Wavefunction-Phase-Qubit-Current-Biased.ipynb

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  {
   "cells": [
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Wavefunctions for a current-biased Josephson-junction phase qubit"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Robert Johansson (robert@riken.jp)"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%pylab inline"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Populating the interactive namespace from numpy and matplotlib\n"
       ]
      }
     ],
     "prompt_number": 1
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from scipy import *\n",
      "from scipy import optimize"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 2
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from wavefunction import *\n",
      "from wavefunction.wavefunction1d import *"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 3
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Problem Parameters"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "h = 6.626e-34\n",
      "h_ = h/(2*pi)\n",
      "e = 1.602e-19\n",
      "Phi0 = h / (2 * e)\n",
      "cf = 1\n",
      "\n",
      "ceta = 0.05\n",
      "J = 0.9725\n",
      "Ic = 13.3e-6\n",
      "Ib = J * Ic\n",
      "Cj = 4.3e-12\n",
      "\n",
      "mm = Cj * (1 + ceta) * (Phi0/(2*pi))**2 * cf\n",
      "Ej = Phi0/(2*pi) * Ic / cf\n",
      "\n",
      "args = {'Ej': Ej, 'Ic': Ic, 'Ib': Ib}\n",
      "\n",
      "k = -h_ ** 2 / (2 * mm)\n",
      "\n",
      "x_min = -pi\n",
      "x_max =  pi\n",
      "N = 750 "
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 4
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Potential"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def U_current_biased(x, args):\n",
      "    \"\"\"\n",
      "    Potential for a current-biased phase qubit potential\n",
      "    (the washboard potential)\n",
      "    \"\"\"\n",
      "    Ej = args['Ej']\n",
      "    Ic = args['Ic']\n",
      "    Ib = args['Ib']\n",
      "\n",
      "    u = - Ej * (cos(x) + Ib / Ic * x)\n",
      "\n",
      "    return u"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 5
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "x = linspace(x_min, x_max, N)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 6
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "U = U_current_biased(x, args)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 7
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# analytical formula for minima points of potential\n",
      "x_opt_min = arcsin(Ib/Ic)\n",
      "print(\"x_opt_min = %f \" % x_opt_min)\n",
      "\n",
      "x_opt_max = -math.asin(Ib/Ic) + pi\n",
      "print(\"x_opt_max = %f\" % x_opt_max)\n",
      "\n",
      "U_min = U_current_biased(x_opt_min, args)\n",
      "U_max = U_current_biased(x_opt_max, args)\n",
      "dU = U_max - U_min\n",
      "dx = x_opt_max - x_opt_min\n",
      "\n",
      "print(\"dU = %f\" % dU)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "x_opt_min = 1.335735 \n",
        "x_opt_max = 1.805858\n",
        "dU = 0.000000\n"
       ]
      }
     ],
     "prompt_number": 11
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Plot potential"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "fig, ax = subplots()\n",
      "\n",
      "ax.plot(x, U/Ej)\n",
      "ax.plot(x_opt_min, U_current_biased(x_opt_min, args) / Ej, 'o')\n",
      "\n",
      "ax.set_ylim(-1.55, -1.5)\n",
      "ax.set_xlim(0.8,2.2)\n",
      "ax.set_xlabel(r'$x$', fontsize=18)\n",
      "ax.set_ylabel(r'$U(x)/E_J$', fontsize=18);"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
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Qgog0jkZZRfu+++5rjNOKDa6/Hlq2VJeciDSORt/UzpuoO+7Udu6EIUNg40bo1s3uNCLi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\nIiJiGxUhERGxjYqQiIjYRkVIRERs8/8BX2rRJqOMY08AAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x38293d0>"
       ]
      }
     ],
     "prompt_number": 12
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Calculate the eigenfunctions"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "u = assemble_u_potential(N, U_current_biased, x, args)\n",
      "\n",
      "K = assemble_K(N, k, x_min, x_max)\n",
      "\n",
      "V = assemble_V(N, u, x_min, x_max)\n",
      "\n",
      "H = K + V\n",
      "\n",
      "evals, evecs = solve_eigenproblem(H)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 13
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Identify bound states"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "nbound = 0\n",
      "boundidx = []\n",
      "\n",
      "for i in range(0,N):\n",
      "    if evals[i] > U_min - 0.5 * dU and evals[i] < U_max + 0.5 * dU:\n",
      "        if inner(evecs[i] * (x_opt_min-dx < x) * (x < x_opt_max), evecs[i]) > 0.95:\n",
      "            nbound = nbound + 1\n",
      "            boundidx.append(i)\n",
      "\n",
      "print \"Found bound states: \", boundidx"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Found bound states:  [91, 92, 94, 96, 97, 99, 101, 102, 104]\n"
       ]
      }
     ],
     "prompt_number": 14
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Plot bounded eigenstates"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "NN = len(boundidx)\n",
      "\n",
      "fig, axes = subplots(NN, 1, figsize=(10, NN * 1), sharex=True, sharey=True)\n",
      "\n",
      "for n, m in enumerate(boundidx):\n",
      "    axes[n].plot(x, real(evecs[m]))\n",
      "\n",
      "axes[n].set_xlim(0.5, 2.5)\n",
      "axes[n].set_xlabel(r'$x$', fontsize=18)\n",
      "\n",
      "fig.tight_layout();"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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MjPR0SRERERERn/P5oBCn00m/fv3Yv38/kydP5plnnqkZxCV6KIuIiIiIeCooB4WEhoay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\n/D/1YEnmYraj+gAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x390d7d0>"
       ]
      }
     ],
     "prompt_number": 15
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Plot bounded eigenstates together with the potential"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "fig, ax = subplots(figsize=(12,8))\n",
      "\n",
      "ax.plot(x, U/Ej, 'k')\n",
      "ax.plot(x_opt_min, U_current_biased(x_opt_min, args) / Ej, '.')\n",
      "\n",
      "for n, m in enumerate(boundidx):\n",
      "    Y0 = evals[m]/Ej * ones(shape(x))\n",
      "    Y = 0.001 * evecs[m] + Y0\n",
      "\n",
      "    ax.plot(x, Y0.real, 'k--')\n",
      "    ax.plot(x, Y.real)\n",
      "    \n",
      "ax.set_ylim(-1.535, -1.52)\n",
      "ax.set_xlim(0.8,2.2)\n",
      "ax.set_xlabel(r'$x$', fontsize=18)\n",
      "ax.set_ylabel(r'$U(x)$', fontsize=18);"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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mZM5W0AVFZBz69euHDz74QOkyiIjuSgiBZcuW4ZtvvsGRI0fQ0Vi/lboZODk5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\nC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7K6UtwoviHOZZ8Th68eFv97/n/FcNVwgVAIhENgPASmQuAlCDeVm/Bc5ylsV9sK87fM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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x4310510>"
       ]
      }
     ],
     "prompt_number": 16
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Evaluate transition matrix elements"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "inner_prod = zeros((len(boundidx), len(boundidx))).astype(np.complex)\n",
      "expect_pos = zeros((len(boundidx), len(boundidx))).astype(np.complex)\n",
      "expect_kin = zeros((len(boundidx), len(boundidx))).astype(np.complex)\n",
      "\n",
      "for i, l in enumerate(boundidx):\n",
      "    for j, k in enumerate(boundidx):\n",
      "    \n",
      "        psi_l = wavefunction_normalize(x, evecs[l])\n",
      "        psi_k = wavefunction_normalize(x, evecs[k])\n",
      "    \n",
      "        inner_prod[i,j] = inner_product(x, psi_l, psi_k)                 # <psi_l|psi_k>\n",
      "        expect_pos[i,j] = inner_product(x, psi_l, x * psi_k)             # <psi_l|x|psi_k>\n",
      "        expect_kin[i,j] = inner_product(x, psi_l, derivative(x, psi_k))  # <psi_l|p|psi_k>"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 17
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print(\"Bound energy-levels:\")\n",
      "\n",
      "(evals[boundidx] - evals[boundidx[0]]).real / Ej"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Bound energy-levels:\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 18,
       "text": [
        "array([ 0.        ,  0.00107872,  0.00213317,  0.003161  ,  0.00415908,\n",
        "        0.005123  ,  0.00604603,  0.00691584,  0.00770281])"
       ]
      }
     ],
     "prompt_number": 18
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print(\"Harmonicity:\")\n",
      "\n",
      "((evals[boundidx] - evals[boundidx[0]]) / (evals[boundidx[1]]-evals[boundidx[0]])).real"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Harmonicity:\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 19,
       "text": [
        "array([ 0.        ,  1.        ,  1.97749688,  2.9303132 ,  3.85555056,\n",
        "        4.74913082,  5.60479901,  6.41112924,  7.14067069])"
       ]
      }
     ],
     "prompt_number": 19
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print \"inner_prod:\\n\"\n",
      "print_matrix(inner_prod)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "inner_prod:\n",
        "\n",
        " 1.000   -0.000   -0.000   -0.000   -0.000    0.000    0.000    0.000   -0.000  \n",
        "-0.000    1.000    0.000   -0.000   -0.000   -0.000   -0.000    0.000    0.000  \n",
        "-0.000    0.000    1.000    0.000   -0.000   -0.000    0.000    0.000    0.000  \n",
        "-0.000   -0.000    0.000    1.000    0.000    0.000   -0.000   -0.000    0.000  \n",
        "-0.000   -0.000   -0.000    0.000    1.000   -0.000    0.000    0.000   -0.000  \n",
        " 0.000   -0.000   -0.000    0.000   -0.000    1.000   -0.000    0.000    0.000  \n",
        " 0.000   -0.000    0.000   -0.000    0.000   -0.000    1.000   -0.000   -0.000  \n",
        " 0.000    0.000    0.000   -0.000    0.000    0.000   -0.000    1.000   -0.000  \n",
        "-0.000    0.000    0.000    0.000   -0.000    0.000   -0.000   -0.000    1.000  \n"
       ]
      }
     ],
     "prompt_number": 20
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print \"expect_pos:\\n\"\n",
      "print_matrix(expect_pos)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "expect_pos:\n",
        "\n",
        " 1.341    0.049   -0.002    0.000   -0.000    0.000   -0.000    0.000   -0.000  \n",
        " 0.049    1.351    0.070   -0.005    0.000   -0.000    0.000   -0.000    0.000  \n",
        "-0.002    0.070    1.363    0.086   -0.007    0.001   -0.000    0.000   -0.000  \n",
        " 0.000   -0.005    0.086    1.376    0.100   -0.010    0.001   -0.000    0.000  \n",
        "-0.000    0.000   -0.007    0.100    1.390    0.113   -0.013    0.002   -0.000  \n",
        " 0.000   -0.000    0.001   -0.010    0.113    1.407    0.125   -0.017    0.002  \n",
        "-0.000    0.000   -0.000    0.001   -0.013    0.125    1.428    0.137   -0.023  \n",
        " 0.000   -0.000    0.000   -0.000    0.002   -0.017    0.137    1.456    0.146  \n",
        "-0.000    0.000   -0.000    0.000   -0.000    0.002   -0.023    0.146    1.515  \n"
       ]
      }
     ],
     "prompt_number": 21
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print \"expect_kin:\\n\"\n",
      "print_matrix(expect_kin)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "expect_kin:\n",
        "\n",
        "-0.000    10.132   -1.024    0.103   -0.019    0.004   -0.001    0.000   -0.000  \n",
        "-10.132   -0.000    14.099   -1.830    0.215   -0.044    0.012   -0.003    0.001  \n",
        " 1.024   -14.099    0.000    16.956   -2.683    0.361   -0.081    0.024   -0.007  \n",
        "-0.103    1.830   -16.956    0.000    19.171   -3.617    0.551   -0.133    0.044  \n",
        " 0.019   -0.215    2.683   -19.171    0.000    20.899   -4.670    0.810   -0.207  \n",
        "-0.004    0.044   -0.361    3.617   -20.899    0.000    22.167   -5.909    1.194  \n",
        " 0.001   -0.012    0.081   -0.551    4.670   -22.167   -0.000    22.850   -7.450  \n",
        "-0.000    0.003   -0.024    0.133   -0.810    5.909   -22.850   -0.000    22.068  \n",
        " 0.000   -0.001    0.007   -0.044    0.207   -1.194    7.450   -22.068    0.000  \n"
       ]
      }
     ],
     "prompt_number": 22
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Software"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%reload_ext version_information\n",
      "%version_information numpy, scipy, matplotlib, wavefunction"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "html": [
        "<table><tr><th>Software</th><th>Version</th></tr><tr><td>Python</td><td>2.7.4 (default, Apr 19 2013, 18:28:01) [GCC 4.7.3]</td></tr><tr><td>IPython</td><td>2.0.0-dev</td></tr><tr><td>OS</td><td>posix [linux2]</td></tr><tr><td>numpy</td><td>1.8.0.dev-895866d</td></tr><tr><td>scipy</td><td>0.13.0.dev-7c6d92e</td></tr><tr><td>matplotlib</td><td>1.3.x</td></tr><tr><td>wavefunction</td><td>1.0.0</td></tr><tr><td colspan='2'>Mon Sep 02 15:16:18 2013 JST</td></tr></table>"
       ],
       "json": [
        "{ \"Software versions\" : [{ \"module\" : \"Python\", \"version\" : \"2.7.4 (default, Apr 19 2013, 18:28:01) [GCC 4.7.3]\" }, { \"module\" : \"IPython\", \"version\" : \"2.0.0-dev\" }, { \"module\" : \"OS\", \"version\" : \"posix [linux2]\" }, { \"module\" : \"numpy\", \"version\" : \"1.8.0.dev-895866d\" }, { \"module\" : \"scipy\", \"version\" : \"0.13.0.dev-7c6d92e\" }, { \"module\" : \"matplotlib\", \"version\" : \"1.3.x\" }, { \"module\" : \"wavefunction\", \"version\" : \"1.0.0\" } ] }"
       ],
       "latex": [
        "\\begin{tabular}{|l|l|}\\hline\n",
        "{\\bf Software} & {\\bf Version} \\\\ \\hline\\hline\n",
        "Python & 2.7.4 (default, Apr 19 2013, 18:28:01) [GCC 4.7.3] \\\\ \\hline\n",
        "IPython & 2.0.0-dev \\\\ \\hline\n",
        "OS & posix [linux2] \\\\ \\hline\n",
        "numpy & 1.8.0.dev-895866d \\\\ \\hline\n",
        "scipy & 0.13.0.dev-7c6d92e \\\\ \\hline\n",
        "matplotlib & 1.3.x \\\\ \\hline\n",
        "wavefunction & 1.0.0 \\\\ \\hline\n",
        "\\hline \\multicolumn{2}{|l|}{Mon Sep 02 15:16:18 2013 JST} \\\\ \\hline\n",
        "\\end{tabular}\n"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 23,
       "text": [
        "Software versions\n",
        "Python 2.7.4 (default, Apr 19 2013, 18:28:01) [GCC 4.7.3]\n",
        "IPython 2.0.0-dev\n",
        "OS posix [linux2]\n",
        "numpy 1.8.0.dev-895866d\n",
        "scipy 0.13.0.dev-7c6d92e\n",
        "matplotlib 1.3.x\n",
        "wavefunction 1.0.0\n",
        "\n",
        "Mon Sep 02 15:16:18 2013 JST"
       ]
      }
     ],
     "prompt_number": 23
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": []
    }
   ],
   "metadata": {}
  }
 ]
}