langle X\\rangle_\\rho X + \\langle Y\\rangle_\\rho Y +\\langle Z\\rangle_\\rho Z\\big),$$\n",
    "com e.g. $\\langle X\\rangle_\\rho = Tr(\\rho X) = (+1)Pr(x_+|\\rho)+(-1)Pr(x_-|\\rho)$.\n",
    "\n",
    "$*$ Estados de __2 qubits:__\n",
    "$\\rho = \\frac{1}{4}\\sum_{j,k=0}^3 \\langle \\sigma_j\\otimes\\sigma_k\\rangle_\\rho  \\sigma_j\\otimes\\sigma_k,$\n",
    "com $\\sigma_0 = I,\\ \\sigma_1=X,\\ \\sigma_2=Y,\\ \\sigma_3=Z$ e e.g. \n",
    "\\begin{align}\n",
    "\\langle X\\otimes Y\\rangle = &(+1)(+1)Pr(x_+,y_+)+(+1)(-1)Pr(x_+,y_-)\\\\\n",
    "& +(-1)(+1)Pr(x_-,y_+)+(-1)(-1)Pr(x_-,y_-).\n",
    "\\end{align}"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e8348e6f",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "* Estados de __n qubits__:\n",
    "$$\\rho = \\frac{1}{2^n}\\sum_{j_0,j_1,\\cdots,j_n=0}^{3}\\langle\\sigma_{j_0}\\otimes\\sigma_{j_1}\\otimes\\cdots\\otimes\\sigma_{j_n}\\rangle_\\rho \\sigma_{j_0}\\otimes\\sigma_{j_1}\\otimes\\cdots\\otimes\\sigma_{j_n}.$$\n",
    "Nesse caso \"temos\" que medir\n",
    "$$4^n -1 = 2^{2n}-1$$\n",
    "valores médios."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cd54eedc",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Tomografia de estados com qiskit"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8c82dbcb",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Estado de 1 qubit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "459b2897",
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 269.064x117.056 with 1 Axes>"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Cria o circuito quântico, sem usar medidas\n",
    "from qiskit import QuantumCircuit\n",
    "qc = QuantumCircuit(1)\n",
    "qc.h(0)\n",
    "qc.s(0)\n",
    "qc.draw(output='mpl') # estado |o+>=(|0>+i|1>)/sqrt(2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "47a18a63",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "8192"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "2**13"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "025ad0e8",
   "metadata": {
    "scrolled": true,
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1500x500 with 2 Axes>"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from qiskit import Aer, execute; simulator = Aer.get_backend('qasm_simulator'); nshots = 2**13\n",
    "import qiskit; from qiskit.ignis.verification.tomography import state_tomography_circuits, StateTomographyFitter\n",
    "qstc = state_tomography_circuits(qc, [0]); job = execute(qstc, backend=simulator, shots=nshots)\n",
    "qstf = StateTomographyFitter(job.result(), qstc); rho = qstf.fit(method='lstsq')\n",
    "qiskit.visualization.plot_state_city(rho)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 239,
   "id": "270852c9",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0.49438517+0.j        , 0.00219711-0.49996365j],\n",
       "       [0.00219711+0.49996365j, 0.50561483+0.j        ]])"
      ]
     },
     "execution_count": 239,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rho"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "06283e8a",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "__Problema__: Prepare o estado $|-\\rangle = (|0\\rangle-|1\\rangle)/\\sqrt{2}$, faça a tomografia de estados usando as funções do Qiskit e mostre a matriz densidade reconstruída."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "716c5081",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Esfera de Bloch\n",
    "\n",
    "Podemos representar qualquer vetor de estado de um qubit por um ponto $(1,\\theta,\\phi)$ na superfície de uma esfera de raio 1 em $\\mathbb{R}^3$.\n",
    "\n",
    "Operador densidade de um qubit: $\\rho = (1/2)(I+xX+yY+zZ)$ <br>\n",
    "Autovalores: $\\lambda_{\\pm} = (1/2)(1\\pm r)$ com $r=\\sqrt{x^2 + y^2 +z^2}$\n",
    "Para ter $\\lambda_- \\ge 0$ os pontos $(x=r\\sin\\theta\\cos\\phi,\\ y=r\\sin\\theta\\sin\\phi,\\ z=r\\cos\\theta)$ devem estar dentro de uma esfera."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "65954369",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\left\\{ 0.5 - 0.5 \\sqrt{x^{2} + y^{2} + z^{2}} : 1, \\  0.5 \\sqrt{x^{2} + y^{2} + z^{2}} + 0.5 : 1\\right\\}$"
      ],
      "text/plain": [
       "⎧             ______________            ______________         ⎫\n",
       "⎨            ╱  2    2    2            ╱  2    2    2          ⎬\n",
       "⎩0.5 - 0.5⋅╲╱  x  + y  + z  : 1, 0.5⋅╲╱  x  + y  + z   + 0.5: 1⎭"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sympy import Matrix, symbols, init_printing, eye\n",
    "init_printing(use_unicode=True)\n",
    "X = Matrix([[0,1],[1,0]]); Y = Matrix([[0,-1j],[1j,0]]); Z = Matrix([[1,0],[0,-1]])\n",
    "x,y,z = symbols('x y z')\n",
    "rho = (1/2)*(eye(2) + x*X + y*Y + z*Z); rho\n",
    "rho.eigenvals()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 240,
   "id": "317a4826",
   "metadata": {
    "scrolled": false,
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1600x400 with 4 Axes>"
      ]
     },
     "execution_count": 240,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from qiskit import QuantumCircuit\n",
    "from qiskit.quantum_info import Statevector\n",
    "from qiskit.visualization import plot_bloch_multivector\n",
    "qc = QuantumCircuit(4) # não faz nada no 1º qubit\n",
    "qc.x(1)\n",
    "qc.h(2)\n",
    "qc.h(3); qc.s(3) \n",
    "state = Statevector(qc)\n",
    "plot_bloch_multivector(state)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "50c5651a",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "celltoolbar": "Slideshow",
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.11.1"
  },
  "rise": {
   "theme": "sky"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}