PKB-qubit.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "from  QCircuit import *\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import tqdm\n",
    "import sympy"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Fancy schematic\n",
    "\"Coherence properties of the 0-π qubit\",  Peter Groszkowski, A Di Paolo, A L Grimsmo, A Blais, D I Schuster, A A Houck and Jens Koch,  New Journal of Physics, Volume 20, April 2018"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 181.149x262.474 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import SchemDraw\n",
    "from SchemDraw import elements as e\n",
    "d= SchemDraw.Drawing()\n",
    "p1 = d.add(e.DOT, label='3', lblloc='bot')\n",
    "d.add(e.JJ, label='$E_{J2}$\\n$C_{J2}$', theta=45, lblloc='bot')\n",
    "p2 = d.add(e.DOT, label='4')\n",
    "d.add(e.INDUCTOR, label='$L2$', theta=135)\n",
    "p3 = d.add(e.DOT, label='1')\n",
    "d.add(e.JJ, label='$E_{J1}$\\n$C_{J1}$', theta=225)\n",
    "p4 = d.add(e.DOT, label='2')\n",
    "d.add(e.INDUCTOR, label='$L1$', endpts=[p4.here, p1.here], lblloc='bot')\n",
    "d.add(e.CAP, endpts=[p1.here, p3.here], label='$C_2$', lblloc='bot')\n",
    "C2b = d.add(e.LINE, d='down', xy=p4.here, l=d.unit*4/3)\n",
    "C2e = d.add(e.LINE, d='down', xy=p2.here, l=d.unit*4/3)\n",
    "d.add(e.CAP, d='right', label='$C_1$', endpts=[C2b.end, C2e.end])\n",
    "d.draw()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Ground node is between L2 and 1\n",
    "PKB = QCircuit()\n",
    "PKB.add_element(QJosephsonJunction('JJ1'), [1, 2])\n",
    "PKB.add_element(QCapacitance('CJ1'), [1, 2])\n",
    "PKB.add_element(QInductance('L1'), [2, 3])\n",
    "PKB.add_element(QJosephsonJunction('JJ2'), [3, 4])\n",
    "PKB.add_element(QCapacitance('CJ2'), [3, 4])\n",
    "PKB.add_element(QInductance('L2'), [4, 'GND'])\n",
    "PKB.add_element(QCapacitance('C1'), [2, 4])\n",
    "PKB.add_element(QCapacitance('C2'), [1, 3])\n",
    "\n",
    "φ = QVariable('φ')\n",
    "θ = QVariable('θ')\n",
    "ζ = QVariable('ζ')\n",
    "φx = QVariable('φ_x')\n",
    "\n",
    "φ.create_grid(160, 12)\n",
    "θ.create_grid(32, 1, centre=np.pi/2.)\n",
    "ζ.create_grid(32, 1)\n",
    "φx.set_parameter(0,0)\n",
    "\n",
    "PKB.add_variable(φ)\n",
    "PKB.add_variable(θ)\n",
    "PKB.add_variable(ζ)\n",
    "PKB.add_variable(φx)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Substitutions form paper:\n",
    "$$\n",
    "\\begin{pmatrix}\n",
    "    2\\varphi \\\\\n",
    "    2\\zeta \\\\\n",
    "    2\\theta \\\\\n",
    "    2\\Sigma\n",
    "\\end{pmatrix} \n",
    "=\n",
    "\\begin{pmatrix}\n",
    "    -1 & +1 & -1 & +1 \\\\\n",
    "    +1 & +1 & -1 & -1 \\\\\n",
    "    -1 & +1 & +1 & -1 \\\\\n",
    "    +1 & +1 & +1 & +1 \n",
    "\\end{pmatrix} \n",
    "\\begin{pmatrix}\n",
    "    \\varphi_1 \\\\\n",
    "    \\varphi_2 \\\\\n",
    "    \\varphi_3 \\\\\n",
    "    \\varphi_4 \\\\\n",
    "\\end{pmatrix}\n",
    "$$\n",
    "Adding extra \"ground\" node between $L_2$ and node 1; \n",
    "$$\\varphi_{1} = \\varphi_{\\mathrm{GND}} + \\varphi_x$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-1.,  1., -1.,  1.],\n",
       "       [ 1.,  1.,  1.,  1.],\n",
       "       [-1., -1.,  1.,  1.],\n",
       "       [ 1., -1., -1.,  1.]])"
      ]
     },
     "execution_count": 94,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "node_map = \\\n",
    "np.linalg.inv(0.5*np.asarray([[-1, +1, -1, +1],\n",
    "                              [+1, +1, -1, -1],\n",
    "                              [-1, +1, +1, -1],\n",
    "                              [+1, +1, +1, +1]]))\n",
    "node_map*2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "metadata": {},
   "outputs": [],
   "source": [
    "node_map = 0.5*np.asarray([[-1, +1, -1, +2], \n",
    "                           [-1, +1, -1,  0],\n",
    "                           [+1, +1, +1,  0],\n",
    "                           [-1, -1, +1,  0], \n",
    "                           [+1, -1, -1,  0]])\n",
    "PKB.map_nodes_linear(['GND', 1, 2, 3, 4], ['φ', 'ζ', 'θ', 'φ_x'], node_map)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle - \\frac{E_{C} E_{CJ} \\partial_{θ}^{2}}{2 \\left(\\frac{E_{C}}{4} + \\frac{E_{CJ}}{4}\\right)} - 2 E_{C} \\partial_{ζ}^{2} + E_{J} \\left(1 - \\cos{\\left(θ - φ \\right)}\\right) + E_{J} \\left(1 - \\cos{\\left(θ + φ \\right)}\\right) + E_{L} \\left(ζ + φ\\right)^{2} + E_{L} \\left(- ζ + φ - φ_{x}\\right)^{2} - 2 E_{CJ} \\partial_{φ}^{2}$"
      ],
      "text/plain": [
       "-E_C*E_{CJ}*\\partial_{θ}**2/(2*(E_C/4 + E_{CJ}/4)) - 2*E_C*\\partial_{ζ}**2 + E_J*(1 - cos(θ - φ)) + E_J*(1 - cos(θ + φ)) + E_L*(ζ + φ)**2 + E_L*(-ζ + φ - φ_x)**2 - 2*E_{CJ}*\\partial_{φ}**2"
      ]
     },
     "execution_count": 96,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "E_J, E_CJ, E_L, E_C = sympy.symbols('E_J, E_{CJ}, E_L, E_C')\n",
    "\n",
    "PKB.find_element('JJ1').set_critical_current(E_J)\n",
    "PKB.find_element('JJ2').set_critical_current(E_J)\n",
    "PKB.find_element('CJ1').set_capacitance(1/(8*E_CJ))\n",
    "PKB.find_element('CJ2').set_capacitance(1/(8*E_CJ))\n",
    "PKB.find_element('L1').set_inductance(1/(2*E_L))\n",
    "PKB.find_element('L2').set_inductance(1/(2*E_L))\n",
    "PKB.find_element('C1').set_capacitance(1/(8*E_C))\n",
    "PKB.find_element('C2').set_capacitance(1/(8*E_C))\n",
    "sympy.trigsimp(sympy.nsimplify(PKB.symbolic_hamiltonian()))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Parameter set 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "metadata": {},
   "outputs": [],
   "source": [
    "E_C = 0.02\n",
    "E_CJ = 20\n",
    "E_J = 10\n",
    "E_L = 0.008\n",
    "\n",
    "PKB.find_element('JJ1').set_critical_current(E_J)\n",
    "PKB.find_element('JJ2').set_critical_current(E_J)\n",
    "PKB.find_element('CJ1').set_capacitance(1/(8*E_CJ))\n",
    "PKB.find_element('CJ2').set_capacitance(1/(8*E_CJ))\n",
    "PKB.find_element('L1').set_inductance(1/(2*E_L))\n",
    "PKB.find_element('L2').set_inductance(1/(2*E_L))\n",
    "PKB.find_element('C1').set_capacitance(1/(8*E_C))\n",
    "PKB.find_element('C2').set_capacitance(1/(8*E_C))\n",
    "ζ.set_parameter(0,0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "<ipython-input-98-6a6b2132b12c>:3: TqdmDeprecationWarning: This function will be removed in tqdm==5.0.0\n",
      "Please use `tqdm.notebook.tqdm` instead of `tqdm.tqdm_notebook`\n",
      "  for flux_id_, flux in enumerate(tqdm.tqdm_notebook(fluxes)):\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "2148308fc155454f88b6bd5ef3e259c8",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "HBox(children=(FloatProgress(value=0.0, max=27.0), HTML(value='')))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    }
   ],
   "source": [
    "eigenenergies = []\n",
    "fluxes = np.linspace(0, 2*np.pi, 27)\n",
    "for flux_id_, flux in enumerate(tqdm.tqdm_notebook(fluxes)):\n",
    "    φx.set_parameter(flux, 0)\n",
    "    PKB.calculate_potentials()\n",
    "    energies, wavefunctions = PKB.diagonalize_phase(num_states=6, maxiter=10000)\n",
    "    eigenenergies.append(energies)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x1e6c2823760>"
      ]
     },
     "execution_count": 99,
     "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": [
    "plt.imshow(np.squeeze(PKB.phase_potential).T)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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G21WfLwyD0eiTq8/wxewyw3SJKhrW0h3Dqokn1ficp3x0zDOP3wDgex/7A75/7SWe7yVkFs55Od/iX6x8A7+YvgeAL40fI9tKWboZ7qXXGv8B5GtpqOdbCt76zJsA/KnHP80PrPw+z2XByyv3JS+NS/7lShizfaT3Tr6cXMJHD8gqM1wejOfFcqzrhZL0yi5ve/Q6AO+7+CrvGLzOwILh6Wp+gU+de5rf6T3Jlg/KtzLB5Q5XxIVbn+ET12z+4AHMqNJJmo36e7E8Gprr77WOPKgqfJVgtYG48b6b9njc87s5hM1ZCLGXY0syL4QQQgghhBBCCCHESSAPLiHENO2V95kVSl95zNV5nmzi/dMcvndNfjpUrgx5n5iEM5pzuF1H2iRSBXxKMj5aiKLL3STxrnNUmbGbhWW83+ZZbo5W+OQ+IYo3mxDFcL3ZEMVkbIyqjKvVJX4lD4/OV3Yu7RuiWLy2zNINo38r5uTaqOaGKLqen9zvfiGK23WS4Ji8Prq/+6KYClGctPv87yNcqJzeCrwrUb28t4QQR6Urwfzs5iLtfIz7hXTVxATzdYi7H/TwKwPK1RDinq9l5CuuCVFq+o8DQhSr3iSn0PCCY/dRGD0enq+PP3WD73jkFd63+nIrRHHAZ3ef4hO3ngPg869fIX99mf6N2RDFcN18BUaXKrLHdvj6x4KHyndceJk/MhWieI5Pbj3HJ649C8DVr1yifzVj6Y1QxuBWRW9rb4hi1TOKfgyv7E28jmESophtV2SbMRfk1gjbHoYQKpgk1L6bEMV2Tq52H7JoIYpH8dxqzqnHH3t/t2GsNJt/bMabHSZ5M8sScxY2oiFuUBPLdfUxhwhRTPISK1Myq3NsGVUW83wCW7bOx8fP8u/PXQb2hijejiGKg5uOXgyNnQ1RdLkxqnq8WoYyfmn8PF+4dGX/EMXXUgY3PNlm0dxf+2+2WTC4kZCvpnypF0J0/6/ifXzu0hOdIYrXmxDFcK/Zlp+EKO7GtssTRsUyn88fBeCNrVUeWXl2T4ji+M1lBm+ENhrc8PQ3KrLNmINsO58bopgcJkSxCQMuJ5sD1d97e7Oh5ieyAFoRYgGQgUsI0c3UwDQOsmqX6qqIu/+5SaJZ5ieZnxjAYlhjXrRyE4yx4YhkJ4ye3J2M7B6TzA9WMlZezxi9WieZX+HV9VX+/dJznUnmHzl0kvmU8XoY2H1m5TKfGnzDniTzK1NJ5vNjSzJv+ySZbyebndvurfdDuTMTkvDltv6vgZYQ4pAcIsk80BixzGxi3Dpqkvl0sisavQzfSyljf1EsBeNWV5L5Kgu7Dibp3iTz+WrcPGQ97Jq4fDGEuL/z/Jv80fUvzCSZv82VZJPch+tu5z1eGSeMq2Bo86lhhU0lmbeLI568dJtvPR/Cw75n9fdmksx/lYHLuZ2HhZnb20sMt9dId0MbJrlh3pFkkyTyByWZr2KXYZXDjUNd3TjF8qzpP8370A8cKv9UnMCTBKNM3bc4psOpzLXyr7V+G6e9X7mb+jXnzBgrZu2FU1ooQ3vVv/2yCuOoOkdTnsJohKVpywC8f5J5i4nPXZaS3ImpFm71WbreY3y1nWR+lTtLIffVrZkk8xeaJPPFIZLM1+GFl/nU6mU+OSfJ/JUmyXw+lWTeb2xO/e19LeHCcJXl6312Xwnlbp17jBdXH+tMMv/IkZLMhwDkYnmJq73LU0nmV3Y9FzY9vY3Q9rNJ5m1Oknk7RJJ5P5Nkfmon7HkLindjZBVCzEUGLiHE4Wg8feKozSz+t5wauO03PGwMLs6ahL6MDEuGk0T1icPqBPbh4JlCYmL09upXTNjqXCgjSRN6/R7LrTwPvp/gs2SyPbQP27jbOK4o5mXYKjquoIYEoK1Bf+LwaRImVHXS114atmVvl5mX2Ki1CjvOIW6V7YsyJPOdqXvwbKgnfh33W5ZU9eCoXgns2oK6o933lDv1+pRPPIQQp5d5zw+zqeeMrxwWrSDeXPNcm0zc833zGuEcZhY8VlseIMnuCLcddy+8k1H1U6po8KoSC95itfdF6XF5hZUTD2Bv4LOEchDOWb6WMLqaMHz5HAAfu/g8Hz33R6hWSqwX6186GDrSjXBO746xvhG8SADSkcfKCh+9PIq+ka8u8fr6k/zcuScA+Pvr3w2DCkviwsQ4wW0nZHdCe/RvwuVbnv5GvfthSTIsQx/T8gD2iaOKE/rw2pq+wZUeNypxowK3G9tsd9TsnBgqFyff7V3i5jG1QBK9f2f7oEXtV46jngeV0bZ41YbBxsgaN1yIroZ+nE+S0Dfe7XO0MW9zB+eavKguTUmyjF69S3UW8p/6ekHNuakdmK2oIC+wvJgsIFbVZOdAgDTkC/PRyOyzNIyJklb9ynosFMY+NhzjhyP8MHgr+rhBTrURd1Uc5yS3N1n5Wp/lQaxrv9dZLoA19YyNWJSTetZ1TVyoZ13XNHzWjNmqKtzzOA9lQVhArL0aIYy72hvytNu66/vo0kdznBYThbifKAeXEEIIIYQQQgghhFho5MElhLg72qtOe3zxDzrVaMcz+JbXUpO3Yt6OQ80Jc1aY28fPrnwmCc5sb46XarLNuY8rdL5r9RpCea1yDyyzLPHtPFfz8pPMq/8s9c6HXSuAoFVAIcTpYs8zqWp1FcHzt33E3J3nZouM3rqT0Li4k28ahrMucbgkCSFEsDfssfZW8ZPndB0umcUyBmnC6qCHjyHv1VIWdqfLXBOyHjyAC1wePFTcuMTGReNdMtcDOEvwvZSqF73LMjftAVxVuLxodmsLuRaLJlcWRQx5mlP3Ti+f2AfRCumv6nxb7ZD2ed5X89r/oLAq9UOHY84uo+HtVr5Sovf1fmODDqbGUS29zI5hZhXXHgf5ju9yqqzwxkRvbaqqyTlVRW/N2Rxtvoh5RLdLbHc3aLnRTNJZLoTfbXu8Nq++zThwps7t+54d+83q4a7yYkkXQpwoMnAJIR48HYM7uMc0BO38X3s+O2CQeKTtwe+hLA10hBAPI/s892HOY3NuuGJr4g/Ns3jKODaz2DGX9qS1nRcM9hgBEjOSdq6wdhl1pePCRlPq7EJJa1HEzRgf9pRZ57ScNTTMWyzZ7x7bx02Fiu6z0DIP9VkPjnltfcQFRJj5as32TR1x5LLv6qSOs1qpL3wFFEVj8D0O7vq+9ZsXYqGRgUsIcXbYb1ByF4PEB1KWEEKIvRxmkll7vnTZao4wWe682lE8aPYzGh3VE+c4kk5roi4W7TewaPUVQpw6lINLCCGEEEIIIYQQQiw08uASQgghhBBnj2PZHe+YPHbl+SuEEELcd+TBJYQQQgghhBBCCCEWGhm4hBBCCCGEEEIIIcRCIwOXEEIIIYQQQgghhFholINLCCGEOEsc4zbrkzKPaSe5u0U7awkhhBBCiAOQges0cz8mKbD/ROV+TExAkxMhhJjHvOf8UYxJgDlrvwBnmBm4Vjmz12k/k6uO575zzXmWJOBsUjc3U17lQ/9ReXxZTq7RVXZd/iHq5r0P5UPTR/nqiH3KvL5N/ZIQQggh9uNe5+MPcqyxSHW9j8jAdVzcyw9qZjJj9SSiNYGwjvL91ERg5kcZz2/OTRJwbvJ6zgTF1xOSOEFpyu8o+0h165qY3K1R7YyIUAhxBunqE1rP+9ln/R6j1GHKdw5LXHi+A6QplmWQpfi0fi+ZLreqoKwa45MVZTRG+cmz3blwfi8Lp/RSqkGK74VyqsThHVh8fLuywsYVbljgxkV4c5yHsmsjV11+rLuv65W45ppN/YpyUre8wOd5+KwooCzxZTU59rB9QaxHYzCb7ZP264vU3wghhBCnk9kxVxxr7VkAnMd+ff+8MVprrDY7B547j47jjan571EX3Q5YDJ07nkySufWczO2rqYXI2bHR/Hoc3Iad9/kAx1HKwSWEEEIIIYQQQgghFpoDPbjM7MeAPwe8F7gCfBn4ReBveu834zHPAi93FHHBe3/7OCp7KphjIZ4XHnK0IoOV1eoV+CQJq/Bp+AuEFfj2tWuLa1zlpiynwzggrOqnKWShDN/L8P2UKgvX8VmCN8OiRdXyMvwbFdg4rpbnBRTFZLUcJuEvTV2TvaEm3k/qVhT4ogwr73Vdy3Kvl9hh6ApTOSELsfQhRDdnUh+H8Mza+1HrnCSZen5alk57Xzk3FRoIzA/1q5+5aRKe7Us9AMqVPsVKSr6Wki+HMoqB4Vu9vRWQjjzpMDwr090Kl3us9PgknFNlRr6SMFoLr0cXjPF5T74en73LJZZ6fBFXC3d6ZBuO3m2jfyuU29/0ZNslLo99TCy/ymK9lhzFwCj6tUdXq36xbtmOJ9ssSLdD/5Fsj7DdMa7uo9oeYu22mdN+vvFYi15geRHrFfvPOrSSOZ7Gs1/7MYQ8nkl9CHFMSB9CdHPm9NHhgXXgaTNzcGt7hCfJ5HWSgEu60ytA8Gxv4wxcEubjAL0M38vC3ziXrlKHd4bFMYMVFTYuII5R3CjHj8dhDhzHHPUceCpKqu3h5aNnVd0mta1hjodWYzvI0jCG7IWxoO/HevbSPfW0Io6F8jJ42tfjqXEe5utVOalXTd2O8+wclZ+cU3vY1+Opqgqvuzy8urjHMdZhQhT/K4Jo/gbwVeA9wE8Cf9zMvsv7qRr8LeCFmfM3D12bB81RwgrnuQESjUhuEh7ShIpYK1dJ3USz4X71DyRNsTRtQkH8Up9qpU+5nJIvxx9m36iSSX1d4UlGnmQYfkBuVOLyEkrf+OWFkJKEfDWUMTrnGK078rXweTmAKvW4OEFJhpBtQn+jon8n1DnbKnDDchJyUgGJNUayqp9QDhLKOEGp0vDXlR43qicoBclOgdsehTbaHWHjHB8NXlYUe9ukJeqmDVsTkFo8VrtVRvH4yk8mIkcJfbx7o9jZ1YcQ987Z0cdh3N/nntfqOxK3Z0Bivd7k2d/L8GmCT5KJf3VFeM7Vz6iyCnWJgw3fSymXM/K1UMboQsruRcfoEowuhuat1nJcv8T7aEjaTUi2ErKNUI9sMyHd8bgCfKxasWyMzsPo0fCcvvjEbT70+Jf4gXOfAeB9/TtcSJa5Ve4A8MnROf7FnW/iN66+lRtfOw9A/42U/m1HulMbuKBKQ9kA+Rrk6xXlauwLlkrMPNUowW2Gfqt/M6F/I2HpZri//q2MbDMn2QkDMhsXoU28bw3ADO/cdBuW5STscZyHwWcyDp/nweCFWbOYYwkH9CHJ3gWW9gLP4Tg7+hDi+JE+hOhmsfVh04ap8Kc19ztgbGWtNA3AxJiVBQOP9TLo94Khh2DwqXoJPnHNPLE29lhep0SophbMfJLg+wnlcigzX0sZnUsYnTPyuPhXDsK4yeI0ORlCb8PTvxMX+u6UZHfGJJsj3M4wXGec4/M8zH8hpGEoJ44gPi/Al5N2yYKdwJKkcVpp0lHUaSSWB5RrffJzoa51PcfrrXqmYRyWhGqQbYZ69u+U8XVBsjPGRrE9aiOVc/g0jjmzBB+NZeENsLLCjeM5oxw3ymEUxld+nGP5eMroZe2QyP2YTSVhzDi0dJ96GAPXD3nvr7Vev2hmN4F/AHwQ+LXWZ1/y3n/iEGWeHHdhIZ5rHW4MWuHHZln4gZFljbdV/eVb5adX4OtBcT1ByVKqfo9yrQ9Avp4xupAyPG+Mz8WV7hVP1aP5MpOhke5AFicB2TakwypMUOItFQMLRq1L4fXwsZLlt9zhHZffBOCda29wLt3lTrEEwB9sPsoXrl/hzmurDF6Pk4sbKf07VbOablWcoAzCRfIVyNeMYjlcoxyEH6AbQ7od6t67kzK47enfCveXbeQkmyMs/vgtLyZW81b+l7ltWE9Q8vBwqK3h1B5hU1bi5PBW4tnV/sNztvQhxPFydvTRXk1rv93xjGn6DV81/Yz3PngL1TkRKo8vyuC1RRiwee+blcCGqsLqZ2R8PvnYf5j3ODPSLLwudx3ZtlEOJp5SuU/xvaTVfziyLSOLw9vepifd9VP9hxXgnVH1Q193a3mV3116nNUkLFRsVq9yKdniRvkYAJ/eeYbfvfU4t26tkt0O5/Q2INvwZLvT/YdrHKUMcFDFBZKxwxu4sZFthffSbci2PeluuP90WOJ2C2w08TJu2iYu1vjENW3aUJYhn8yqWQ8AABLoSURBVBdAUcZVSt98L1OrqfX3RvvlIfsF9R9CHBfShxDdLKY+ugxbs95X++S5amhvfJOmWL+HHwQDT7Xcp1ztN4t/+WpC0RoXQXQWGUMyCv19Mpp4NwFUPUe+4hidD9fYvWzsvqVk8PgW73gkNP3b197kQrrDrTgR/vzmo3zhjUe4/bUVAJZfy1h+PWXpRo/e7UG4zlbwRG88p0ZjyCeeVBXgR2Xw8Adcvw+9LNga+tFDq5dRLfUoV8Pcenw+Y/dSys5j4f523lKRPbHFOx4N9fz6tTeaev7h5hUAvnDtEW5fXWHptdBGS9dT+rd7ZNuhDdw4GpdS1ziylH1H2Zs4tAC4fBIRkG2VYRFyKzq17Iyw4TjcY23QixsSdZkwmzxmbdtJ48gy4zzUwYEGrhnx1Hwy/n3ioPNPFQcYt/ZdiW/vHFWHkEATTkhj4ErxWRqMV3UiXe+nEvo2A+C6jCzFL2WU0VsrXwtW19FFa1bgy7US61fNqfkwIb2TNEL1KVSZwxVQ1SvwS8boAgyvhEH96hMbfPcTL/MnL/w7AL6rf3NqBf631i7y/y59M7/pnmOrWg+FVAngKHvhwm5mBX68DuN1T3EuThwGJWbgR45iM4ZCJg7z4Irw2hUeV1RNaKQ3m7RN2yI/pw1tT9iJn/y//tf68e/3nTYTFnPTQjE79CTlTOlDiGPmzOljygBSdh9Hd9/rAYbDY6tSTd2bLcV/94tPksS/b93zWcqXeTtfvo9XD3hg/9ZfDM6cPoQ4RqQPIbp5oPo4unfyIcp0ez222t5YZq2ong5nlBhCCIQwwmwSDVUNMorVjHwtfD5acxTLFpxF6ioURjr0pLuh/KTnccXkWmXPGK8aw4uhHsNHK5af3OL9T36JH774aWAyl75ebgPwm2uP8kv99/Bxng3n5Ku4kZGMk1a6hgpXz1kJC5Xm/cSD3AxPy7CXJE2kl6/TDg0yqqWMYiW8Hq8lDC8Yw8vR0PTENt/59Cv8yKVQz+8evMHlZIVb5Q6/tX4RgBeW3sPH3FvZrUJol1UOqol3VjKOmwqlNAauYsn2pL1wY6PcqefUYJ7GUJgUYVMjK8uJw1VVhoM6sOh4Mr3oGOb35mqPrv0dlO42yfwH4t/fn3n/b5lZYWZ3zOwFM3v3XZYvxCIjfQjRjfQhRDfShxDdSB9CdCN9CMHhQhSnMLMngP8O+Ij3/t/Gt0fA3wP+NXANeCchJvi3zOzbvPezQqvL+nHgxwEGLB+99kdlNsSkFToSXu4TalIvx1dxX/S6nLIMYRGtci1e59Ahit5jZiQxvjVLjSo1vIGV4b1ixzpCFKOldk6IYjKO4R/Rur3l1vn16ut4fTdYaj/WEaK489oqgzfDOf1bzA1RdHl0Gy3A5UaxG35K5SCZE6IYYnyzzbDmnuwU2G7eJOC7mxBF8rzZLj60afSQm9ne9K4S2d3DCsVC60OI+8zC62OOa33nofO2pq436Igev5bWSUFbHsBpMkk6X7NPiCJZSjXoUa7HvAvnM4bnE4aXQlJ4gHzV43u+6T/cIUIU8yVjfN4YPhJOKh4f8dzj1/nOyyFf7XuW6xDFVSCEKH78+nO8fPUy6dXgMj+4ZvRu7w1RLJaiB/CahTxcq+HzalCF1b9WiGLvtjG44RncDs/6/u2cZGOMG07yZzVtU3v81rkx27RDFPMCP84n+S6KAvJ8eqOWo4QoHtMmJwuvDyHuI9KHEN3cV33cj827WuFm5qrJ/Lr+2KwZkFiXt4+3SaoB4nwyjo3c0JFuhbQH9QHJ+GghiknPBa+mOJ7wzrHjVvmN6ut4YzdEOn20I0Qxr0MUrxuDW57eZtlsluN2c2yYh/pCTO4+mdPWnkv1XytLfFFg1trkzSykp4j328uMsmdU0dNqJ1vh4zzLjVGox8c6QhSHV1dYeiOUMbjp6W9U80MUxxOvrnTX7xuimG7luOEkcT35zGZzMUSxi7khivMS8e+DHWUHOzNbBT4KPA58m/f+q/sc+xTwOeAF7/2fP6jsdbvov90+dOi6HAtKMn9iSeZpJZnnHpLMMy/JfM0xJZn/iP+F3/Hev/egIs6cPoQ4BA+NPh5QknnuS5L5oiPJfFxU2eRQSeb/6CGTzN+cSjLPIZLMx9yKc5PMO/o3YOlmuJf+reLYksz78cRI1uxq1N5F6YA+pHOg1epPHhp9CHEXSB9CdHOm9fEQJ5knJplnJsm8byeZr8pJ+OWCJZm3mSTzzCSZ526TzIf/NB9/pPonnfo4tAeXmQ0IOzC8FfjAfuKJlf6Kmf0m8L7DXuOBcxSLdJ1vxSz+tza0uKkJjj+EKGcxM3x70pMkuDQlSRN6af1DTma8z6JVs16RrhPktgw8SeIgTelHMaz0Mnw/bbY29VmCN2tyYVlehn+jYpL4Li+gKKYH/c5IWnHBpMnkAdOO024S+k5bbn1ZNpOJcOgRvoeZH/jcCcb9WGk4gDOpDyGOiTOhj/q50jzjauN6/LzTo6ts+ghfTBvqm80xakNLmmIuJkif97xvUydfTRNsOyPZCoOabKPP4HpKvpaSR0NSMcjwadacagWkI08aF0jS3QqXe6z0+LiQUmVGvpIw+nLMX/HFy/zL85d4Yf1bQ5WWSyz1+LhAYjvBYNa7bVy6FQd2mxXZdtnKOxHKr1dQiyVHMTCKfswpEfs7K5isBu6UZJtFs/KZbM8kZy3KuW2zN19jha8HVXGl1Lc2KfHt74VDeP/e4xbWbc6EPoS4T0gfQnSzsPqYzWnazK8Byn3GVPGU+Hd2Dm5xIxzv3MToBViSkLhk7xy9HflTTvfr5gxzCUkaN87pZSz3spgLK86lo7Gn3hzIiiosvNVRSqO4mFYUzZijWVBrO77M806qx5lxp2dvDkZxzDVjO7AsJb2WkvXCWHCpH+vZq8dXk3rWXmqWlzCeJLcPzidlMK7V9arbom7HeXaOyk/OKUuqGWOWn9oA7i6jq+BIY6xDGbjMLAP+KfBtwPd673/3kOUb7LeJoxCLj/QhRDfShxDdSB9CdCN9CNGN9CHEfA40cJmZA34e+BDwJw+7zaiZPQ28H/hn91TD08as9dCXwcjYrBYffW8nbw7Im9dNCGTLQtq1ReqU99OsRdRNrLxA8LZyDte4de61wHrv8VUVrMvt8jvKPlLdZr2umgOPEEo4fYG7O+8YkT6E6OZM6qPruTO7q2LruTj1UeVbK48xF1TrWe1nc0d10XLPt8Q1q3hpmpJlGUt1Pi+Y9rKF4PHU2tnXipJmV9pWHkSfJhP3915KNUjxvbirTuLwjmbV0pVjbFzhhsUkpH2ch7LbORTcJGelr+vV3hq8rl8dTliUwX0/rz22iskKYX3sYfuCtlv8Aa7ve7gP/c2Z1IcQx4T0IUQ3Z04fc+bXhzqt7rbNgBJf1K/npJHo8grbr+9vzcfDzo7Rwz6OV9zMHLieR9ceTFVrvHFgGp09bVCPTeoUEy0v85n7mbUdmFkz75+tZ5PjK46ffMfYqLM95tHloXVCEVaH8eD634A/DfwPwLaZfUfrs696779qZn+bkO3i44Qkdl8PfJiQselvHm+VTyn38qXNiHharPG9uy9977n7uX3ehbHpUHU7Bcao+4T0IUQ3D68+DmEIm14caT1LD3DNn2XPAK5OZt82as0uRLTq52dD/GpaoZIuSXCt/JOdbv6VbxZI2gOnzvIPUbd5yd8P5eI+VebxhRQeIw+vPoQ4GOlDiG6kjzYdBrK79aGYol6Uu9vzj2OsMa+M2fEknI66ngIOY+D6/vj3v4n/2vwU8JOEZHV/CfiPgTXgOvBrwE957z9/HBV9KLlfP7JDWsXFoZA+hOhG+jiIAwYthypidgBndvyxB0cxuh3LiHK2zLMx6JpB+hCiG+lDiG6kjwfFIo0/Fqmu95EDDVze+2cPcczPAj97HBUSYpGQPoToRvoQohvpQ4hupA8hupE+hOjm0LsoCiGEEGIBuB8rePL8FUIIIYQQpxzzp8SVzcyuAdsE98mHmcuoDU5bGzzjvX/kJCsgfTSctt/GSXDa2kD6OD2ctt/GSXDa2kD6OD2ctt/GSXDa2kD6OD2ctt/GSXDa2kD6OD2ctt/GSXDa2qBTH6fGwAVgZv/We//ek67HSaI2UBt0oXZRG4DaoAu1i9oA1AZdqF3UBqA26ELtojYAtUEXahe1ASxWGxxtqyYhhBBCCCGEEEIIIU4ZMnAJIYQQQgghhBBCiIXmtBm4fuakK3AKUBuoDbpQu6gNQG3QhdpFbQBqgy7ULmoDUBt0oXZRG4DaoAu1i9oAFqgNTlUOLiGEEEIIIYQQQgghjspp8+ASQgghhBBCCCGEEOJInLiBy8yeMrNfMLM7ZrZhZr9oZk+fdL3uB2b2QTPzc/7dnjnugpn9H2Z23cy2zewjZvbuk6r3vWBmT5rZ/2pmHzeznXi/z845bmBm/5OZvWZmu/H4PzbnOGdmHzazV8xsaGafMbMffRD3chJIH9JHPE76mIP0IX3E46SPOUgf0kc8TvqYg/QhfcTjpI85SB/SRzxuIfVxogYuM1sGfg14J/AfAf8h8Hbg35jZyknW7T7zV4DvbP373voDMzPgBeBPAH8Z+FEgI7TJkw++qvfM24A/A9wCfmOf4/5P4C8A/y3wg8BrwK+Y2TfPHPfTwE8Cfxf4fuATwD8xsx843mqfPNKH9NFC+phB+pA+WkgfM0gf0kcL6WMG6UP6aCF9zCB9SB8tFlMf3vsT+wf8VaAE3tZ67zmgAP7Lk6zbfbrfDwIe+N59jvmReMwfb713DrgJ/C8nfQ93cc+u9f//NN7bszPHfFN8/z9pvZcCnwdeaL13BRgBPzVz/q8CL530vd6HtpM+9h4jfXjpI96X9LH3GOnDSx/xvqSPvcdIH176iPclfew9Rvrw0ke8L+lj7zHSh18cfZx0iOIPA5/w3n+xfsN7/zLwMcIP6WHkh4Gr3vt/U7/hvb8D/DIL2Cbe++oQh/0wkAP/d+u8AvjHwPeZWT++/X1AD/i5mfN/Dni3mT137zU+VUgfe5E+kD4i0sdepA+kj4j0sRfpA+kjIn3sRfpA+ohIH3uRPlgcfZy0gesbgc/Oef9zwLsecF0eJD9vZqWZ3TCzfzQT07xfmzxtZqsPpooPlG8EXvbe78y8/zmCYN7WOm4EfHHOcXD2fjPSh/QB0kcX0of0AdJHF9KH9AHSRxfSh/QB0kcX0of0AQusj/RBX3CGi4TYz1luAhcecF0eBHeAvw28CGwA7wH+BvBxM3uP9/5NQpu8Mufcm/HvBWDr/lf1gbLf76D+vP5720e/x32OOytIH9IHSB9dSB/SB0gfXUgf0gdIH11IH9IHSB9dSB/SByywPk7awAUhtnMWe+C1eAB47z8NfLr11otm9uvA/0dIbPcThHt/aNokcth7fhjb5qG5X+mjE+mjm4fmfqWPTqSPbh6a+5U+OpE+unlo7lf66ET66OahuV/po5OF1cdJhyjeYr5V7wLzLYZnDu/9p4AvAO+Lb92ku03gbLbLQfd8s/X3QtzJYr/jzgrSh/QB0kcX0of0AdJHF9KH9AHSRxfSh/QB0kcX0of0AQusj5M2cH2OELc5y7uA33vAdTlJ2pbP/drky977s+b+COGen4vb0rZ5FzBmEtP7OaAPfN2c4+Ds/Wakj4D0IX3MQ/oISB/Sxzykj4D0IX3MQ/oISB/Sxzykj4D0saD6OGkD1wvAd5jZW+s3zOxZ4P3xszOPmb0XeAfw2/GtF4AnzOwDrWPWgR/i7LbJC0AG/On6DTNLgT8L/Gvv/Si+/a8IgvoPZs7/88Bn4w4fZwnpQ/oA6aML6UP6AOmjC+lD+gDpowvpQ/oA6aML6UP6gAXWh+3NB/YAL262AnwG2CXEt3rgp4E14PmzZg01s58HXgY+BdwmJLH7MLADfIv3/rqZOeA3gaeAv05wefww8DzwTd77r5xE3e8FM/ux+N8PAf8Z8J8D14Br3vsX4zH/mLDN6F8ntNFfAn4Q+K7oJlqX9T8Cf42Q/O9TBJH9ReBHvPe//EBu6AEhfUgf0kc30of0IX10I31IH9JHN9KH9CF9dCN9SB8Lrw/v/Yn+A54G/ilh14JN4J8Dz550ve7TvX4YeImwW0MOfAX4GeAtM8ddBH6WELO6A/wqQTwnfg93ed++499HW8csAX8HeB0YEizmH5xTVkJ42L5K2JL0JeDHTvoe72PbSR/Sh/TR3XbSh/QhfXS3nfQhfUgf3W0nfUgf0kd320kf0sfC6uNEPbiEEEIIIYQQQgghhLhXTjoHlxBCCCGEEEIIIYQQ94QMXEIIIYQQQgghhBBioZGBSwghhBBCCCGEEEIsNDJwCSGEEEIIIYQQQoiFRgYuIYQQQgghhBBCCLHQyMAlhBBCCCGEEEIIIRYaGbiEEEIIIYQQQgghxEIjA5cQQgghhBBCCCGEWGhk4BJCCCGEEEIIIYQQC83/D/PD5SlUyvVeAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 1296x288 with 6 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axes = plt.subplots(1,6,figsize=(18,4))\n",
    "for i in range(6):\n",
    "    axes[i].imshow(np.squeeze(np.abs(wavefunctions[..., i])).T)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\ProgramData\\Anaconda3\\envs\\py38\\lib\\site-packages\\numpy\\core\\_asarray.py:85: ComplexWarning: Casting complex values to real discards the imaginary part\n",
      "  return array(a, dtype, copy=False, order=order)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "([<matplotlib.axis.YTick at 0x1e6c2933d60>,\n",
       "  <matplotlib.axis.YTick at 0x1e6c28fdbb0>,\n",
       "  <matplotlib.axis.YTick at 0x1e6c294c490>,\n",
       "  <matplotlib.axis.YTick at 0x1e6c2982df0>,\n",
       "  <matplotlib.axis.YTick at 0x1e6c298c3d0>,\n",
       "  <matplotlib.axis.YTick at 0x1e6c298c970>,\n",
       "  <matplotlib.axis.YTick at 0x1e6c298cf10>,\n",
       "  <matplotlib.axis.YTick at 0x1e6c29924f0>,\n",
       "  <matplotlib.axis.YTick at 0x1e6c2982fd0>,\n",
       "  <matplotlib.axis.YTick at 0x1e6c29927c0>,\n",
       "  <matplotlib.axis.YTick at 0x1e6c2992d60>],\n",
       " <a list of 11 Text yticklabel objects>)"
      ]
     },
     "execution_count": 88,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 288x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(4,4))\n",
    "plt.plot(fluxes/(2*np.pi), (np.asarray(eigenenergies).T - np.min(eigenenergies, axis=1)).T)\n",
    "plt.yticks(np.linspace(0,2, 11))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "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": "3.8.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}