Lecture-0-Introduction-to-QuTiP.ipynb

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     "source": [
      "# Lecture 0 - Introduction to QuTiP - The Quantum Toolbox in Python\n",
      "\n",
      "Author: J. R. Johansson (robert@riken.jp), http://dml.riken.jp/~rob/\n",
      "\n",
      "The latest version of this [IPython notebook](http://ipython.org/ipython-doc/dev/interactive/htmlnotebook.html) lecture is available at [http://github.com/jrjohansson/qutip-lectures](http://github.com/jrjohansson/qutip-lectures).\n",
      "\n",
      "The other notebooks in this lecture series are indexed at [http://jrjohansson.github.com](http://jrjohansson.github.com)."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%matplotlib inline\n",
      "import matplotlib.pyplot as plt\n",
      "import numpy as np\n",
      "from IPython.display import Image"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 1
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     "source": [
      "## Introduction\n",
      "\n",
      "QuTiP is a python package for calculations and numerical simulations of quantum systems. \n",
      "\n",
      "It includes facilities for representing and doing calculations with quantum objects such state vectors (wavefunctions), as bras/kets/density matrices, quantum operators of single and composite systems, and superoperators (useful for defining master equations).\n",
      "\n",
      "It also includes solvers for a time-evolution of quantum systems, according to: Schrodinger equation, von Neuman equation, master equations, Floquet formalism, Monte-Carlo quantum trajectors, experimental implementations of the stochastic Schrodinger/master equations.\n",
      "\n",
      "For more information see the project web site at http://qutip.googlecode.com, and the documentation at http://qutip.googlecode.com/svn/doc/2.1.0/html/index.html."
     ]
    },
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     "source": [
      "### Installation\n",
      "\n",
      "To install QuTiP, download the latest release from http://code.google.com/p/qutip/downloads/list or get the latest code from https://github.com/qutip/qutip, and run\n",
      "\n",
      "    $ sudo python setup.py install\n",
      "\n",
      "in the source code directory. For more detailed installation instructions and a list of dependencies that must be installed on the system (basically python+cython+numpy+scipy+matplotlib), see http://qutip.googlecode.com/svn/doc/2.1.0/html/installation.html."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "To use QuTiP in a Python program, first inlude the `qutip` module:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from qutip import *"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 2
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "This will make the functions and classes in QuTiP available in the rest of the program."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Quantum object class: `qobj`\n",
      "\n",
      "At the heart of the QuTiP package is the `Qobj` class, which is used for representing quantum object such as states and operator. \n",
      "\n",
      "The `Qobj` class contains all the information required to describe a quantum system, such as its matrix representation, composite structure and dimensionality. "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "Image(filename='images/qobj.png')"
     ],
     "language": "python",
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     "outputs": [
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IZxWEwe6Ou68A1AwFOMJ1MEfz27KsB553CaTjqBwjmN9mOLx/lxLH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kw1E7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\n",
       "prompt_number": 3,
       "text": [
        "<IPython.core.display.Image at 0x2f229d0>"
       ]
      }
     ],
     "prompt_number": 3
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Creating and inspecting quantum objects"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We can create a new quantum object using the `Qobj` class constructor, like this:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "q = Qobj([[1], [0]])\n",
      "\n",
      "q"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": [
        "$\\text{Quantum object: dims = [[2], [1]], shape = [2, 1], type = ket}\\\\[1em]\\begin{pmatrix}1.0\\\\0.0\\\\\\end{pmatrix}$"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 4,
       "text": [
        "Quantum object: dims = [[2], [1]], shape = [2, 1], type = ket\n",
        "Qobj data =\n",
        "[[ 1.]\n",
        " [ 0.]]"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Here we passed python list as an argument to the class constructor. The data in this list is used to construct the matrix representation of the quantum objects, and the other properties of the quantum object is by default computed from the same data.\n",
      "\n",
      "We can inspect the properties of a `Qobj` instance using the following class method:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# the dimension, or composite Hilbert state space structure\n",
      "q.dims"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 5,
       "text": [
        "[[2], [1]]"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# the shape of the matrix data representation\n",
      "q.shape"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 6,
       "text": [
        "[2, 1]"
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# the matrix data itself. in sparse matrix format. \n",
      "q.data"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 7,
       "text": [
        "<2x1 sparse matrix of type '<type 'numpy.complex128'>'\n",
        "\twith 1 stored elements in Compressed Sparse Row format>"
       ]
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# get the dense matrix representation\n",
      "q.full()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 8,
       "text": [
        "array([[ 1.+0.j],\n",
        "       [ 0.+0.j]])"
       ]
      }
     ],
     "prompt_number": 8
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# some additional properties\n",
      "q.isherm, q.type "
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 9,
       "text": [
        "(False, 'ket')"
       ]
      }
     ],
     "prompt_number": 9
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Using `Qobj` instances for calculations\n",
      "\n",
      "With `Qobj` instances we can do arithmetic and apply a number of different operations using class methods:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "sy = Qobj([[0,-1j], [1j,0]])  # the sigma-y Pauli operator\n",
      "\n",
      "sy"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": [
        "$\\text{Quantum object: dims = [[2], [2]], shape = [2, 2], type = oper, isherm = True}\\\\[1em]\\begin{pmatrix}0.0 & -1.0j\\\\1.0j & 0.0\\\\\\end{pmatrix}$"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 10,
       "text": [
        "Quantum object: dims = [[2], [2]], shape = [2, 2], type = oper, isherm = True\n",
        "Qobj data =\n",
        "[[ 0.+0.j  0.-1.j]\n",
        " [ 0.+1.j  0.+0.j]]"
       ]
      }
     ],
     "prompt_number": 10
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "sz = Qobj([[1,0], [0,-1]]) # the sigma-z Pauli operator\n",
      "\n",
      "sz"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": [
        "$\\text{Quantum object: dims = [[2], [2]], shape = [2, 2], type = oper, isherm = True}\\\\[1em]\\begin{pmatrix}1.0 & 0.0\\\\0.0 & -1.0\\\\\\end{pmatrix}$"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 11,
       "text": [
        "Quantum object: dims = [[2], [2]], shape = [2, 2], type = oper, isherm = True\n",
        "Qobj data =\n",
        "[[ 1.  0.]\n",
        " [ 0. -1.]]"
       ]
      }
     ],
     "prompt_number": 11
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# some arithmetic with quantum objects\n",
      "\n",
      "H = 1.0 * sz + 0.1 * sy\n",
      "\n",
      "print(\"Qubit Hamiltonian = \\n\")\n",
      "H"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Qubit Hamiltonian = \n",
        "\n"
       ]
      },
      {
       "latex": [
        "$\\text{Quantum object: dims = [[2], [2]], shape = [2, 2], type = oper, isherm = True}\\\\[1em]\\begin{pmatrix}1.0 & -0.100j\\\\0.100j & -1.0\\\\\\end{pmatrix}$"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 12,
       "text": [
        "Quantum object: dims = [[2], [2]], shape = [2, 2], type = oper, isherm = True\n",
        "Qobj data =\n",
        "[[ 1.+0.j   0.-0.1j]\n",
        " [ 0.+0.1j -1.+0.j ]]"
       ]
      }
     ],
     "prompt_number": 12
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Example of modifying quantum objects using the `Qobj` methods:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# The hermitian conjugate\n",
      "sy.dag()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": [
        "$\\text{Quantum object: dims = [[2], [2]], shape = [2, 2], type = oper, isherm = True}\\\\[1em]\\begin{pmatrix}0.0 & -1.0j\\\\1.0j & 0.0\\\\\\end{pmatrix}$"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 13,
       "text": [
        "Quantum object: dims = [[2], [2]], shape = [2, 2], type = oper, isherm = True\n",
        "Qobj data =\n",
        "[[ 0.+0.j  0.-1.j]\n",
        " [ 0.+1.j  0.+0.j]]"
       ]
      }
     ],
     "prompt_number": 13
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# The trace\n",
      "H.tr()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 14,
       "text": [
        "0.0"
       ]
      }
     ],
     "prompt_number": 14
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Eigen energies\n",
      "H.eigenenergies()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 15,
       "text": [
        "array([-1.00498756,  1.00498756])"
       ]
      }
     ],
     "prompt_number": 15
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "For a complete list of methods and properties of the `Qobj` class, see the [QuTiP documentation](http://qutip.googlecode.com/svn/doc/2.1.0/html/index.html) or try `help(Qobj)` or `dir(Qobj)`."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## States and operators\n",
      "\n",
      "Normally we do not need to create `Qobj` instances from stratch, using its constructor and passing its matrix represantation as argument. Instead we can use functions in QuTiP that generates common states and operators for us. Here are some examples of built-in state functions:\n",
      "\n",
      "### State vectors"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Fundamental basis states (Fock states of oscillator modes)\n",
      "\n",
      "N = 2 # number of states in the Hilbert space\n",
      "n = 1 # the state that will be occupied\n",
      "\n",
      "basis(N, n)    # equivalent to fock(N, n)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": [
        "$\\text{Quantum object: dims = [[2], [1]], shape = [2, 1], type = ket}\\\\[1em]\\begin{pmatrix}0.0\\\\1.0\\\\\\end{pmatrix}$"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 16,
       "text": [
        "Quantum object: dims = [[2], [1]], shape = [2, 1], type = ket\n",
        "Qobj data =\n",
        "[[ 0.]\n",
        " [ 1.]]"
       ]
      }
     ],
     "prompt_number": 16
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "fock(4, 2) # another example"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": [
        "$\\text{Quantum object: dims = [[4], [1]], shape = [4, 1], type = ket}\\\\[1em]\\begin{pmatrix}0.0\\\\0.0\\\\1.0\\\\0.0\\\\\\end{pmatrix}$"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 17,
       "text": [
        "Quantum object: dims = [[4], [1]], shape = [4, 1], type = ket\n",
        "Qobj data =\n",
        "[[ 0.]\n",
        " [ 0.]\n",
        " [ 1.]\n",
        " [ 0.]]"
       ]
      }
     ],
     "prompt_number": 17
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# a coherent state\n",
      "coherent(N=10, alpha=1.0)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": [
        "$\\text{Quantum object: dims = [[10], [1]], shape = [10, 1], type = ket}\\\\[1em]\\begin{pmatrix}0.607\\\\0.607\\\\0.429\\\\0.248\\\\0.124\\\\0.055\\\\0.023\\\\0.009\\\\0.003\\\\0.001\\\\\\end{pmatrix}$"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 18,
       "text": [
        "Quantum object: dims = [[10], [1]], shape = [10, 1], type = ket\n",
        "Qobj data =\n",
        "[[ 0.60653066]\n",
        " [ 0.60653066]\n",
        " [ 0.42888194]\n",
        " [ 0.24761511]\n",
        " [ 0.12380753]\n",
        " [ 0.0553686 ]\n",
        " [ 0.02260303]\n",
        " [ 0.00854887]\n",
        " [ 0.00299672]\n",
        " [ 0.00110007]]"
       ]
      }
     ],
     "prompt_number": 18
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Density matrices"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# a fock state as density matrix\n",
      "fock_dm(5, 2) # 5 = hilbert space size, 2 = state that is occupied"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": [
        "$\\text{Quantum object: dims = [[5], [5]], shape = [5, 5], type = oper, isherm = True}\\\\[1em]\\begin{pmatrix}0.0 & 0.0 & 0.0 & 0.0 & 0.0\\\\0.0 & 0.0 & 0.0 & 0.0 & 0.0\\\\0.0 & 0.0 & 1.0 & 0.0 & 0.0\\\\0.0 & 0.0 & 0.0 & 0.0 & 0.0\\\\0.0 & 0.0 & 0.0 & 0.0 & 0.0\\\\\\end{pmatrix}$"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 19,
       "text": [
        "Quantum object: dims = [[5], [5]], shape = [5, 5], type = oper, isherm = True\n",
        "Qobj data =\n",
        "[[ 0.  0.  0.  0.  0.]\n",
        " [ 0.  0.  0.  0.  0.]\n",
        " [ 0.  0.  1.  0.  0.]\n",
        " [ 0.  0.  0.  0.  0.]\n",
        " [ 0.  0.  0.  0.  0.]]"
       ]
      }
     ],
     "prompt_number": 19
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# coherent state as density matrix\n",
      "coherent_dm(N=8, alpha=1.0)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": [
        "$\\text{Quantum object: dims = [[8], [8]], shape = [8, 8], type = oper, isherm = True}\\\\[1em]\\begin{pmatrix}0.368 & 0.368 & 0.260 & 0.150 & 0.075 & 0.034 & 0.014 & 0.006\\\\0.368 & 0.368 & 0.260 & 0.150 & 0.075 & 0.034 & 0.014 & 0.006\\\\0.260 & 0.260 & 0.184 & 0.106 & 0.053 & 0.024 & 0.010 & 0.004\\\\0.150 & 0.150 & 0.106 & 0.061 & 0.031 & 0.014 & 0.006 & 0.002\\\\0.075 & 0.075 & 0.053 & 0.031 & 0.015 & 0.007 & 0.003 & 0.001\\\\0.034 & 0.034 & 0.024 & 0.014 & 0.007 & 0.003 & 0.001 & 5.276\\times10^{-04}\\\\0.014 & 0.014 & 0.010 & 0.006 & 0.003 & 0.001 & 4.990\\times10^{-04} & 2.126\\times10^{-04}\\\\0.006 & 0.006 & 0.004 & 0.002 & 0.001 & 5.276\\times10^{-04} & 2.126\\times10^{-04} & 9.058\\times10^{-05}\\\\\\end{pmatrix}$"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 20,
       "text": [
        "Quantum object: dims = [[8], [8]], shape = [8, 8], type = oper, isherm = True\n",
        "Qobj data =\n",
        "[[  3.67879439e-01   3.67879455e-01   2.60129900e-01   1.50187300e-01\n",
        "    7.50858773e-02   3.36199110e-02   1.35485515e-02   5.77267786e-03]\n",
        " [  3.67879455e-01   3.67879470e-01   2.60129911e-01   1.50187306e-01\n",
        "    7.50858804e-02   3.36199124e-02   1.35485520e-02   5.77267810e-03]\n",
        " [  2.60129900e-01   2.60129911e-01   1.83939513e-01   1.06198399e-01\n",
        "    5.30937031e-02   2.37728537e-02   9.58026722e-03   4.08189737e-03]\n",
        " [  1.50187300e-01   1.50187306e-01   1.06198399e-01   6.13141770e-02\n",
        "    3.06539153e-02   1.37253761e-02   5.53121524e-03   2.35670388e-03]\n",
        " [  7.50858773e-02   7.50858804e-02   5.30937031e-02   3.06539153e-02\n",
        "    1.53253712e-02   6.86197771e-03   2.76532136e-03   1.17822997e-03]\n",
        " [  3.36199110e-02   3.36199124e-02   2.37728537e-02   1.37253761e-02\n",
        "    6.86197771e-03   3.07246966e-03   1.23818035e-03   5.27555757e-04]\n",
        " [  1.35485515e-02   1.35485520e-02   9.58026722e-03   5.53121524e-03\n",
        "    2.76532136e-03   1.23818035e-03   4.98976640e-04   2.12600691e-04]\n",
        " [  5.77267786e-03   5.77267810e-03   4.08189737e-03   2.35670388e-03\n",
        "    1.17822997e-03   5.27555757e-04   2.12600691e-04   9.05835068e-05]]"
       ]
      }
     ],
     "prompt_number": 20
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# thermal state\n",
      "n = 1 # average number of thermal photons\n",
      "thermal_dm(8, n)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": [
        "$\\text{Quantum object: dims = [[8], [8]], shape = [8, 8], type = oper, isherm = True}\\\\[1em]\\begin{pmatrix}0.502 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\\\\0.0 & 0.251 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\\\\0.0 & 0.0 & 0.125 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\\\\0.0 & 0.0 & 0.0 & 0.063 & 0.0 & 0.0 & 0.0 & 0.0\\\\0.0 & 0.0 & 0.0 & 0.0 & 0.031 & 0.0 & 0.0 & 0.0\\\\0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.016 & 0.0 & 0.0\\\\0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.008 & 0.0\\\\0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.004\\\\\\end{pmatrix}$"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 21,
       "text": [
        "Quantum object: dims = [[8], [8]], shape = [8, 8], type = oper, isherm = True\n",
        "Qobj data =\n",
        "[[ 0.50196078  0.          0.          0.          0.          0.          0.\n",
        "   0.        ]\n",
        " [ 0.          0.25098039  0.          0.          0.          0.          0.\n",
        "   0.        ]\n",
        " [ 0.          0.          0.1254902   0.          0.          0.          0.\n",
        "   0.        ]\n",
        " [ 0.          0.          0.          0.0627451   0.          0.          0.\n",
        "   0.        ]\n",
        " [ 0.          0.          0.          0.          0.03137255  0.          0.\n",
        "   0.        ]\n",
        " [ 0.          0.          0.          0.          0.          0.01568627\n",
        "   0.          0.        ]\n",
        " [ 0.          0.          0.          0.          0.          0.\n",
        "   0.00784314  0.        ]\n",
        " [ 0.          0.          0.          0.          0.          0.          0.\n",
        "   0.00392157]]"
       ]
      }
     ],
     "prompt_number": 21
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Operators"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "#### Qubit (two-level system) operators"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Pauli sigma x\n",
      "sigmax()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": [
        "$\\text{Quantum object: dims = [[2], [2]], shape = [2, 2], type = oper, isherm = True}\\\\[1em]\\begin{pmatrix}0.0 & 1.0\\\\1.0 & 0.0\\\\\\end{pmatrix}$"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 22,
       "text": [
        "Quantum object: dims = [[2], [2]], shape = [2, 2], type = oper, isherm = True\n",
        "Qobj data =\n",
        "[[ 0.  1.]\n",
        " [ 1.  0.]]"
       ]
      }
     ],
     "prompt_number": 22
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Pauli sigma y\n",
      "sigmay()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": [
        "$\\text{Quantum object: dims = [[2], [2]], shape = [2, 2], type = oper, isherm = True}\\\\[1em]\\begin{pmatrix}0.0 & -1.0j\\\\1.0j & 0.0\\\\\\end{pmatrix}$"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 23,
       "text": [
        "Quantum object: dims = [[2], [2]], shape = [2, 2], type = oper, isherm = True\n",
        "Qobj data =\n",
        "[[ 0.+0.j  0.-1.j]\n",
        " [ 0.+1.j  0.+0.j]]"
       ]
      }
     ],
     "prompt_number": 23
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Pauli sigma z\n",
      "sigmaz()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": [
        "$\\text{Quantum object: dims = [[2], [2]], shape = [2, 2], type = oper, isherm = True}\\\\[1em]\\begin{pmatrix}1.0 & 0.0\\\\0.0 & -1.0\\\\\\end{pmatrix}$"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 24,
       "text": [
        "Quantum object: dims = [[2], [2]], shape = [2, 2], type = oper, isherm = True\n",
        "Qobj data =\n",
        "[[ 1.  0.]\n",
        " [ 0. -1.]]"
       ]
      }
     ],
     "prompt_number": 24
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "#### Harmonic oscillator operators"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#  annihilation operator\n",
      "\n",
      "destroy(N=8) # N = number of fock states included in the Hilbert space"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": [
        "$\\text{Quantum object: dims = [[8], [8]], shape = [8, 8], type = oper, isherm = False}\\\\[1em]\\begin{pmatrix}0.0 & 1.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\\\\0.0 & 0.0 & 1.414 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\\\\0.0 & 0.0 & 0.0 & 1.732 & 0.0 & 0.0 & 0.0 & 0.0\\\\0.0 & 0.0 & 0.0 & 0.0 & 2.0 & 0.0 & 0.0 & 0.0\\\\0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 2.236 & 0.0 & 0.0\\\\0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 2.449 & 0.0\\\\0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 2.646\\\\0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\\\\\\end{pmatrix}$"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 25,
       "text": [
        "Quantum object: dims = [[8], [8]], shape = [8, 8], type = oper, isherm = False\n",
        "Qobj data =\n",
        "[[ 0.          1.          0.          0.          0.          0.          0.\n",
        "   0.        ]\n",
        " [ 0.          0.          1.41421356  0.          0.          0.          0.\n",
        "   0.        ]\n",
        " [ 0.          0.          0.          1.73205081  0.          0.          0.\n",
        "   0.        ]\n",
        " [ 0.          0.          0.          0.          2.          0.          0.\n",
        "   0.        ]\n",
        " [ 0.          0.          0.          0.          0.          2.23606798\n",
        "   0.          0.        ]\n",
        " [ 0.          0.          0.          0.          0.          0.\n",
        "   2.44948974  0.        ]\n",
        " [ 0.          0.          0.          0.          0.          0.          0.\n",
        "   2.64575131]\n",
        " [ 0.          0.          0.          0.          0.          0.          0.\n",
        "   0.        ]]"
       ]
      }
     ],
     "prompt_number": 25
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# creation operator\n",
      "\n",
      "create(N=8) # equivalent to destroy(5).dag()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": [
        "$\\text{Quantum object: dims = [[8], [8]], shape = [8, 8], type = oper, isherm = False}\\\\[1em]\\begin{pmatrix}0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\\\\1.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\\\\0.0 & 1.414 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\\\\0.0 & 0.0 & 1.732 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\\\\0.0 & 0.0 & 0.0 & 2.0 & 0.0 & 0.0 & 0.0 & 0.0\\\\0.0 & 0.0 & 0.0 & 0.0 & 2.236 & 0.0 & 0.0 & 0.0\\\\0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 2.449 & 0.0 & 0.0\\\\0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 2.646 & 0.0\\\\\\end{pmatrix}$"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 26,
       "text": [
        "Quantum object: dims = [[8], [8]], shape = [8, 8], type = oper, isherm = False\n",
        "Qobj data =\n",
        "[[ 0.          0.          0.          0.          0.          0.          0.\n",
        "   0.        ]\n",
        " [ 1.          0.          0.          0.          0.          0.          0.\n",
        "   0.        ]\n",
        " [ 0.          1.41421356  0.          0.          0.          0.          0.\n",
        "   0.        ]\n",
        " [ 0.          0.          1.73205081  0.          0.          0.          0.\n",
        "   0.        ]\n",
        " [ 0.          0.          0.          2.          0.          0.          0.\n",
        "   0.        ]\n",
        " [ 0.          0.          0.          0.          2.23606798  0.          0.\n",
        "   0.        ]\n",
        " [ 0.          0.          0.          0.          0.          2.44948974\n",
        "   0.          0.        ]\n",
        " [ 0.          0.          0.          0.          0.          0.\n",
        "   2.64575131  0.        ]]"
       ]
      }
     ],
     "prompt_number": 26
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# the position operator is easily constructed from the annihilation operator\n",
      "a = destroy(8)\n",
      "\n",
      "x = a + a.dag()\n",
      "\n",
      "x"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": [
        "$\\text{Quantum object: dims = [[8], [8]], shape = [8, 8], type = oper, isherm = True}\\\\[1em]\\begin{pmatrix}0.0 & 1.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\\\\1.0 & 0.0 & 1.414 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\\\\0.0 & 1.414 & 0.0 & 1.732 & 0.0 & 0.0 & 0.0 & 0.0\\\\0.0 & 0.0 & 1.732 & 0.0 & 2.0 & 0.0 & 0.0 & 0.0\\\\0.0 & 0.0 & 0.0 & 2.0 & 0.0 & 2.236 & 0.0 & 0.0\\\\0.0 & 0.0 & 0.0 & 0.0 & 2.236 & 0.0 & 2.449 & 0.0\\\\0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 2.449 & 0.0 & 2.646\\\\0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 2.646 & 0.0\\\\\\end{pmatrix}$"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 27,
       "text": [
        "Quantum object: dims = [[8], [8]], shape = [8, 8], type = oper, isherm = True\n",
        "Qobj data =\n",
        "[[ 0.          1.          0.          0.          0.          0.          0.\n",
        "   0.        ]\n",
        " [ 1.          0.          1.41421356  0.          0.          0.          0.\n",
        "   0.        ]\n",
        " [ 0.          1.41421356  0.          1.73205081  0.          0.          0.\n",
        "   0.        ]\n",
        " [ 0.          0.          1.73205081  0.          2.          0.          0.\n",
        "   0.        ]\n",
        " [ 0.          0.          0.          2.          0.          2.23606798\n",
        "   0.          0.        ]\n",
        " [ 0.          0.          0.          0.          2.23606798  0.\n",
        "   2.44948974  0.        ]\n",
        " [ 0.          0.          0.          0.          0.          2.44948974\n",
        "   0.          2.64575131]\n",
        " [ 0.          0.          0.          0.          0.          0.\n",
        "   2.64575131  0.        ]]"
       ]
      }
     ],
     "prompt_number": 27
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "#### Using `Qobj` instances we can check some well known commutation relations:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def commutator(op1, op2):\n",
      "    return op1 * op2 - op2 * op1"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 28
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "$[a, a^1] = 1$"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "a = destroy(5)\n",
      "\n",
      "commutator(a, a.dag())"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": [
        "$\\text{Quantum object: dims = [[5], [5]], shape = [5, 5], type = oper, isherm = True}\\\\[1em]\\begin{pmatrix}1.0 & 0.0 & 0.0 & 0.0 & 0.0\\\\0.0 & 1.0 & 0.0 & 0.0 & 0.0\\\\0.0 & 0.0 & 1.000 & 0.0 & 0.0\\\\0.0 & 0.0 & 0.0 & 1.0 & 0.0\\\\0.0 & 0.0 & 0.0 & 0.0 & -4.0\\\\\\end{pmatrix}$"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 29,
       "text": [
        "Quantum object: dims = [[5], [5]], shape = [5, 5], type = oper, isherm = True\n",
        "Qobj data =\n",
        "[[ 1.  0.  0.  0.  0.]\n",
        " [ 0.  1.  0.  0.  0.]\n",
        " [ 0.  0.  1.  0.  0.]\n",
        " [ 0.  0.  0.  1.  0.]\n",
        " [ 0.  0.  0.  0. -4.]]"
       ]
      }
     ],
     "prompt_number": 29
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "**Ops...** The result is not identity! Why? Because we have truncated the Hilbert space. But that's OK as long as the highest Fock state isn't involved in the dynamics in our truncated Hilbert space. If it is, the approximation that the truncation introduces might be a problem."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "$[x,p] = i$"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "x =       (a + a.dag())/sqrt(2)\n",
      "p = -1j * (a - a.dag())/sqrt(2)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 30
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "commutator(x, p)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": [
        "$\\text{Quantum object: dims = [[5], [5]], shape = [5, 5], type = oper, isherm = False}\\\\[1em]\\begin{pmatrix}1.000j & 0.0 & 0.0 & 0.0 & 0.0\\\\0.0 & 1.0j & 0.0 & 0.0 & 0.0\\\\0.0 & 0.0 & 1.000j & 0.0 & 0.0\\\\0.0 & 0.0 & 0.0 & 1.000j & 0.0\\\\0.0 & 0.0 & 0.0 & 0.0 & -4.000j\\\\\\end{pmatrix}$"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 31,
       "text": [
        "Quantum object: dims = [[5], [5]], shape = [5, 5], type = oper, isherm = False\n",
        "Qobj data =\n",
        "[[ 0.+1.j  0.+0.j  0.+0.j  0.+0.j  0.+0.j]\n",
        " [ 0.+0.j  0.+1.j  0.+0.j  0.+0.j  0.+0.j]\n",
        " [ 0.+0.j  0.+0.j  0.+1.j  0.+0.j  0.+0.j]\n",
        " [ 0.+0.j  0.+0.j  0.+0.j  0.+1.j  0.+0.j]\n",
        " [ 0.+0.j  0.+0.j  0.+0.j  0.+0.j  0.-4.j]]"
       ]
      }
     ],
     "prompt_number": 31
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Same issue with the truncated Hilbert space, but otherwise OK."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Let's try some Pauli spin inequalities\n",
      "\n",
      "$[\\sigma_x, \\sigma_y] = 2i \\sigma_z$"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "commutator(sigmax(), sigmay()) - 2j * sigmaz()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": [
        "$\\text{Quantum object: dims = [[2], [2]], shape = [2, 2], type = oper, isherm = True}\\\\[1em]\\begin{pmatrix}0.0 & 0.0\\\\0.0 & 0.0\\\\\\end{pmatrix}$"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 32,
       "text": [
        "Quantum object: dims = [[2], [2]], shape = [2, 2], type = oper, isherm = True\n",
        "Qobj data =\n",
        "[[ 0.  0.]\n",
        " [ 0.  0.]]"
       ]
      }
     ],
     "prompt_number": 32
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "$-i \\sigma_x \\sigma_y \\sigma_z = \\mathbf{1}$"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "-1j * sigmax() * sigmay() * sigmaz()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": [
        "$\\text{Quantum object: dims = [[2], [2]], shape = [2, 2], type = oper, isherm = True}\\\\[1em]\\begin{pmatrix}1.0 & 0.0\\\\0.0 & 1.0\\\\\\end{pmatrix}$"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 33,
       "text": [
        "Quantum object: dims = [[2], [2]], shape = [2, 2], type = oper, isherm = True\n",
        "Qobj data =\n",
        "[[ 1.  0.]\n",
        " [ 0.  1.]]"
       ]
      }
     ],
     "prompt_number": 33
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "$\\sigma_x^2 = \\sigma_y^2 = \\sigma_z^2 = \\mathbf{1}$"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "sigmax()**2 == sigmay()**2 == sigmaz()**2 == qeye(2)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 34,
       "text": [
        "True"
       ]
      }
     ],
     "prompt_number": 34
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Composite systems\n",
      "\n",
      "In most cases we are interested in coupled quantum systems, for example coupled qubits, a qubit coupled to a cavity (oscillator mode), etc.\n",
      "\n",
      "To define states and operators for such systems in QuTiP, we use the `tensor` function to create `Qobj` instances for the composite system.\n",
      "\n",
      "For example, consider a system composed of two qubits. If we want to create a Pauli $\\sigma_z$ operator that acts on the first qubit and leaves the second qubit unaffected (i.e., the operator $\\sigma_z \\otimes \\mathbf{1}$), we would do:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "sz1 = tensor(sigmaz(), qeye(2))\n",
      "\n",
      "sz1"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": [
        "$\\text{Quantum object: dims = [[2, 2], [2, 2]], shape = [4, 4], type = oper, isherm = True}\\\\[1em]\\begin{pmatrix}1.0 & 0.0 & 0.0 & 0.0\\\\0.0 & 1.0 & 0.0 & 0.0\\\\0.0 & 0.0 & -1.0 & 0.0\\\\0.0 & 0.0 & 0.0 & -1.0\\\\\\end{pmatrix}$"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 35,
       "text": [
        "Quantum object: dims = [[2, 2], [2, 2]], 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. -1.]]"
       ]
      }
     ],
     "prompt_number": 35
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We can easily verify that this two-qubit operator does indeed have the desired properties:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "psi1 = tensor(basis(N,1), basis(N,0)) # excited first qubit\n",
      "psi2 = tensor(basis(N,0), basis(N,1)) # excited second qubit"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 36
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "sz1 * psi1 == psi1 # this should not be true, because sz1 should flip the sign of the excited state of psi1"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 37,
       "text": [
        "False"
       ]
      }
     ],
     "prompt_number": 37
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "sz1 * psi2 == psi2 # this should be true, because sz1 should leave psi2 unaffected"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 38,
       "text": [
        "True"
       ]
      }
     ],
     "prompt_number": 38
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Above we used the `qeye(N)` function, which generates the identity operator with `N` quantum states. If we want to do the same thing for the second qubit we can do:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "sz2 = tensor(qeye(2), sigmaz())\n",
      "\n",
      "sz2"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": [
        "$\\text{Quantum object: dims = [[2, 2], [2, 2]], shape = [4, 4], type = oper, isherm = True}\\\\[1em]\\begin{pmatrix}1.0 & 0.0 & 0.0 & 0.0\\\\0.0 & -1.0 & 0.0 & 0.0\\\\0.0 & 0.0 & 1.0 & 0.0\\\\0.0 & 0.0 & 0.0 & -1.0\\\\\\end{pmatrix}$"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 39,
       "text": [
        "Quantum object: dims = [[2, 2], [2, 2]], 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. -1.]]"
       ]
      }
     ],
     "prompt_number": 39
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Note the order of the argument to the `tensor` function, and the correspondingly different matrix representation of the two operators `sz1` and `sz2`.\n",
      "\n",
      "Using the same method we can create coupling terms of the form $\\sigma_x \\otimes \\sigma_x$:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "tensor(sigmax(), sigmax())"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": [
        "$\\text{Quantum object: dims = [[2, 2], [2, 2]], shape = [4, 4], type = oper, isherm = True}\\\\[1em]\\begin{pmatrix}0.0 & 0.0 & 0.0 & 1.0\\\\0.0 & 0.0 & 1.0 & 0.0\\\\0.0 & 1.0 & 0.0 & 0.0\\\\1.0 & 0.0 & 0.0 & 0.0\\\\\\end{pmatrix}$"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 40,
       "text": [
        "Quantum object: dims = [[2, 2], [2, 2]], shape = [4, 4], type = oper, isherm = True\n",
        "Qobj data =\n",
        "[[ 0.  0.  0.  1.]\n",
        " [ 0.  0.  1.  0.]\n",
        " [ 0.  1.  0.  0.]\n",
        " [ 1.  0.  0.  0.]]"
       ]
      }
     ],
     "prompt_number": 40
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Now we are ready to create a `Qobj` representation of a coupled two-qubit Hamiltonian: $H = \\epsilon_1 \\sigma_z^{(1)} + \\epsilon_2 \\sigma_z^{(2)} + g \\sigma_x^{(1)}\\sigma_x^{(2)}$"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "epsilon = [1.0, 1.0]\n",
      "g = 0.1\n",
      "\n",
      "sz1 = tensor(sigmaz(), qeye(2))\n",
      "sz2 = tensor(qeye(2), sigmaz())\n",
      "\n",
      "H = epsilon[0] * sz1 + epsilon[1] * sz2 + g * tensor(sigmax(), sigmax())\n",
      "\n",
      "H"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": [
        "$\\text{Quantum object: dims = [[2, 2], [2, 2]], shape = [4, 4], type = oper, isherm = True}\\\\[1em]\\begin{pmatrix}2.0 & 0.0 & 0.0 & 0.100\\\\0.0 & 0.0 & 0.100 & 0.0\\\\0.0 & 0.100 & 0.0 & 0.0\\\\0.100 & 0.0 & 0.0 & -2.0\\\\\\end{pmatrix}$"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 41,
       "text": [
        "Quantum object: dims = [[2, 2], [2, 2]], shape = [4, 4], type = oper, isherm = True\n",
        "Qobj data =\n",
        "[[ 2.   0.   0.   0.1]\n",
        " [ 0.   0.   0.1  0. ]\n",
        " [ 0.   0.1  0.   0. ]\n",
        " [ 0.1  0.   0.  -2. ]]"
       ]
      }
     ],
     "prompt_number": 41
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "To create composite systems of different types, all we need to do is to change the operators that we pass to the `tensor` function (which can take an arbitrary number of operator for composite systems with many components).\n",
      "\n",
      "For example, the Jaynes-Cumming Hamiltonian for a qubit-cavity system:\n",
      "\n",
      "$H = \\omega_c a^\\dagger a - \\frac{1}{2}\\omega_a \\sigma_z + g (a \\sigma_+ + a^\\dagger \\sigma_-)$"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "wc = 1.0 # cavity frequency\n",
      "wa = 1.0 # qubit/atom frenqency\n",
      "g = 0.1  # coupling strength\n",
      "\n",
      "# cavity mode operator\n",
      "a = tensor(destroy(5), qeye(2))\n",
      "\n",
      "# qubit/atom operators\n",
      "sz = tensor(qeye(5), sigmaz())   # sigma-z operator\n",
      "sm = tensor(qeye(5), destroy(2)) # sigma-minus operator\n",
      "\n",
      "# the Jaynes-Cumming Hamiltonian\n",
      "H = wc * a.dag() * a - 0.5 * wa * sz + g * (a * sm.dag() + a.dag() * sm)\n",
      "\n",
      "H"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": [
        "$\\text{Quantum object: dims = [[5, 2], [5, 2]], shape = [10, 10], type = oper, isherm = True}\\\\[1em]\\begin{pmatrix}-0.500 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\\\\0.0 & 0.500 & 0.100 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\\\\0.0 & 0.100 & 0.500 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\\\\0.0 & 0.0 & 0.0 & 1.500 & 0.141 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\\\\0.0 & 0.0 & 0.0 & 0.141 & 1.500 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\\\\0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 2.500 & 0.173 & 0.0 & 0.0 & 0.0\\\\0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.173 & 2.500 & 0.0 & 0.0 & 0.0\\\\0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 3.500 & 0.200 & 0.0\\\\0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.200 & 3.500 & 0.0\\\\0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 4.500\\\\\\end{pmatrix}$"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 42,
       "text": [
        "Quantum object: dims = [[5, 2], [5, 2]], shape = [10, 10], type = oper, isherm = True\n",
        "Qobj data =\n",
        "[[-0.5         0.          0.          0.          0.          0.          0.\n",
        "   0.          0.          0.        ]\n",
        " [ 0.          0.5         0.1         0.          0.          0.          0.\n",
        "   0.          0.          0.        ]\n",
        " [ 0.          0.1         0.5         0.          0.          0.          0.\n",
        "   0.          0.          0.        ]\n",
        " [ 0.          0.          0.          1.5         0.14142136  0.          0.\n",
        "   0.          0.          0.        ]\n",
        " [ 0.          0.          0.          0.14142136  1.5         0.          0.\n",
        "   0.          0.          0.        ]\n",
        " [ 0.          0.          0.          0.          0.          2.5\n",
        "   0.17320508  0.          0.          0.        ]\n",
        " [ 0.          0.          0.          0.          0.          0.17320508\n",
        "   2.5         0.          0.          0.        ]\n",
        " [ 0.          0.          0.          0.          0.          0.          0.\n",
        "   3.5         0.2         0.        ]\n",
        " [ 0.          0.          0.          0.          0.          0.          0.\n",
        "   0.2         3.5         0.        ]\n",
        " [ 0.          0.          0.          0.          0.          0.          0.\n",
        "   0.          0.          4.5       ]]"
       ]
      }
     ],
     "prompt_number": 42
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Note that \n",
      "\n",
      "$a \\sigma_+ = (a \\otimes \\mathbf{1}) (\\mathbf{1} \\otimes \\sigma_+)$\n",
      "\n",
      "so the following two are identical:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "a = tensor(destroy(3), qeye(2))\n",
      "sp = tensor(qeye(3), create(2))\n",
      "\n",
      "a * sp"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": [
        "$\\text{Quantum object: dims = [[3, 2], [3, 2]], shape = [6, 6], type = oper, isherm = False}\\\\[1em]\\begin{pmatrix}0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\\\\0.0 & 0.0 & 1.0 & 0.0 & 0.0 & 0.0\\\\0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\\\\0.0 & 0.0 & 0.0 & 0.0 & 1.414 & 0.0\\\\0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\\\\0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\\\\\\end{pmatrix}$"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 43,
       "text": [
        "Quantum object: dims = [[3, 2], [3, 2]], shape = [6, 6], type = oper, isherm = False\n",
        "Qobj data =\n",
        "[[ 0.          0.          0.          0.          0.          0.        ]\n",
        " [ 0.          0.          1.          0.          0.          0.        ]\n",
        " [ 0.          0.          0.          0.          0.          0.        ]\n",
        " [ 0.          0.          0.          0.          1.41421356  0.        ]\n",
        " [ 0.          0.          0.          0.          0.          0.        ]\n",
        " [ 0.          0.          0.          0.          0.          0.        ]]"
       ]
      }
     ],
     "prompt_number": 43
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "tensor(destroy(3), create(2))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": [
        "$\\text{Quantum object: dims = [[3, 2], [3, 2]], shape = [6, 6], type = oper, isherm = False}\\\\[1em]\\begin{pmatrix}0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\\\\0.0 & 0.0 & 1.0 & 0.0 & 0.0 & 0.0\\\\0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\\\\0.0 & 0.0 & 0.0 & 0.0 & 1.414 & 0.0\\\\0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\\\\0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\\\\\\end{pmatrix}$"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 44,
       "text": [
        "Quantum object: dims = [[3, 2], [3, 2]], shape = [6, 6], type = oper, isherm = False\n",
        "Qobj data =\n",
        "[[ 0.          0.          0.          0.          0.          0.        ]\n",
        " [ 0.          0.          1.          0.          0.          0.        ]\n",
        " [ 0.          0.          0.          0.          0.          0.        ]\n",
        " [ 0.          0.          0.          0.          1.41421356  0.        ]\n",
        " [ 0.          0.          0.          0.          0.          0.        ]\n",
        " [ 0.          0.          0.          0.          0.          0.        ]]"
       ]
      }
     ],
     "prompt_number": 44
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Unitary dynamics\n",
      "\n",
      "Unitary evolution of a quantum system in QuTiP can be calculated with the `mesolve` function. \n",
      "\n",
      "`mesolve` is short for Master-eqaution solve (for dissipative dynamics), but if no collapse operators (which describe the dissipation) are given to the solve it falls back on the unitary evolution of the Schrodinger (for initial states in state vector for) or the von Neuman equation (for initial states in density matrix form).\n",
      "\n",
      "The evolution solvers in QuTiP returns a class of type `Odedata`, which contains the solution to the problem posed to the evolution solver. \n",
      "\n",
      "For example, considor a qubit with Hamiltonian $H = \\sigma_x$ and initial state $\\left|1\\right>$ (in the sigma-z basis): Its evolution can be calculated as follows:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Hamiltonian\n",
      "H = sigmax()\n",
      "\n",
      "# initial state\n",
      "psi0 = basis(2, 0)\n",
      "\n",
      "# list of times for which the solver should store the state vector\n",
      "tlist = np.linspace(0, 10, 100)\n",
      "\n",
      "result = mesolve(H, psi0, tlist, [], [])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 45
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "result"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 46,
       "text": [
        "Odedata object with sesolve data.\n",
        "---------------------------------\n",
        "states = True\n",
        "num_collapse = 0"
       ]
      }
     ],
     "prompt_number": 46
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The `result` object contains a list of the wavefunctions at the times requested with the `tlist` array. "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "len(result.states)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 47,
       "text": [
        "100"
       ]
      }
     ],
     "prompt_number": 47
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "result.states[-1] # the finial state"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": [
        "$\\text{Quantum object: dims = [[2], [1]], shape = [2, 1], type = ket}\\\\[1em]\\begin{pmatrix}-0.839\\\\0.544j\\\\\\end{pmatrix}$"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 48,
       "text": [
        "Quantum object: dims = [[2], [1]], shape = [2, 1], type = ket\n",
        "Qobj data =\n",
        "[[-0.8390774+0.j        ]\n",
        " [ 0.0000000+0.54401206j]]"
       ]
      }
     ],
     "prompt_number": 48
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Expectation values\n",
      "\n",
      "The expectation values of an operator given a state vector or density matrix (or list thereof) can be calculated using the `expect` function. "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "expect(sigmaz(), result.states[-1])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 49,
       "text": [
        "0.40810176186454994"
       ]
      }
     ],
     "prompt_number": 49
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "expect(sigmaz(), result.states)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 50,
       "text": [
        "array([ 1.        ,  0.97966324,  0.91948013,  0.82189857,  0.69088756,\n",
        "        0.53177579,  0.3510349 ,  0.15601625, -0.04534808, -0.24486795,\n",
        "       -0.43442821, -0.60631884, -0.75354841, -0.87012859, -0.95131766,\n",
        "       -0.99381332, -0.99588712, -0.95745468, -0.88007921, -0.76690787,\n",
        "       -0.62254375, -0.45285867, -0.26475429, -0.06588149,  0.13567091,\n",
        "        0.33170513,  0.51424779,  0.67587427,  0.81001063,  0.91120109,\n",
        "        0.97532984,  0.99978853,  0.9835823 ,  0.92737033,  0.83343897,\n",
        "        0.70560878,  0.54907906,  0.37021643,  0.17629587, -0.02479521,\n",
        "       -0.22487778, -0.41581382, -0.58983733, -0.73987014, -0.85980992,\n",
        "       -0.94477826, -0.9913192 , -0.99753971, -0.96318677, -0.88965766,\n",
        "       -0.77994308, -0.63850553, -0.4710978 , -0.28452892, -0.08638732,\n",
        "        0.11526793,  0.31223484,  0.49650212,  0.660575  ,  0.79778003,\n",
        "        0.90253662,  0.97058393,  0.99915421,  0.98708537,  0.9348683 ,\n",
        "        0.84462688,  0.72003156,  0.56615011,  0.38924141,  0.19650096,\n",
        "       -0.00423183, -0.20479249, -0.39702355, -0.57310633, -0.72587894,\n",
        "       -0.84912758, -0.93783928, -0.9884058 , -0.99877041, -0.9685115 ,\n",
        "       -0.89885984, -0.79264843, -0.65419728, -0.4891377 , -0.30418323,\n",
        "       -0.10685663,  0.09481617,  0.29263248,  0.47854644,  0.64499632,\n",
        "        0.785212  ,  0.89349043,  0.96542751,  0.9980973 ,  0.99017096,\n",
        "        0.94197089,  0.85545757,  0.73414984,  0.58298172,  0.40810176])"
       ]
      }
     ],
     "prompt_number": 50
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "fig, axes = plt.subplots(1,1)\n",
      "\n",
      "axes.plot(tlist, expect(sigmaz(), result.states))\n",
      "\n",
      "axes.set_xlabel(r'$t$', fontsize=20)\n",
      "axes.set_ylabel(r'$\\left<\\sigma_z\\right>$', fontsize=20);"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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33nhDbRsNRVAQUFdHKYRGxsyiApgj9sV9pH+qq2m17+8v2hLtcLj2V1RUFD79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\nTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x2fcb290>"
       ]
      }
     ],
     "prompt_number": 51
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "If we are only interested in expectation values, we could pass a list of operators to the `mesolve` function that we want expectation values for, and have the solver compute then and store the results in the `Odedata` class instance that it returns.\n",
      "\n",
      "For example, to request that the solver calculates the expectation values for the operators $\\sigma_x, \\sigma_y, \\sigma_z$:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "result = mesolve(H, psi0, tlist, [], [sigmax(), sigmay(), sigmaz()])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 52
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Now the expectation values are available in `result.expect[0]`, `result.expect[1]`, and `result.expect[2]`:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "fig, axes = plt.subplots(1,1)\n",
      "\n",
      "axes.plot(tlist, result.expect[2], label=r'$\\left<\\sigma_z\\right>$')\n",
      "axes.plot(tlist, result.expect[1], label=r'$\\left<\\sigma_y\\right>$')\n",
      "axes.plot(tlist, result.expect[0], label=r'$\\left<\\sigma_x\\right>$')\n",
      "\n",
      "axes.set_xlabel(r'$t$', fontsize=20)\n",
      "axes.legend(loc=2);"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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WTp48iXXr1uHtt9/G448/rvPcFStW4MSJE0bbXgiNBqispMu2FyLVP1VJ25xG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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x2fbd290>"
       ]
      }
     ],
     "prompt_number": 53
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Dissipative dynamics\n",
      "\n",
      "To add dissipation to a problem, all we need to do is to define a list of collapse operators to the call to the `mesolve` solver.\n",
      "\n",
      "A collapse operator is an operator that describes how the system is interacting with its environment. \n",
      "\n",
      "For example, consider a quantum harmonic oscillator with Hamiltonian \n",
      "\n",
      "$H = \\hbar\\omega a^\\dagger a$\n",
      "\n",
      "and which loses photons to its environment with a relaxation rate $\\kappa$. The collapse operator that describes this process is \n",
      "\n",
      "$\\sqrt{\\kappa} a$\n",
      "\n",
      "since $a$ is the photon annihilation operator of the oscillator. \n",
      "\n",
      "To program this problem in QuTiP:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "w = 1.0               # oscillator frequency\n",
      "kappa = 0.1           # relaxation rate\n",
      "a = destroy(10)       # oscillator annihilation operator\n",
      "rho0 = fock_dm(10, 5) # initial state, fock state with 5 photons\n",
      "H = w * a.dag() * a   # Hamiltonian\n",
      "\n",
      "# A list of collapse operators\n",
      "c_ops = [sqrt(kappa) * a]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 54
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "tlist = np.linspace(0, 50, 100)\n",
      "\n",
      "# request that the solver return the expectation value of the photon number state operator a.dag() * a\n",
      "result = mesolve(H, rho0, tlist, c_ops, [a.dag() * a]) "
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 55
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "fig, axes = plt.subplots(1,1)\n",
      "axes.plot(tlist, result.expect[0])\n",
      "axes.set_xlabel(r'$t$', fontsize=20)\n",
      "axes.set_ylabel(r\"Photon number\", fontsize=16);"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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qACJBJivLFIKvv4Zdu8zxr3+ZpbB/+lNo394sf132aNZMrQa5kAqASIjIzYXd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\nUCoAIiIOpQIgIuJQKgAiIg71/0KJNU+mXP0jAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x3113a90>"
       ]
      }
     ],
     "prompt_number": 56
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Software versions"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from qutip.ipynbtools import version_table\n",
      "\n",
      "version_table()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "html": [
        "<table><tr><th>Software</th><th>Version</th></tr><tr><td>Cython</td><td>0.20.1</td></tr><tr><td>SciPy</td><td>0.13.3</td></tr><tr><td>QuTiP</td><td>3.0.0.dev-927c867</td></tr><tr><td>Python</td><td>2.7.5+ (default, Feb 27 2014, 19:37:08) \n",
        "[GCC 4.8.1]</td></tr><tr><td>IPython</td><td>2.0.0</td></tr><tr><td>OS</td><td>posix [linux2]</td></tr><tr><td>Numpy</td><td>1.8.1</td></tr><tr><td>matplotlib</td><td>1.3.1</td></tr><tr><td colspan='2'>Wed Jul 02 15:30:51 2014 JST</td></tr></table>"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 57,
       "text": [
        "<IPython.core.display.HTML at 0x3104390>"
       ]
      }
     ],
     "prompt_number": 57
    }
   ],
   "metadata": {}
  }
 ]
}