{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# QuTiP example: Energy-levels of a quantum systems as a function of a single parameter"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "J.R. Johansson and P.D. Nation\n",
    "\n",
    "For more information about QuTiP see [http://qutip.org](http://qutip.org)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from numpy import pi"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "from qutip import *"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Energy spectrum of three coupled qubits"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "def compute(w1list, w2, w3, g12, g13):\n",
    "\n",
    "    # Pre-compute operators for the hamiltonian\n",
    "    sz1 = tensor(sigmaz(), qeye(2), qeye(2))\n",
    "    sx1 = tensor(sigmax(), qeye(2), qeye(2))\n",
    "\n",
    "    sz2 = tensor(qeye(2), sigmaz(), qeye(2))\n",
    "    sx2 = tensor(qeye(2), sigmax(), qeye(2))\n",
    "\n",
    "    sz3 = tensor(qeye(2), qeye(2), sigmaz())\n",
    "    sx3 = tensor(qeye(2), qeye(2), sigmax())\n",
    "  \n",
    "    idx = 0\n",
    "    evals_mat = np.zeros((len(w1list),2*2*2))\n",
    "    for w1 in w1list:\n",
    "\n",
    "        # evaluate the Hamiltonian\n",
    "        H = w1 * sz1 + w2 * sz2 + w3 * sz3 + g12 * sx1 * sx2 + g13 * sx1 * sx3\n",
    "\n",
    "        # find the energy eigenvalues of the composite system\n",
    "        evals, ekets = H.eigenstates()\n",
    "\n",
    "        evals_mat[idx,:] = np.real(evals)\n",
    "\n",
    "        idx += 1\n",
    "\n",
    "    return evals_mat"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "w1  = 1.0 * 2 * pi   # atom 1 frequency: sweep this one\n",
    "w2  = 0.9 * 2 * pi   # atom 2 frequency\n",
    "w3  = 1.1 * 2 * pi   # atom 3 frequency\n",
    "g12 = 0.05 * 2 * pi   # atom1-atom2 coupling strength\n",
    "g13 = 0.05 * 2 * pi   # atom1-atom3 coupling strength\n",
    "\n",
    "w1list = np.linspace(0.75, 1.25, 50) * 2 * pi # atom 1 frequency range"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "evals_mat = compute(w1list, w2, w3, g12, g13)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
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dd84rbQwaVGytkjIDtSRJBXvvPXj4YXjiCXjqqZpNUdZZBw4+OAfonXbKazlL\nan0M1JIktbAlS+D55+Ghh+DBB+G11/L5oUNhn31ygN55Z1hzzWLrlFQeA7UkSS1g9mwYMyYH6Icf\nhunT82TBHXaACy+EvffOq2+41rPU9hioJUmqkIkTc4B+6KE8FnrRIujfH/baK/dE77GHOwxK7YGB\nWpKkFSQl+Mc/4K674L778m6EkFfjOPPMHKK33TZvrCKp/fCPtCRJzZBSHgN95525vfkmdOqUJxGe\ncEIeyrHOOkVXKamSDNSSJC2HCRNqQvQ//1kTos86Cw44wCXtpI7EQC1JUpneeCMP57jzzhyoI/J6\n0KefnkP0aqsVXaGkIhioJUlqxLvvwujROUS/+moO0d/8JlxxBXzve7D66kVXKKloZQXqiDgDuBGY\nA1wHfB34j5TSmArWJklSIT77DO6+G0aNylt9A2y/PVx2WQ7RQ4YUW5+k1qXcHupjUkqXRsQeQH/g\nCOAWwEAtSWoXFi2Cxx6DW26B+++HBQtggw3gvPPg8MNhrbWKrlBSa1VuoK5eZn4v4JaU0oQIl56X\nJLVtKcG4cTlE33YbfPIJDBwIxx8PRx4JI0a40YqkppUbqMdFxBhgOPC/IqIvUFW5siRJqpwpU/K4\n6FGj8kTDbt1g331ziP72t6Fr16IrlNSWlBuojwW+BkxMKX0eEQOAoytXliRJK9YXX8Af/wg33AB/\n/nPund5+e7jmGjjooLyDoSQtj3IDdQI2AvYGfgX0BnpUqihJklaU8ePh+uvhD3+AmTPzWOj//M/c\nG7322kVXJ6k9KDdQX0ke4rELOVDPAe4BtqxQXZIkLbfPPoNbb8290ePG5SEdBxwAxx4Lu+ySN2GR\npBWl3EC9dUpp84j4O0BKaWZEdKtgXZIkLZOqKnj66dwbfc89eYjHZpvlpe4OPxxWWaXoCiW1V+UG\n6kUR0Zk89IOIGISTEiVJrcAHH8BNN+Xe6IkTYaWV4Oijc2/05pu7Soekyis3UF8G3AesGhHnAQcC\nP6tYVZIkNWLJkrxm9DXXwEMP5d7pnXeGX/0qD+3o2bPoCiV1JGUF6pTS6IgYB+xKXpN6v5TSGxWt\nTJKkOqZOzUM6rrsOJk+G1VaDn/4090avs07R1UnqqBoN1BHRL6U0OyJWAT4Gbqt1bZWU0oxKFyhJ\n6tiWLIExY2DkSHjwwfx8t93gwgvz2tHdnNEjqWBN9VDfSl4qbxx5/HTUeXTBIUlSRUyblsdFX3st\nTJoEq67uD9+6AAAgAElEQVQKZ5+ddzG0N1pSa9JooE4p7V16HN4y5UiSOrKqKnj88Tw2+oEHcm/0\nrrvCBRfAd79rb7Sk1qmsMdQRsXk9p2cBk1JKi1dsSZKkjmb6dLjxxhyk33kHBg2CH/8490avu27R\n1UlS45ZlY5fNgX+Qh3v8G/AasFJEnJxSGlOh+iRJ7VRK8Le/wZVXwl13wYIFsMMO8F//BfvvD927\nF12hJJWn3EA9FTg2pTQBICI2Iu+YeA5wL2CgliSVZe7cvIvhlVfmbcH79oXjjoOTT4aNNy66Okla\nduUG6vWrwzRASun1iNgwpTQxXDFfklSGCRPgqqtg1CiYMyfvYnjNNXDYYdCnT9HVSdLyKzdQvx4R\nVwG3l54fUjrXHVhUkcokSW3ewoVw7705SD/zTJ5UeMghuTd6m23cxVBS+1BuoD4KOAU4s/T8f4Cz\nyWF65wrUJUlqw95/P/c+X3stfPQRDB8O55+ftwQfOLDo6iRpxWoyUEdEZ+C6lNLhwIX13DJ3hVcl\nSWpzUoInn4Tf/x7uvz8vgfed78App8Aee0CnTkVXKEmV0WSgTiktiYi1IqJbSmlhSxQlSWo7Zs/O\n46KvvBLeeAMGDMhL3p10Uu6ZlqT2rtwhHxOB/4mIB4B51SdTShdVpCpJUqs3YULujb7llrxyx5Zb\nwk03wcEHQ8+eRVcnSS2n3ED9Tql1AvpWrhxJUmu2aBH88Y85SD/9dF4r+vvfh1NPzYFakjqisgJ1\nSumXABHRK6X0eWVLkiS1Nh9+mCcYXn01TJ0Kw4bBf/83HHOMkwwlqdytx7cFrgf6AEMjYjPgxJTS\nKZUsTpJUnOqdDK+4Iu9kuGhRnlx49dWw117QuXPRFUpS61DukI9LgD2ABwBSSuMjYoeKVSVJKsz8\n+XDbbXlYx8svQ79+eUjHySfD+usXXZ0ktT7lBmpSSlPq7Iq4ZMWXI0kqyrvv5g1Yrr8eZszI24Bf\nfTUcfrg7GUpSY8oN1FMiYjsgRURX4AzgjcqVJUlqCVVV8Oc/52EdDz2U14rebz/44Q9hxx3dyVCS\nylFuoD4JuBRYA/gAGAOcWqmiJEmVNXs23HxzDtJvvgmrrgrnngsnnghrrll0dZLUtpS7ysd04PBl\n+cIRsSYwClgNSMDIlNKlde4JclDfC/gc+EFK6eVleR9JUvlefz2PjR41Kq8dvdVWeR3pgw7KS+BJ\nkpZduat8DAKOB4bVfk1K6ZhGXrYY+HFK6eWI6AuMi4jHU0qv17pnT2C9UtsauKr0KElaQRYvzsM5\nLr8cnngCunWDQw917WhJWlHKHfJxPzAW+DNlTkZMKU0DppWO50TEG+QhI7UD9XeBUSmlBPwtIlaO\niMGl10qSmmH6dLjuujzRcPLkPJTjN7+B446DQYOKrk6S2o9yA3WvlNJPl/dNImIY8HXg+TqX1gCm\n1Hr+funcUoE6Ik4ATgAYOnTo8pYhSR3CuHF5bPRtt8GCBbDzznDxxbDvvtCl7LWdJEnl6lTmfQ9F\nxF7L8wYR0Qe4BzgzpTR7eb5GSmlkSmlESmnEILtVJOlLFi6EW2+FbbeFESPyRizHHAOvvZaHeRxw\ngGFakiql3P+8ngGcGxELgYVAACml1K+xF5WW2LsHGJ1SureeWz4Aas8n/0rpnCSpDB98ANdcAyNH\nwkcfwXrrwSWXwFFHwcorF12dJHUM5a7y0XdZv3BpBY/rgTdSShc1cNsDwA8j4nbyZMRZjp+WpMal\nBGPH5mEd996b15L+znfy2tG77ZbXkpYktZxyV/kI8rJ5w1NKvy4tiTc4pfRCIy/7BnAE8GpEvFI6\ndy4wFCCldDXwMHnJvLfJy+YdvVzfhSR1APPmwejROUi/+ir07w8/+lHeEnzttYuuTpI6rnKHfFwJ\nVAG7AL8G5gK/BxpccCml9Cx5aEiDSqt7uEGMJDXi7bfhyivhhhtg1izYbLO8esehh0KvXkVXJ0kq\nN1BvnVLaPCL+DpBSmhkR3SpYlyR1aFVV8OijuTf6kUfyhMIDD8zDOrbbzi3BJak1KTdQL4qIzuQd\nD6s3eqmqWFWS1EHNmJF7oq+6CiZOhNVXh1/8Ak44AQYPLro6SVJ9yg3UlwH3AatGxHnAgcDPKlaV\nJHUwL7+ctwS/9Vb44gvYfns477y83F03/z1Qklq1clf5GB0R44BdyeOi90spvVHRyiSpnVuwIK8X\n/fvfw9/+lsdDH3lk3hJ8002Lrk6SVK5lWeb/LWB29WsiYmhKaXJFqpKkdmzyZLj66jyx8JNPYP31\nXTtaktqycpfNOw34OfARsITSxi6AfSiSVIaU4M9/zr3RDz6Yz+2zT+6N3nVX146WpLZsWXZK3CCl\n9Gkli5Gk9mbmTLj55twj/a9/wcCBcM45cNJJsNZaRVcnSVoRyg3UU4BZlSxEktqTcePy2tG33Qbz\n58M228CoUXDQQdCjR9HVSZJWpHID9UTgqYj4E7Cg+mQjW4pLUoczfz7ccUcO0i++mCcZHnFE3snw\na18rujpJUqWUG6gnl1q3UpMklbz5Zh7ScdNNeYjHV78Kl12WV+xYaaWiq5MkVVq5y+b9EiAieqWU\nPq9sSZLU+i1enCcXXnllnmzYpUteM/rkk2HHHd3JUJI6knJX+dgWuB7oAwyNiM2AE1NKp1SyOElq\nbaZMgeuvz0veffABrLkm/PrXcNxxeVdDSVLHU+6Qj0uAPYAHAFJK4yNih4pVJUmtyJIl8MgjcM01\n8PDDeQm83XfPS+B95zu5d1qS1HGV/b+BlNKUWPrfMJes+HIkqfX44IOa3ugpU2C11eA//iP3Rg8f\nXnR1kqTWouxl8yJiOyBFRFfyutRuPS6p3VmyBMaMyb3RDz2Un++2G1x8Mey7L3TtWnSFkqTWptxA\nfRJwKbAG8AEwBji1UkVJUkubOhVuuCH3Rk+aBKuuCj/5CRx/PKy9dtHVSZJas3JX+ZgOHF7hWiSp\nRS1eDI8+mod1PPhg7o3edVe44AL47nehm4uESpLKUO4qH5fVc3oW8FJK6f4VW5IkVdbbb+fe6Jtu\ngmnTcm/0WWfBCSfAuusWXZ0kqa0pd8hHD2BD4K7S8+8B7wKbRcTOKaUzK1GcJK0on38O99yTe6Of\nfho6dYK99oJjj80rdTg2WpK0vMoN1JsC30gpLQGIiKuAscD2wKsVqk2SmiUlePnlHKJvvRVmzYJ1\n1oHf/AaOOgqGDCm6QklSe1BuoO5P3tRlVul5b2CVlNKSiFhQkcokaTnNmAGjR+cgPX489OgBBx6Y\nl7vbYQd3MZQkrVjlBurzgVci4ikggB2A30REb+DPFapNksq2cGGeYHjLLfDAA/n5FlvkrcEPPRRW\nXrnoCiVJ7VW5q3xcHxEPA1uVTp2bUppaOv5JRSqTpCakBC+9lEP0bbfB9OkwaBCcfDIcfTRstlnR\nFUqSOoJGA3VEbJhS+mdEbF46NaX0uHpErJ5Sermy5UnSl02enId0jBoF//wndO+el7k78si8JbgT\nDCVJLampHuofA8cDF9ZzLQG7rPCKJKkec+bkVTpGjYKnnsq909/8Zl7u7qCDHNIhSSpOo4E6pXR8\n6XHnlilHkmosXAh//nNeoePee2H+/LxKxy9+Af/+7+5gKElqHZoa8nFOSun80vFBKaW7al37TUrp\n3EoXKKljWbQInngC7rgD7rsPPvss9z4feWRu227rKh2SpNalqSEf3yev8AHwv6jZ2AXg24CBWlKz\nLV6ch3HceWfuif70U+jbN4+LPuQQ2G23PE5akqTWqKlAHQ0c1/dcksq2ZAmMHZt7ou+5Bz75BHr3\nhn33zSF6jz3y+tGSJLV2TQXq1MBxfc8lqVGLF8Nf/wp33QV33w0ffgi9esHee8PBB+etwHv2LLpK\nSZKWTVOBerOImE3uje5ZOqb03L4jSU2aNQseewwefBAefjjvYtijRw7PhxwC3/lO7pmWJKmtamqV\nj84tVYik9uPdd3OAfuABePrp3DM9YEAOz/vsA9/+dh4jLUlSe1Du1uOS1KAlS+CFF3KAfvBBmDAh\nn99ww7xO9D775NU5OvtXdElSO2SglrRcPvwQnnwSxoyBP/0pTyrs3Bl22AGOPTaH6HXXLbpKSZIq\nz0AtqSwzZuThG088kdvrr+fzK68Me+5ZM5Sjf/9i65QkqaUZqCXVa84cePbZmgD997/n7b579cq9\n0D/4AeyyC3ztaw7lkCR1bAZqSUDekfDFF+GZZ3KAfuGFPJmwWzfYbjv45S9zgN5yy3xOkiRlBmqp\nA1qwAMaPz6H5hRfg+efhzTfztc6dc2g+55wcoLfbzrWhJUlqjIFaaueqquCtt3Jorg7Qr7wCixbl\n66uvDltvDUcdBVttlVu/fsXWLElSW2KgltqRzz7LkwUnTMjttdfgpZfy5ioAffrAiBHwox/lEL3V\nVrDGGhBRbN2SJLVlBmqpDZo1Kwfm2uF5wgSYOrXmnl69YKON4NBDa3qeN9zQCYSSJK1oBmqplZo1\nK+84WN0mTsxDNyZMgA8+qLmvVy/46lfhW9/KAXrjjXNbay3o1Km4+iVJ6igM1FJBFiyASZOWDsy1\nA/SMGUvf369f3ihll11yYK4Oz8OGGZwlSSqSgVpawRYsyLsITp2a27Rp9T9++unSr+vWLYfj4cPz\n8Izhw5du/fs71lmSpNbIQC01IiWYNy+H3+nTa1p9zz/+OIflukEZoEsXGDw4t3XWge23z8drrQVr\nr50D8+DB9jRLktQWGajVrqUEn3+ed/2bNSu3zz6reax9XPdxxowclhcsqP9rR8CAATBwYH5cd928\ng+DgwTBkyNKPAwcaliVJaq8M1CpcVRXMn5+D7+efL33cUJs3D+bOzUF57tzGj1Nq/P07dYKVV4aV\nVqp5XHvtvLlJdVgeOHDpNmBAvtcVMyRJkoG6g6mqyht6LFxY02o/r+/aggU1beHC8p7Pnw9ffFHT\n6j6vfW7hwmX/Pjp1ymsq9+kDffvWHA8ZUv/5vn2XDsy1H3v3dmyyJElafgbqMixYAOPGwZIlNW3x\n4qWfN3au+nz1cd3nda/VbosWNX5u0aL6W0PXqqpW/M8nArp3z61bt/zYsyf06FHzuNJKsNpqS5+r\n3Xr1WrbWvbshWJIktQ4VC9QRcQOwN/BxSmmTeq6vBPwBGFqq43cppRsrVU9zfPQRfOMblfnanTvn\nCWtduuTjrl1rnle3+s5Vtx498vXarfo1DbVu3XKrfVz3efVx1641Ybl2YK79vEsXw60kSeq4KtlD\nfRNwBTCqgeunAq+nlPaJiEHAvyJidEppOQYAVNaqq8Kjj+bAWx2Aq48bO1cdkOuG5urjTp0MopIk\nSW1dxQJ1SumZiBjW2C1A34gIoA8wA1hcqXqao0cP2GOPoquQJElSa1TkGOorgAeAqUBf4JCUUr0j\nfCPiBOAEgKFDh7ZYgZIktSYp5VZV1XRr6L7a56uP6ztX3/WmHquP67ve0HHtc43dX87zuq2x6029\ntiVa7c90Wc819/XlnGvs+Yo4XpZzjz0Gq6++bH9eWlKRgXoP4BVgF2Ad4PGIGJtSml33xpTSSGAk\nwIgRI1KLVilJWi4pLT1JuqHJ1/VNui53Infd46YmijfVqqoaP1d9XM5j3eNynpcTktUyqvcOiKhs\nq+89yj3X3NeXc66p57WHr9Z3T1PH5Z5r7cvUFhmojwb+b0opAW9HxLvAhsALBdYkSa1eSnm5ybpL\nUVa3ZVnisqklNBs611SrDrOtRX1zXOprnTo1fb76uFOnPB+mW7cvn+/cuSYEVJ+rbg09r76/9rWm\nWkOvqQ46jZ2vHYYaOlfOtbr31He9oePa5xq7v5zndVtj15t6rbSsigzUk4FdgbERsRqwATCxwHok\nqdkWL67ZVKh2mzOn6Q2L6tvYqKH121eUclb7qT7u1SsvgdnYKkL1rTZU97jcVYxqT+RuaHJ3OZPF\n3aVUUqVVctm824CdgIER8T7wc6ArQErpauDXwE0R8SoQwE9TStMrVY8kNWbxYpg9u2b7+dpb0Td0\nXF9obmir+oZUr8Pes+eX11tfeeV8vr6126tb7Wvdu9c81rfEZd3n3brZGydJK0IlV/k4tInrU4Hd\nK/X+kjquhQth+vTcPv208cfq49lfmr3xZdUhd6WVcuvbFwYP/vLOnPU9r261g3PPnvaeSlJ74E6J\nktqMzz+HadNymzq15rjuuRkzGv4affvCgAEwcGB+XH/9fNy//9Jhue5xv355eIIkSXUZqCW1Cinl\n3uJ3383tvfdqjidPzmG5vl7krl3zUkqDB8N668EOO+TjQYNqQvPAgbmtskoe7iBJ0opkoJbUYhYs\ngLfegrffXjowV7d585a+f8AAGD4cNtoIdtstB+XabciQHJIdNiFJKpKBWtIK98UX8OabMGECvP56\nbhMm5CBdeym1Pn1yYF57bdh113w8bFjNY79+RX0HkiSVz0AtabktWlQTlms/vv123oQCcu/xuuvC\nxhvDgQfm3ub118+BecAAV5mQJLV9BmpJZUkpB+UXXqhpf/97zTJxnTvnMcybbAKHHJKD88Yb5/Ds\nuGVJUntmoJZUr2nT4MUXa8Lziy/m9ZchL/m2xRZw6qkwYgT827/lMG1wliR1RAZqSVRVwfjx8MQT\n8Ne/5vA8ZUq+1rlzDswHHwxbbglbbZV7n7v4Xw9JkgADtdQhpQT//GcO0E88AU89VbN289prw/bb\n5+C85Zbw9a/nHmlJklQ/A7XUAaSUl6WrDtBPPgkffpivrbUW7Lcf7LIL7LxzXopOkiSVz0AttVPT\np8Ojj9aE6EmT8vnVV8/huboNH15snZIktXUGaqmdqB7G8eCDuf31r3lsdP/+uef5Jz/JAXrDDV2q\nTpKkFclALbVhixbBs8/WhOi3387nv/Y1+NnPYO+982oc7iQoSVLlGKilNuazz+CRR3KAfuSR/Lxb\nt9z7fNZZOUSvuWbRVUqS1HEYqKU24MMP4a674L77YOxYWLwYBg3Kkwn33Rd22y1v4y1JklqegVpq\npaZPh3vugTvugKefzuOhN9oIzj4b9tkHtt46rxEtSZKKZaCWWpGZM3Mv9B13wF/+AkuWwAYb5PHQ\n1dt5S5Kk1sVALRVs9mx44IEcoh97LE80HD4czjknh+hNN3VVDkmSWjMDtVSAL77IIfr22+Hhh2HB\ngjyR8PTTc4geMcIQLUlSW2GgllpISvDcc3Dzzbk3etYsGDwYTjwxh+httnF5O0mS2iIDtVRhkybB\nqFG5vf029OoF3/seHHUU7LSTEwslSWrrDNRSBcydC3ffnXujn3oqn9tpJ/jf/zuH6b59i6xOkiSt\nSAZqaQWpqoInn8wh+p574PPPYd114Ve/giOOgGHDiq5QkiRVgoFaaqb33oMbboCbboIpU6BfPzj8\n8DykY7vtnFwoSVJ7Z6CWlsPChXmVjmuvhccfz+d23x3OPx+++13o2bPY+iRJUssxUEvL4M034brr\ncm/0J5/kpe7+8z/hmGNg6NCiq5MkSUUwUEtNmD8/j4m+9lp45pm8Kse++8Jxx8Eee7hKhyRJHZ2B\nWmrAq6/mEH3LLfDZZ7DOOvDb38IPfgCrr150dZIkqbUwUEu1zJ8Pd94JV10Fzz8P3brlZe6OOy4v\ne+fGK5IkqS4DtQS89RZcfXUeGz1jBmy4IVx8cV7ubsCAoquTJEmtmYFaHdbixfDgg7k3+vHHoUsX\n2H9/OOUU2HFHl7uTJEnlMVCrw5k6NY+NvvZa+OCDvFLHr38Nxx4LgwcXXZ0kSWprDNTqEFKCJ56A\nK6+E++/PuxrusUd+vtdeuXdakiRpeRgj1K7NmpXHRV95ZV5DesAAOOssOPHEvGqHJElScxmo1S69\n/jpccQWMGgXz5sG22+bl7w48EHr0KLo6SZLUnhio1W4sXgwPPQSXX56Hd3TvDoceCj/8IWyxRdHV\nSZKk9spArTZv+vS8HfhVV8HkyXmS4W9/m9eOHjiw6OokSVJ7Z6BWm/Xyy7k3+rbbYMEC2GUXuOQS\n2GcfJxlKkqSWY+xQm7JoEdx9dw7Szz0HvXvDMcfAqafCxhsXXZ0kSeqIDNRqEz75BEaOzKt1TJ0K\n666be6OPOgpWXrno6iRJUkdmoFarNn48XHop3HprHtax++55Q5Zvfxs6dSq6OkmSJAO1WqElS+CB\nB3KQfvpp6NULjj4aTjsNNtqo6OokSZKWZqBWq/HZZ3D99Xn96Pfeg6FD4fzz82od/fsXXZ0kSVL9\nDNQq3D//mScZ3nxz3oTlm9+E3/0OvvtdV+uQJEmtn3FFhUgJHn88Tyx85BHo1g0OOwxOPx2+/vWi\nq5MkSSqfgVotav58GD06B+kJE2C11eCXv4STToJVVy26OkmSpGVnoFaL+PDDvOTdVVflnQ032wxu\nugm+//28RbgkSVJbZaBWRb3yClx8cd7NcPHivIvhj34EO+4IEUVXJ0mS1HwGaq1wS5bAQw/lIP30\n03k3wxNPzOOj11uv6OokSZJWrIptjRERN0TExxHxWiP37BQRr0TEhIh4ulK1qGXMnZuXvNtgA9hv\nP3j3XbjgAnj//byKh2FakiS1R5Xsob4JuAIYVd/FiFgZuBL4dkppckQ4Ja2Nev/9HKSvuSavJb3N\nNvDb38L++7vsnSRJav8qFndSSs9ExLBGbjkMuDelNLl0/8eVqkWV8fLLcNFFcMcdUFUF3/teHh+9\n7bZFVyZJktRyiuw/XB/oGhFPAX2BS1NKDfVmnwCcADB06NAWK1BfVlWVx0dfdFEeH923b94S/PTT\nYdiwoquTJElqeUUG6i7AFsCuQE/guYj4W0rpzbo3ppRGAiMBRowYkVq0SgF5B8NRo/JEw7fegjXX\nzLsZHnccrLRS0dVJkiQVp8hA/T7waUppHjAvIp4BNgO+FKhVnKlT4fe/h6uvhhkzYMst4fbb8/AO\nx0dLkiRVcJWPMtwPbB8RXSKiF7A18EaB9aiWV1+FH/wgD+P47W/zutFjx8Lzz8MhhximJUmSqlUs\nFkXEbcBOwMCIeB/4OdAVIKV0dUrpjYh4FPgHUAVcl1JqcIk9VV5K8PjjcOGFMGYM9OqV148+4wxY\nd92iq5MkSWqdKrnKx6Fl3HMBcEGlalB5Fi7MOxleeGHumV59dTjvPDjpJFhllaKrkyRJat38h/sO\nbObMPDb68sth2jTYZBO48UY49FDo3r3o6iRJktoGA3UHNHEiXHIJ3HBDXr1jt91ykN59d4goujpJ\nkqS2xUDdgTz/fF7q7t57oXPn3BN91lmw2WZFVyZJktR2GajbuaoqePDBHKSffRZWXhnOOSdvxjJk\nSNHVSZIktX0G6nZq/vy8EctFF8Gbb+bl7y69FI45Bvr0Kbo6SZKk9sNA3c588glceSVccQVMnw5b\nbOFGLJIkSZVkxGon3norbwt+443wxRew995w9tmwww5ONJQkSaokA3Ub99e/5vHRf/wjdO0KRxyR\nJxputFHRlUmSJHUMBuo2aMkSeOABuOACeO456N8fzj0XfvjDvCmLJEmSWo6Bug2pnmh44YV5iMew\nYXDZZXmiYe/eRVcnSZLUMRmo24BPP80TDS+/PE86HDEC7rgDDjjAiYaSJElFM461YhMn5omGN9wA\nn38Oe+0FP/kJ7LijEw0lSZJaCwN1K/Tii3l89D335B0NDz88r9ix8cZFVyZJkqS6DNStRErwyCNw\n/vnw9NOw0kq5N/q002CNNYquTpIkSQ0xUBds4UK49da89N2ECfCVr+RJh8cdB/36FV2dJEmSmmKg\nLsjs2TByJFxyCXzwAfzbv+UVPL7//byetCRJktoGA3ULmzoVLr0Urr46h+pddoHrr4fdd3eioSRJ\nUltkoG4hEybkYR2jR+eNWQ46KI+R3mKLoiuTJElScxioKyglGDs2TzT805+gZ0848cS8Nfjw4UVX\nJ0mSpBXBQF0BS5bAH/+Yl757/nkYOBB++Us45ZR8LEmSpPbDQL0CVW8N/rvfwdtvw9pr5x0OjzoK\nevUqujpJkiRVgoF6BZgxA666Ci67DD7+OG8NftddsP/+eWMWSZIktV8G6maYPDlvDX7ttTBvHuy5\nJ5xzjluDS5IkdSQG6uXwj3/k8dG33ZaD86GH5q3BN9206MokSZLU0gzUZUoJnnoqr9jx6KPQuzec\nfjqceSYMHVp0dZIkSSqKgboM77yTdzB86SVYdVU47zw4+WTo37/oyiRJklQ0A3UZhgyBbt3gmmvg\nyCOhR4+iK5IkSVJrYaAuQ8+e8D//U3QVkiRJao06FV2AJEmS1JYZqCVJkqRmMFBLkiRJzWCgliRJ\nkprBQC1JkiQ1g4FakiRJagYDtSRJktQMBmpJkiSpGQzUkiRJUjMYqCVJkqRmMFBLkiRJzWCgliRJ\nkprBQC1JkiQ1Q6SUiq5hmUTEJ8CkouvoQAYC04suQhXlZ9wx+Dl3DH7O7Z+fcctaK6U0qKmb2lyg\nVsuKiJdSSiOKrkOV42fcMfg5dwx+zu2fn3Hr5JAPSZIkqRkM1JIkSVIzGKjVlJFFF6CK8zPuGPyc\nOwY/5/bPz7gVcgy1JEmS1Az2UEuSJEnNYKAWEfHtiPhXRLwdEf9Rz/WVIuLBiBgfERMi4ugi6lTz\nlPE594+I+yLiHxHxQkRsUkSdWn4RcUNEfBwRrzVwPSListLvwD8iYvOWrlHNV8bnvGFEPBcRCyLi\n7JauTytGGZ/z4aU/x69GxF8jYrOWrlE1DNQdXER0Bn4P7AlsBBwaERvVue1U4PWU0mbATsCFEdGt\nRQtVs5T5OZ8LvJJS2hQ4Eri0ZavUCnAT8O1Gru8JrFdqJwBXtUBNWvFuovHPeQZwOvC7FqlG/6+9\n+w+yqqzjOP7++KMBAWWyxjIzijKkEFBELUzRrOnHCAKOqGlYOsMUFlAOzNTUNOgMTc04NgzRhLj9\noDRLHWJgHCd0oGxDZRdWEI0BQsIy+2GigC777Y/nWTnc7u5euLv3ut7Pa2Zn73POc5/zPefsvXx5\n7uJypTIAAAcXSURBVPfc01ea6P487wAuiohRwAJcW11XTqhtPLAtIrZHxKvA3cCkkj4BDJEkYDDp\nzbq9tmFalSo5zyOBNQARsRUYJumU2oZp1YiItaTXZ1cmAT+NpBkYKumdtYnOektP5zkino+Ix4DX\naheV9bYKzvOjEfHv3GwGTqtJYFaWE2p7F/Bsob07LytaBJwJ7AHagK9GREdtwrNeUsl53ghMAZA0\nHngPfoN+s6nk78DM+p8vAqvrHUQjc0Jtlfgk0AqcCowBFkk6sb4hWR9YSJqxbAVuBlqAg/UNyczM\nuiNpIimhnlfvWBrZcfUOwOrur8C7C+3T8rKiG4CFkb5jcZukHcAIYH1tQrRe0ON5joj/ks41ubxn\nB7C9VgFaTVTyejezfkLSWcBS4FMR8c96x9PIPENtjwEfkPTefKHhdGBFSZ9dwKUAuab2gzjR6m96\nPM+ShhYuNr0RWJuTbHvzWAFcn7/t43zgxYh4rt5BmdmRk3Q6cB9wXUQ8U+94Gp1nqBtcRLRLmgU8\nCBwLLIuIzZJm5vVLSFcPN0lqAwTMi4gX6ha0HbEKz/OZwE8kBbCZ9BGi9SOSfkn6Jp63SdoNfBs4\nHl4/x6uATwPbgFfIn0hY/9LTeZb0DuBx4ESgQ9JsYKT/g9y/VPB6/hZwMrA4fahIe0SMq0+05jsl\nmpmZmZlVwSUfZmZmZmZVcEJtZmZmZlYFJ9RmZmZmZlVwQm1mZmZmVgUn1GZmZmZmVXBCbWYNQdJB\nSa2Fn/n1julISbpY0sr8+PLOfZA0WdLIQr8Zkk4ttJcW1/dRbF+R9JSk5RX2Hybpmj6K5WOSNkhq\nlzStL7ZhZlbk76E2s0axLyLG9OaAko6LiPbeHLNSEbGCQzfnmQysBLbk9gzgSWBP7ntjDUL6EvDx\niNhdYf9hwDXAL/ogll2kY/D1PhjbzOz/eIbazBqapJ2SvpNnNNskjcjLB0laJmm9pBZJk/LyGZJW\nSFoD/E7SMZIWS9oq6SFJqyRNk3SJpAcK27lM0v1ltr9Q0hZJmyR9Py9rkrRE0uOSnpH02TLPmyFp\nkaSPAJcD38sz7/OAccDy3B4o6RFJ4/Lz9kq6TdJGSc357qdIGp7bbZJulbS3i+M1V9KT+Wd2XrYE\neB+wWtKckv7DJK3Lx3dDjhdgIXBhjnGOpAGS7srbb5E0sbCfD+Rju1PSrBxDS473raUxRsTOiNgE\ndHR95s3Meo8TajNrFANLSj6uKqx7ISLOBn7IoVnNbwBrImI8MJGUsA7K684GpkXERcAU0mzrSOA6\n4ILc52FghKS35/YNwLJiQJJOBq4APhQRZwG3FlYPA8YDnwGWSBpQbqci4lHSTPUtETEmIr5Lukve\ntbm9r+Qpg4DmiBgNrAVuysvvAO6IiFFA2VlmSefk/TgPOB+4SdLYiJhJmg2fGBG3lzzteeCyfHyv\nAn6Ql88H1uUYbwe+nHYnRgFXk+7a2bnPHyYd53OB24BXImIs8Efg+nKxmpnVkhNqM2sU+3Ly1vlz\nT2Hdffn3E6REFuATwHxJrcAjwADg9LzuoYj4V348Abg3Ijoi4m+kRJpIt6H9GfA5SUNJifbqkphe\nBPYDd0qaQrodeKdf5TH/DGwHRlSx70WvkspD4PD9vQC4Nz/uqgxjAnB/RLwcEXtJx+3CHrZ3PPBj\nSW15/K5quScAPweIiK3AX4Az8rqHI+KliPgH6Zj9Ni9vK8RvZlY3rqE2M4MD+fdBDr0vCpgaEU8X\nO0o6D3i5wnHvIiV/+0lJ92H11hHRLmk8cCkwDZgFXNK5umSs0vbRei0n+3D4/vaVOcDfgdGkSZz9\nRzHGgcLjjkK7A/87ZmZvAJ6hNjMr70HgZkkCkDS2i35/AKbmWupTgIs7V0TEHlIpxDdJyfVhJA0G\nToqIVaTEc3Rh9ZV5zOGk+uSnS59f8BIwpJt2JZqBqfnx9C76rAMmSzohl79ckZd15yTguYjoIJXE\nHNtFjOuAawEknUH6NKC7fTYze8NwQm1mjaK0hnphD/0XkMoVNknanNvl/IZUc7yFVLKwgVSW0Gk5\n8GxEPFXmuUOAlZI2Ab8H5hbW7QLWk8pEZkZEdzO7dwO35Av1hgNNpLrrVkkDu9/N180G5uZY3l+y\nDwBExIY89nrgT8DSiGjpYdzFwOclbSSVrXTO7m8CDuaLI+fkfsfk0pB7gBkRcaDsiD2QdK6k3cCV\nwI/y+TMz6zM69MmfmZkdDUmDI2JvvshwPfDRXE+NpEVAS0TceQTjNQErI+LXfRJw+W2eQKozD0nT\ngasjYlKttm9m1p+59szMrHor84WHbwEWFJLpJ0gzsl+rZ3AVOgdYlEtc/gN8oc7xmJn1G56hNjMz\nMzOrgmuozczMzMyq4ITazMzMzKwKTqjNzMzMzKrghNrMzMzMrApOqM3MzMzMquCE2szMzMysCv8D\nXFfMCickHLYAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10bd25b00>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(12,6))\n",
    "\n",
    "for n in [1,2,3]:\n",
    "    ax.plot(w1list / (2*pi), (evals_mat[:,n]-evals_mat[:,0]) / (2*pi), 'b')\n",
    "\n",
    "ax.set_xlabel('Energy splitting of atom 1')\n",
    "ax.set_ylabel('Eigenenergies')\n",
    "ax.set_title('Energy spectrum of three coupled qubits');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Versions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table><tr><th>Software</th><th>Version</th></tr><tr><td>QuTiP</td><td>4.2.0</td></tr><tr><td>Numpy</td><td>1.13.1</td></tr><tr><td>SciPy</td><td>0.19.1</td></tr><tr><td>matplotlib</td><td>2.0.2</td></tr><tr><td>Cython</td><td>0.25.2</td></tr><tr><td>Number of CPUs</td><td>2</td></tr><tr><td>BLAS Info</td><td>INTEL MKL</td></tr><tr><td>IPython</td><td>6.1.0</td></tr><tr><td>Python</td><td>3.6.1 |Anaconda custom (x86_64)| (default, May 11 2017, 13:04:09) \n",
       "[GCC 4.2.1 Compatible Apple LLVM 6.0 (clang-600.0.57)]</td></tr><tr><td>OS</td><td>posix [darwin]</td></tr><tr><td colspan='2'>Wed Jul 19 22:16:09 2017 MDT</td></tr></table>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from qutip.ipynbtools import version_table\n",
    "\n",
    "version_table()"
   ]
  }
 ],
 "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": "3.6.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}