Ejemplos mínimos del uso de qutip.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "brutal-marriage",
   "metadata": {},
   "source": [
    "# Qutip\n",
    "\n",
    "Qutip es una librería de Python que permite construir representaciones matriciales (tensoriales) de operadores en MC de forma eficiente y más o menos transparente. También permite resolver ecuaciones de evolución para sistemas abiertos, calcular valores medios y estimadores de correlaciones cuánticas.\n",
    "Acá van algunos ejemplos."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "supported-married",
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "\n",
    "import numpy as np\n",
    "import qutip \n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "id": "artistic-hayes",
   "metadata": {},
   "outputs": [],
   "source": [
    "### Estado de una base canónica en dimensión 3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "id": "decreased-heritage",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "Quantum object: dims = [[3], [1]], shape = (3, 1), type = ket\\begin{equation*}\\left(\\begin{array}{*{11}c}0.0\\\\0.0\\\\1.0\\\\\\end{array}\\right)\\end{equation*}"
      ],
      "text/plain": [
       "Quantum object: dims = [[3], [1]], shape = (3, 1), type = ket\n",
       "Qobj data =\n",
       "[[0.]\n",
       " [0.]\n",
       " [1.]]"
      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\n",
    "qutip.basis(3,2)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "saved-motor",
   "metadata": {},
   "source": [
    "### Combinación lineal de estados de una base canónica"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "id": "adjusted-participation",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "Quantum object: dims = [[3], [1]], shape = (3, 1), type = ket\\begin{equation*}\\left(\\begin{array}{*{11}c}0.0\\\\1.0j\\\\1.0\\\\\\end{array}\\right)\\end{equation*}"
      ],
      "text/plain": [
       "Quantum object: dims = [[3], [1]], shape = (3, 1), type = ket\n",
       "Qobj data =\n",
       "[[0.+0.j]\n",
       " [0.+1.j]\n",
       " [1.+0.j]]"
      ]
     },
     "execution_count": 67,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "psi=(qutip.basis(3,2)+1j * qutip.basis(3,1))\n",
    "psi"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "id": "incredible-group",
   "metadata": {},
   "outputs": [],
   "source": [
    "### Normalizamos el estado que construimos"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "id": "acquired-james",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "Quantum object: dims = [[3], [1]], shape = (3, 1), type = ket\\begin{equation*}\\left(\\begin{array}{*{11}c}0.0\\\\0.707j\\\\0.707\\\\\\end{array}\\right)\\end{equation*}"
      ],
      "text/plain": [
       "Quantum object: dims = [[3], [1]], shape = (3, 1), type = ket\n",
       "Qobj data =\n",
       "[[0.        +0.j        ]\n",
       " [0.        +0.70710678j]\n",
       " [0.70710678+0.j        ]]"
      ]
     },
     "execution_count": 72,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "psi = psi/ psi.norm()\n",
    "psi"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "id": "prescribed-throat",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-0.5+0j)"
      ]
     },
     "execution_count": 78,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "###  Constrimos otro estado y calculamos el overlap\n",
    "\n",
    "chi = qutip.basis(3,0)-qutip.basis(3,2)\n",
    "chi = chi/chi.norm()\n",
    "\n",
    "psi.overlap(chi)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "id": "effective-florist",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "Quantum object: dims = [[1], [1]], shape = (1, 1), type = bra\\begin{equation*}\\left(\\begin{array}{*{11}c}-0.500\\\\\\end{array}\\right)\\end{equation*}"
      ],
      "text/plain": [
       "Quantum object: dims = [[1], [1]], shape = (1, 1), type = bra\n",
       "Qobj data =\n",
       "[[-0.5]]"
      ]
     },
     "execution_count": 80,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# o\n",
    "ov=chi.dag()*psi\n",
    "ov"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "round-utilization",
   "metadata": {},
   "source": [
    "notar que con overlap obtenemos un número complejo, y con el producto escalar un tensor 1-1. Para recuperar el número complejo, calculamos su traza:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "id": "italic-interference",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-0.5"
      ]
     },
     "execution_count": 82,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ov.tr()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cooperative-accordance",
   "metadata": {},
   "source": [
    "### Matriz que representa la componente z de un espín con s=2:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "spoken-glossary",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "Quantum object: dims = [[5], [5]], shape = (5, 5), type = oper, isherm = True\\begin{equation*}\\left(\\begin{array}{*{11}c}0.0 & 1.0 & 0.0 & 0.0 & 0.0\\\\1.0 & 0.0 & 1.225 & 0.0 & 0.0\\\\0.0 & 1.225 & 0.0 & 1.225 & 0.0\\\\0.0 & 0.0 & 1.225 & 0.0 & 1.0\\\\0.0 & 0.0 & 0.0 & 1.0 & 0.0\\\\\\end{array}\\right)\\end{equation*}"
      ],
      "text/plain": [
       "Quantum object: dims = [[5], [5]], shape = (5, 5), type = oper, isherm = True\n",
       "Qobj data =\n",
       "[[0.         1.         0.         0.         0.        ]\n",
       " [1.         0.         1.22474487 0.         0.        ]\n",
       " [0.         1.22474487 0.         1.22474487 0.        ]\n",
       " [0.         0.         1.22474487 0.         1.        ]\n",
       " [0.         0.         0.         1.         0.        ]]"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qutip.jmat(2)[0]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bright-trailer",
   "metadata": {},
   "source": [
    "### Operadores de subida\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "realistic-experience",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "Quantum object: dims = [[4], [4]], shape = (4, 4), type = oper, isherm = False\\begin{equation*}\\left(\\begin{array}{*{11}c}0.0 & 0.0 & 0.0 & 0.0\\\\1.0 & 0.0 & 0.0 & 0.0\\\\0.0 & 1.414 & 0.0 & 0.0\\\\0.0 & 0.0 & 1.732 & 0.0\\\\\\end{array}\\right)\\end{equation*}"
      ],
      "text/plain": [
       "Quantum object: dims = [[4], [4]], shape = (4, 4), type = oper, isherm = False\n",
       "Qobj data =\n",
       "[[0.         0.         0.         0.        ]\n",
       " [1.         0.         0.         0.        ]\n",
       " [0.         1.41421356 0.         0.        ]\n",
       " [0.         0.         1.73205081 0.        ]]"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qutip.create(4)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "handled-jurisdiction",
   "metadata": {},
   "source": [
    "### $A^\\dagger - A =0$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "id": "pretty-convergence",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "Quantum object: dims = [[4], [4]], shape = (4, 4), type = oper, isherm = True\\begin{equation*}\\left(\\begin{array}{*{11}c}0.0 & 0.0 & 0.0 & 0.0\\\\0.0 & 0.0 & 0.0 & 0.0\\\\0.0 & 0.0 & 0.0 & 0.0\\\\0.0 & 0.0 & 0.0 & 0.0\\\\\\end{array}\\right)\\end{equation*}"
      ],
      "text/plain": [
       "Quantum object: dims = [[4], [4]], shape = (4, 4), type = oper, isherm = True\n",
       "Qobj data =\n",
       "[[0. 0. 0. 0.]\n",
       " [0. 0. 0. 0.]\n",
       " [0. 0. 0. 0.]\n",
       " [0. 0. 0. 0.]]"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ad = qutip.create(4)\n",
    "\n",
    "ad.dag()  -qutip.destroy(4)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "positive-continent",
   "metadata": {},
   "source": [
    "### Conmutador de operadores de subida y bajada, proyectados a dimensión finita:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "id": "hairy-edmonton",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "Quantum object: dims = [[4], [4]], shape = (4, 4), type = oper, isherm = True\\begin{equation*}\\left(\\begin{array}{*{11}c}1.0 & 0.0 & 0.0 & 0.0\\\\0.0 & 1.0 & 0.0 & 0.0\\\\0.0 & 0.0 & 1.000 & 0.0\\\\0.0 & 0.0 & 0.0 & -3.000\\\\\\end{array}\\right)\\end{equation*}"
      ],
      "text/plain": [
       "Quantum object: dims = [[4], [4]], shape = (4, 4), type = oper, isherm = True\n",
       "Qobj data =\n",
       "[[ 1.  0.  0.  0.]\n",
       " [ 0.  1.  0.  0.]\n",
       " [ 0.  0.  1.  0.]\n",
       " [ 0.  0.  0. -3.]]"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qutip.commutator(qutip.destroy(4),qutip.create(4))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "daily-internship",
   "metadata": {},
   "source": [
    "### Ejemplo de construccion de un Hamiltoniano, un estado, y encontramos un espectro."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "id": "sophisticated-awareness",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "El espectro de H es  [-1.  -0.2  0.2  1. ]\n"
     ]
    }
   ],
   "source": [
    "## Parámetros del Hamiltoniano\n",
    "\n",
    "J=1.\n",
    "b=.1\n",
    "## Hamiltoniano de dos cuerpos\n",
    "\n",
    "H= b*(qutip.tensor(qutip.sigmaz(),qutip.identity(2))+\n",
    "      qutip.tensor(qutip.identity(2),qutip.sigmaz())\n",
    "     ) + J*(\n",
    "    qutip.tensor(qutip.sigmap(),qutip.sigmam())+\n",
    "   qutip.tensor(qutip.sigmam(),qutip.sigmap()))\n",
    "\n",
    "print(\"El espectro de H es \", H.eigenenergies())\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "psychological-fiber",
   "metadata": {},
   "source": [
    "### Construimos un estado inicial, y lo hacemos evolucionar con H. Finalmente graficamos la entropía en los subsistemas"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "id": "internal-imperial",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7fb0fd4dfb50>"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "rho0 = qutip.tensor(qutip.projection(2,1,1),.5*qutip.identity(2))\n",
    "\n",
    "# Evolución de rho0 con H\n",
    "ts=np.linspace(0,10,100)\n",
    "res=qutip.mesolve(H, rho0, ts)\n",
    "\n",
    "\n",
    "plt.title(\"Entropía de von Neumann para los estados reducidos como función de t\")\n",
    "plt.plot(ts,[qutip.entropy_vn(rho.ptrace([0]))  for rho in res.states], label=\"primer spin\")\n",
    "plt.plot(ts,[qutip.entropy_vn(rho.ptrace([1]))  for rho in res.states],label=\"segundo espin\")\n",
    "plt.plot(ts,[qutip.entropy_vn(rho.ptrace([0]))+qutip.entropy_vn(rho.ptrace([1]))  for rho in res.states],label=\"suma de entropías\")\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "parliamentary-parallel",
   "metadata": {},
   "source": [
    "### Evolución con decoherencia vía dínamica de Lindblad\n",
    "\n",
    "Aquí hacemos lo mismo que antes, pero introducimos un operador de colapso:\n",
    "\n",
    "$$\n",
    "{\\bf i}\\frac{d\\rho}{dt}=[{\\bf H},\\rho] \n",
    "+ {\\bf i}\\sum_i ({\\bf C}_i \\rho {\\bf C}_i^\\dagger-\\frac{\\{\\rho,{\\bf C}_i^\\dagger {\\bf C}_i  \\}}{2})\n",
    "$$\n",
    "En el ejemplo, ${\\bf C}_i={\\bf C}_1 = .2(\\sigma_z^{(1)}+\\sigma_z^{(2)})$\n",
    "\n",
    "Los detalles están en el help:\n",
    "\n",
    "[http://qutip.org/docs/3.1.0/guide/dynamics/dynamics-master.html](http://qutip.org/docs/3.1.0/guide/dynamics/dynamics-master.html)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "id": "sharing-hypothesis",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7fb0fed057f0>]"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "rho0 = qutip.tensor(qutip.projection(2,1,1),.5*qutip.identity(2))\n",
    "\n",
    "# Evolución de rho0 con H\n",
    "ts=np.linspace(0,10,100)\n",
    "collapseops = [.3*qutip.tensor(qutip.identity(2),qutip.sigmaz()),\n",
    "               .3*qutip.tensor(qutip.sigmaz(),qutip.identity(2))]\n",
    "\n",
    "res=qutip.mesolve(H, rho0, ts, collapseops)\n",
    "\n",
    "\n",
    "plt.title(\"Entropía de von neumann para los estados reducidos como función de t\")\n",
    "plt.plot(ts,[qutip.entropy_vn(rho.ptrace([0]))  for rho in res.states], label=\"primer spin\")\n",
    "plt.plot(ts,[qutip.entropy_vn(rho.ptrace([1]))  for rho in res.states],label=\"segundo espin\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "interesting-movie",
   "metadata": {},
   "source": [
    "### Hamiltoniano de más de dos partículas\n",
    "\n",
    "Acá va un ejemplo de como podés construir un Hamiltoniano con interacciones de pares\n",
    "$$\n",
    "{\\bf H}=J\\sum_i (\\sigma_{x, i}\\sigma_{x, i+1 mod N}+\\sigma_{y, i}\\sigma_{y, i+1 mod N})\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "id": "mathematical-soldier",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7fb0fbe88280>]"
      ]
     },
     "execution_count": 86,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "n = 5\n",
    "idop = qutip.identity(2)\n",
    "pairintxx = qutip.tensor(qutip.sigmax(),qutip.sigmax())\n",
    "pairintyy = qutip.tensor(qutip.sigmay(),qutip.sigmay())\n",
    "\n",
    "Vxx = (sum([\n",
    "    qutip.tensor([idop for i in range(j) ]+[pairintxx]+ [idop for i in range(n-j-2)])\n",
    "                 for j in range(n-2)]) + \n",
    "qutip.tensor([qutip.sigmax()]+[idop for i in range(n-2)]+[qutip.sigmax()]))\n",
    "\n",
    "\n",
    "Vyy = (sum([\n",
    "    qutip.tensor([idop for i in range(j) ]+[pairintyy]+ [idop for i in range(n-j-2)])\n",
    "                 for j in range(n-2)]) + \n",
    "qutip.tensor([qutip.sigmay()]+[idop for i in range(n-2)]+[qutip.sigmay()]))\n",
    "\n",
    "\n",
    "H = Vxx+Vyy\n",
    "\n",
    "plt.title(\"Espectro\")\n",
    "plt.plot(H.eigenenergies())"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "twenty-benchmark",
   "metadata": {},
   "source": [
    "### Aquí armamos el estado térmico asociado a este H"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "id": "bibliographic-guyana",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7fb0fc848430>]"
      ]
     },
     "execution_count": 97,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "T=3.\n",
    "rho=(-H/T).expm()\n",
    "rho = rho/rho.tr()\n",
    "\n",
    "\n",
    "plt.title(\"Distribución de probabilidad para los estados\")\n",
    "plt.plot(rho.eigenenergies())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "presidential-philip",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}