# Commits

committed cef1a37

Fixed a few typos here and there

• Participants
• Parent commits 86ed7c8
• Branches master

# File docs/notebooks/demo.ipynb

      "cell_type": "markdown",
      "metadata": {},
      "source": [
-      "The central data structure underlying most of QuTiP is a class called qutip.Qobj.  A Qobj can be used to represent either a bra/ket state vector, *or* a quantum operator.  All of these are represented internally by sparse matrices (for example a ket vector is just an $n \\times 1$ sparse matrix, while operators are $n \\times n$ where $n$ is the size of the Hilbert space that we're operating on).  Vectors and operators can be instantiated in many different ways in QuTiP, but the simplest is just to explicitly state their elements in some basis.  For example to create a 4-dimensional bra vector:"
+      "The central data structure underlying most of QuTiP is a class called qutip.Qobj.  A Qobj can be used to represent either a *bra/ket* state vector, *or* a quantum operator.  All of these are represented internally by sparse matrices (for example a *ket* vector is just an $n \\times 1$ sparse matrix, while operators are $n \\times n$ where $n$ is the size of the Hilbert space that we're operating on).  Vectors and operators can be instantiated in many different ways in QuTiP, but the simplest is just to explicitly state their elements in some basis.  For example to create a 2-dimensional *bra* vector:"
      ]
     },
     {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
-      "QuTiP tells us that this particular Qobj represents a bra (due to its shape) and displays its elements.  We can easily get the corresponding ket vector using the Qobj.dag() method:"
+      "QuTiP tells us that this particular Qobj represents a bra (due to its shape) and displays its elements.  We can easily get the corresponding *ket* vector using the Qobj.dag() method:"
      ]
     },
     {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
-      "QuTiP recognizes that as an $n \\times n$ matrix this Qobj represents an operator.  It also tells use automatically that it is Hermitian (it does not, however, mention whether it is unitary but non-Hermitian).  Operators can operate on a state using Python's standard multiplication operator *, producing a new ket vector:"
+      "QuTiP recognizes that being an $n \\times n$ matrix this Qobj represents an operator.  It also automatically makes note that it is Hermitian (it does not, however, mention whether it is unitary but non-Hermitian).  Operators can operate on a state using Python's standard multiplication operator *, producing a new *ket* vector:"
      ]
     },
     {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
-      "This is fairly straightforward if you are already familiar with the circuit being implemented, but I found it difficult, just be looking at the code (without the circuit diagram) to understand wha tthis is doing.  Now we can apply this circuit to the input $|0\\rangle |1\\rangle$ by applying the circuit as an operator..."
+      "This is fairly straightforward if you are already familiar with the circuit being implemented; but I found it difficult, just be looking at the code (without the circuit diagram) to understand what this is doing.  Now we can apply this circuit to the input $|0\\rangle |1\\rangle$ by applying the circuit as an operator..."
      ]
     },
     {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
-      "Alternatively, one can provide a single integer, and a state will be returned that can represent that integer in the smallest required number of qubits:"
+      "Alternatively, one can provide a single integer, and a state is created that represents that integer in the smallest required number of qubits:"
      ]
     },
     {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
-      "To represent an integer (say, 3) in a larger space of more than 2 qubits one can manually specify the n_qubits= argument.  When using this option the bit string representation is always used as it is less ambiguous (though this may not scale well with larger integers; a still have as a \"todo\" item to find a resolution to that problem):"
+      "To represent an integer (say, 3) in a larger space of more than 2 qubits one can manually specify the n_qubits= argument.  When using this option the bit string representation is always used as it is less ambiguous (though this may not scale well with larger integers; I still have as a \"todo\" item to find a resolution to that problem):"
      ]
     },
     {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
-      "As with the Bra and Ket classes it is backed by a Qobj with all its capabilities:"
+      "As with the Bra and Ket classes it is backed by a fully-capable Qobj:"
      ]
     },
     {
      "cell_type": "code",
      "collapsed": false,
      "input": [
-      "o = Operator([[1, 2],\n",
+      "O = Operator([[1, 2],\n",
       "              [3, 4]], name='O')\n",
-      "o"
+      "O"
      ],
      "language": "python",
      "metadata": {},
       {
        "metadata": {},
        "output_type": "pyout",
-       "prompt_number": 30,
+       "prompt_number": 32,
        "text": [
         "1.0"
        ]
       }
      ],
-     "prompt_number": 30
+     "prompt_number": 32
     },
     {
      "cell_type": "markdown",
      "metadata": {},
      "outputs": [
       {
-       "ename": "NameError",
-       "evalue": "global name 'oper' is not defined",
-       "output_type": "pyerr",
-       "traceback": [
-        "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m\n\u001b[1;31mNameError\u001b[0m                                 Traceback (most recent call last)",
-        "\u001b[1;32m<ipython-input-31-c1f59c35ba19>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m()\u001b[0m\n\u001b[1;32m----> 1\u001b[1;33m \u001b[0mKet\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m0\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m|\u001b[0m\u001b[0mBra\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m0\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m",
-        "\u001b[1;32m/home/iguananaut/src/pyqc/pyqc/braket.pyc\u001b[0m in \u001b[0;36m__or__\u001b[1;34m(self, other)\u001b[0m\n\u001b[0;32m    142\u001b[0m         \u001b[1;32melif\u001b[0m \u001b[0mresult\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mshape\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;36m0\u001b[0m\u001b[1;33m]\u001b[0m \u001b[1;33m==\u001b[0m \u001b[0mresult\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mshape\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    143\u001b[0m             \u001b[1;31m# Otherwise return a non-scalar operator\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 144\u001b[1;33m             \u001b[1;32mreturn\u001b[0m \u001b[0mOperator\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0moper\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    145\u001b[0m         \u001b[1;32melse\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    146\u001b[0m             \u001b[1;31m# This could be a bra times an operator which would return a bra\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
-        "\u001b[1;31mNameError\u001b[0m: global name 'oper' is not defined"
+       "latex": [
+        "$$\\begin{pmatrix}1.0 & 0.0\\\\0.0 & 0.0\\\\\\end{pmatrix}$$"
+       ],
+       "metadata": {},
+       "output_type": "pyout",
+       "prompt_number": 33,
+       "text": [
+        "Operator([[ 1.  0.]\n",
+        "          [ 0.  0.]])"
        ]
       }
      ],
-     "prompt_number": 31
+     "prompt_number": 33
     },
     {
      "cell_type": "markdown",
        ],
        "metadata": {},
        "output_type": "pyout",
-       "prompt_number": 32,
+       "prompt_number": 34,
        "text": [
         "Operator([[ 1.  1.]\n",
         "          [ 2.  2.]],\n",
        ]
       }
      ],
-     "prompt_number": 32
+     "prompt_number": 34
     },
     {
      "cell_type": "code",
        "output_type": "display_data"
       }
      ],
-     "prompt_number": 33
+     "prompt_number": 35
     },
     {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
-      "Note that this means we do have to use the * operator even when the context is unambiguous, where as sometimes in equations the $\\otimes$ symbol can be dropped.  For example it is common to write the tensor product of two vectors like $|0\\rangle|0\\rangle$.  But with PyQC it is necessary to write:"
+      "Note that this means we do have to use the * operator even when the context is unambiguous, whereas sometimes in equations the $\\otimes$ symbol can be dropped.  For example it is common to write the tensor product of two vectors like $|0\\rangle|0\\rangle$.  But with PyQC it is necessary to write:"
      ]
     },
     {
        ],
        "metadata": {},
        "output_type": "pyout",
-       "prompt_number": 34,
+       "prompt_number": 36,
        "text": [
         "Ket(0, 0)"
        ]
       }
      ],
-     "prompt_number": 34
+     "prompt_number": 36
     },
     {
      "cell_type": "markdown",
        ],
        "metadata": {},
        "output_type": "pyout",
-       "prompt_number": 35,
+       "prompt_number": 37,
        "text": [
         "Quantum object: dims = [[2], [1]], shape = [2, 1], type = ket\n",
         "Qobj data =\n",
        ]
       }
      ],
-     "prompt_number": 35
+     "prompt_number": 37
     },
     {
      "cell_type": "markdown",
        "output_type": "pyerr",
        "traceback": [
         "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m\n\u001b[1;31mValueError\u001b[0m                                Traceback (most recent call last)",
-        "\u001b[1;32m<ipython-input-36-ea3a9f20b444>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m()\u001b[0m\n\u001b[0;32m      1\u001b[0m Gate([[1, 2],\n\u001b[1;32m----> 2\u001b[1;33m       [3, 4]])\n\u001b[0m",
+        "\u001b[1;32m<ipython-input-38-ea3a9f20b444>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m()\u001b[0m\n\u001b[0;32m      1\u001b[0m Gate([[1, 2],\n\u001b[1;32m----> 2\u001b[1;33m       [3, 4]])\n\u001b[0m",
         "\u001b[1;32m/home/iguananaut/src/pyqc/pyqc/operator.pyc\u001b[0m in \u001b[0;36m__call__\u001b[1;34m(cls, *args, **kwargs)\u001b[0m\n\u001b[0;32m     71\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     72\u001b[0m         \u001b[0margs\u001b[0m \u001b[1;33m=\u001b[0m \u001b[1;33m(\u001b[0m\u001b[0mqobj\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;33m)\u001b[0m \u001b[1;33m+\u001b[0m \u001b[0margs\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m---> 73\u001b[1;33m         \u001b[0minst\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mcls\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m__new__\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mcls\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m*\u001b[0m\u001b[0margs\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m     74\u001b[0m         \u001b[0minst\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m__init__\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m*\u001b[0m\u001b[0margs\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     75\u001b[0m         \u001b[1;32mreturn\u001b[0m \u001b[0minst\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
         "\u001b[1;32m/home/iguananaut/src/pyqc/pyqc/operator.pyc\u001b[0m in \u001b[0;36m__new__\u001b[1;34m(cls, *args, **kwargs)\u001b[0m\n\u001b[0;32m    252\u001b[0m             raise ValueError(\n\u001b[0;32m    253\u001b[0m                 \u001b[1;34m'Input matrix for {0} must be a 2^n x 2^n unitary:\\n'\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 254\u001b[1;33m                 '{1}'.format(cls.__name__, qobj))\n\u001b[0m\u001b[0;32m    255\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    256\u001b[0m         \u001b[1;32mreturn\u001b[0m \u001b[0msuper\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mOperator\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mcls\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m__new__\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mcls\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m*\u001b[0m\u001b[0margs\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
         "\u001b[1;31mValueError\u001b[0m: Input matrix for Gate must be a 2^n x 2^n unitary:\nQuantum object: dims = [[2], [2]], shape = [2, 2], type = oper, isherm = False\nQobj data =\n[[ 1.  2.]\n [ 3.  4.]]"
        ]
       }
      ],
-     "prompt_number": 36
+     "prompt_number": 38
     },
     {
      "cell_type": "code",
        "output_type": "pyerr",
        "traceback": [
         "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m\n\u001b[1;31mValueError\u001b[0m                                Traceback (most recent call last)",
-        "\u001b[1;32m<ipython-input-37-8ce006854f8b>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m()\u001b[0m\n\u001b[0;32m      1\u001b[0m Gate([[1, 0, 0],\n\u001b[0;32m      2\u001b[0m       \u001b[1;33m[\u001b[0m\u001b[1;36m0\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;36m1\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;36m0\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m----> 3\u001b[1;33m       [0, 0, 1]])\n\u001b[0m",
+        "\u001b[1;32m<ipython-input-39-8ce006854f8b>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m()\u001b[0m\n\u001b[0;32m      1\u001b[0m Gate([[1, 0, 0],\n\u001b[0;32m      2\u001b[0m       \u001b[1;33m[\u001b[0m\u001b[1;36m0\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;36m1\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;36m0\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m----> 3\u001b[1;33m       [0, 0, 1]])\n\u001b[0m",
         "\u001b[1;32m/home/iguananaut/src/pyqc/pyqc/operator.pyc\u001b[0m in \u001b[0;36m__call__\u001b[1;34m(cls, *args, **kwargs)\u001b[0m\n\u001b[0;32m     71\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     72\u001b[0m         \u001b[0margs\u001b[0m \u001b[1;33m=\u001b[0m \u001b[1;33m(\u001b[0m\u001b[0mqobj\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;33m)\u001b[0m \u001b[1;33m+\u001b[0m \u001b[0margs\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m---> 73\u001b[1;33m         \u001b[0minst\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mcls\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m__new__\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mcls\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m*\u001b[0m\u001b[0margs\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m     74\u001b[0m         \u001b[0minst\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m__init__\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m*\u001b[0m\u001b[0margs\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     75\u001b[0m         \u001b[1;32mreturn\u001b[0m \u001b[0minst\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
         "\u001b[1;32m/home/iguananaut/src/pyqc/pyqc/operator.pyc\u001b[0m in \u001b[0;36m__new__\u001b[1;34m(cls, *args, **kwargs)\u001b[0m\n\u001b[0;32m    252\u001b[0m             raise ValueError(\n\u001b[0;32m    253\u001b[0m                 \u001b[1;34m'Input matrix for {0} must be a 2^n x 2^n unitary:\\n'\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 254\u001b[1;33m                 '{1}'.format(cls.__name__, qobj))\n\u001b[0m\u001b[0;32m    255\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    256\u001b[0m         \u001b[1;32mreturn\u001b[0m \u001b[0msuper\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mOperator\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mcls\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m__new__\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mcls\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m*\u001b[0m\u001b[0margs\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
         "\u001b[1;31mValueError\u001b[0m: Input matrix for Gate must be a 2^n x 2^n unitary:\nQuantum object: dims = [[3], [3]], shape = [3, 3], type = oper, isherm = True\nQobj data =\n[[ 1.  0.  0.]\n [ 0.  1.  0.]\n [ 0.  0.  1.]]"
        ]
       }
      ],
-     "prompt_number": 37
+     "prompt_number": 39
     },
     {
      "cell_type": "markdown",
       {
        "metadata": {},
        "output_type": "pyout",
-       "prompt_number": 38,
+       "prompt_number": 40,
        "text": [
         "pyqc.operator.Gate"
        ]
       }
      ],
-     "prompt_number": 38
+     "prompt_number": 40
     },
     {
      "cell_type": "markdown",
        ],
        "metadata": {},
        "output_type": "pyout",
-       "prompt_number": 39,
+       "prompt_number": 41,
        "text": [
         "Gate([[-1.  0.]\n",
         "      [ 0.  1.]],\n",
        ]
       }
      ],
-     "prompt_number": 39
+     "prompt_number": 41
     },
     {
      "cell_type": "markdown",
        ],
        "metadata": {},
        "output_type": "pyout",
-       "prompt_number": 40,
+       "prompt_number": 42,
        "text": [
         "Gate([[ 1.  0.]\n",
         "      [ 0. -1.]],\n",
        ]
       }
      ],
-     "prompt_number": 40
+     "prompt_number": 42
     },
     {
      "cell_type": "code",
        ],
        "metadata": {},
        "output_type": "pyout",
-       "prompt_number": 41,
+       "prompt_number": 43,
        "text": [
         "Gate([[ 0.70710678  0.70710678]\n",
         "      [ 0.70710678 -0.70710678]],\n",
        ]
       }
      ],
-     "prompt_number": 41
+     "prompt_number": 43
     },
     {
      "cell_type": "code",
        ],
        "metadata": {},
        "output_type": "pyout",
-       "prompt_number": 42,
+       "prompt_number": 44,
        "text": [
         "Gate([[  1.00000000e+00+0.j   0.00000000e+00+0.j]\n",
         "      [  0.00000000e+00+0.j   6.12303177e-17+1.j]],\n",
        ]
       }
      ],
-     "prompt_number": 42
+     "prompt_number": 44
     },
     {
      "cell_type": "code",
        ],
        "metadata": {},
        "output_type": "pyout",
-       "prompt_number": 43,
+       "prompt_number": 45,
        "text": [
         "CnotGate([[ 1.  0.  0.  0.]\n",
         "          [ 0.  1.  0.  0.]\n",
        ]
       }
      ],
-     "prompt_number": 43
+     "prompt_number": 45
     },
     {
      "cell_type": "markdown",
        "output_type": "display_data"
       }
      ],
-     "prompt_number": 44
+     "prompt_number": 46
     },
     {
      "cell_type": "code",
        ],
        "metadata": {},
        "output_type": "pyout",
-       "prompt_number": 45,
+       "prompt_number": 47,
        "text": [
         "Quantum object: dims = [[4], [1]], shape = [4, 1], type = ket\n",
         "Qobj data =\n",
        ]
       }
      ],
-     "prompt_number": 45
+     "prompt_number": 47
     },
     {
      "cell_type": "markdown",
       {
        "metadata": {},
        "output_type": "pyout",
-       "prompt_number": 46,
+       "prompt_number": 48,
        "text": [
         "-0.9999999999999996"
        ]
       }
      ],
-     "prompt_number": 46
+     "prompt_number": 48
     },
     {
      "cell_type": "markdown",
        ],
        "metadata": {},
        "output_type": "pyout",
-       "prompt_number": 47,
+       "prompt_number": 49,
        "text": [
         "Ket(1, 1)"
        ]
       }
      ],
-     "prompt_number": 47
+     "prompt_number": 49
     },
     {
      "cell_type": "markdown",
        ],
        "metadata": {},
        "output_type": "pyout",
-       "prompt_number": 48,
+       "prompt_number": 50,
        "text": [
         "Ket(1, 1)"
        ]
       }
      ],
-     "prompt_number": 48
+     "prompt_number": 50
     },
     {
      "cell_type": "markdown",
        "metadata": {},
        "output_type": "pyout",
        "png": "iVBORw0KGgoAAAANSUhEUgAAAJIAAABCBAMAAABOa5KSAAAAMFBMVEX///+qqqoyMjK6urrc3NwQ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\nWbkvevYc7xcSrO32HxDeqFdjYXuIAAAAAElFTkSuQmCC\n",
-       "prompt_number": 49,
+       "prompt_number": 51,
        "text": [
         "Gate([[ 0.70710678  0.          0.          0.70710678]\n",
         "      [ 0.70710678  0.          0.         -0.70710678]\n",
        ]
       }
      ],
-     "prompt_number": 49
+     "prompt_number": 51
     },
     {
      "cell_type": "markdown",
      "outputs": [
       {
        "latex": [
-        "$\\left|10\\right>$"
+        "$\\left|11\\right>$"
        ],
        "metadata": {},
        "output_type": "pyout",
-       "prompt_number": 50,
+       "prompt_number": 52,
        "text": [
-        "Ket(1, 0)"
+        "Ket(1, 1)"
        ]
       }
      ],
-     "prompt_number": 50
+     "prompt_number": 52
     },
     {
      "cell_type": "markdown",
      "language": "python",
      "metadata": {},
      "outputs": [],
-     "prompt_number": 51
+     "prompt_number": 53
     },
     {
      "cell_type": "markdown",
        "metadata": {},
        "output_type": "pyout",
        "png": "iVBORw0KGgoAAAANSUhEUgAAATIAAABoBAMAAACAimHTAAAAMFBMVEX///+qqqoyMjK6urrc3NwQ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\n",
-       "prompt_number": 52,
+       "prompt_number": 54,
        "text": [
         "Gate([[  3.53553391e-01+0.j           3.53553391e-01+0.j\n",
         "         3.53553391e-01+0.j           3.53553391e-01+0.j\n",
        ]
       }
      ],
-     "prompt_number": 52
+     "prompt_number": 54
     },
     {
      "cell_type": "markdown",
        ]
       }
      ],
-     "prompt_number": 53
+     "prompt_number": 55
     },
     {
      "cell_type": "markdown",
        ],
        "metadata": {},
        "output_type": "pyout",
-       "prompt_number": 54,
+       "prompt_number": 56,
        "text": [
         "Quantum object: dims = [[8], [1]], shape = [8, 1], type = ket\n",
         "Qobj data =\n",
        ]
       }
      ],
-     "prompt_number": 54
+     "prompt_number": 56
     },
     {
      "cell_type": "code",
        "output_type": "display_data",
        "png": 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        "text": [
-        "<matplotlib.figure.Figure at 0x3a72850>"
+        "<matplotlib.figure.Figure at 0x381f950>"
        ]
       }
      ],
-     "prompt_number": 55
+     "prompt_number": 57
     },
     {
      "cell_type": "markdown",
        "output_type": "display_data",
        "png": 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4BLGAXREN7yAYDkAsYHdEwxsIhs0RCzgF0XA/gmFjxAJOQzTcjWBY4LX81xp8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\nGAAAQwgGAMAQggEAMIRgAAAM+f+B10F64nM/GAAAAABJRU5ErkJggg==\n",
        "text": [
-        "<matplotlib.figure.Figure at 0x3ad6d50>"
+        "<matplotlib.figure.Figure at 0x3a82090>"
        ]
       }
      ],
-     "prompt_number": 56
+     "prompt_number": 58
     },
     {
      "cell_type": "markdown",
        "output_type": "display_data",
        "png": 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HLV4b1MG41AcHPtDzO5+/7K2rvffvVUx0zFWYDKGKYMAq98tcJa9NbvN1F7aaUpSi9f+9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\nrkJggg==\n",
        "text": [
-        "<matplotlib.figure.Figure at 0x41c4f50>"
+        "<matplotlib.figure.Figure at 0x40afed0>"
        ]
       }
      ],
-     "prompt_number": 57
+     "prompt_number": 59
     },
     {
      "cell_type": "markdown",
        "output_type": "display_data",
        "png": 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        "text": [
-        "<matplotlib.figure.Figure at 0x3ad6bd0>"
+        "<matplotlib.figure.Figure at 0x381f610>"
        ]
       }
      ],
-     "prompt_number": 58
+     "prompt_number": 60
     },
     {
      "cell_type": "code",
        "output_type": "display_data",
        "png": 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        "text": [
-        "<matplotlib.figure.Figure at 0x41c2bd0>"
+        "<matplotlib.figure.Figure at 0x40afed0>"
        ]
       }
      ],
-     "prompt_number": 59
+     "prompt_number": 61
     },
     {
      "cell_type": "markdown",
       "\n",
       "$R_k = \\left(\\matrix{1 & 0 \\cr 0 & e^{2\\pi i/2^k}}\\right)$\n",
       "\n",
-      "This is an example of a parameterized Gate.  One goal of PyQC that I have not yet implemented is an interface for easily defining custom parameterized gates, but R_k should give a flavor of how they would work.  By default R_k is evaluated with $k = 0$:"
+      "This is an example of a parameterized Gate.  One goal of PyQC that I have not yet implemented is an interface for easily defining custom parameterized gates, but R_k should give a flavor of how they would work.  By default R_k is equivalent to $R_0$:"
      ]
     },
     {
        ],
        "metadata": {},
        "output_type": "pyout",
-       "prompt_number": 60,
+       "prompt_number": 62,
        "text": [
         "RkGate([[ 1. +0.00000000e+00j  0. +0.00000000e+00j]\n",
         "        [ 0. +0.00000000e+00j  1. -2.44921271e-16j]],\n",
        ]
       }
      ],
-     "prompt_number": 60
+     "prompt_number": 62
     },
     {
      "cell_type": "markdown",
        ],
        "metadata": {},
        "output_type": "pyout",
-       "prompt_number": 61,
+       "prompt_number": 63,
        "text": [
         "RkGate([[  1.00000000e+00+0.j   0.00000000e+00+0.j]\n",
         "        [  0.00000000e+00+0.j   6.12303177e-17+1.j]],\n",
        ]
       }
      ],
-     "prompt_number": 61
+     "prompt_number": 63
     },
     {
      "cell_type": "markdown",
      "language": "python",
      "metadata": {},
      "outputs": [],
-     "prompt_number": 62
+     "prompt_number": 64
     },
     {
      "cell_type": "code",
      "language": "python",
      "metadata": {},
      "outputs": [],
-     "prompt_number": 63
+     "prompt_number": 65
     },
     {
      "cell_type": "code",
        "metadata": {},
        "output_type": "pyout",
        "png": "iVBORw0KGgoAAAANSUhEUgAAAhoAAACNBAMAAAADa87HAAAAMFBMVEX///+qqqoyMjK6urrc3NwQ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\nAElFTkSuQmCC\n",
-       "prompt_number": 64,
+       "prompt_number": 66,
        "text": [
         "Gate([[  2.50000000e-01+0.j           2.50000000e-01+0.j\n",
         "         2.50000000e-01+0.j           2.50000000e-01+0.j\n",
        ]
       }
      ],
-     "prompt_number": 64
+     "prompt_number": 66
     },
     {
      "cell_type": "markdown",
        "output_type": "display_data",
        "png": 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WQsdjhU3iKhphvYTFbothZmAms3sTIbQPi8XCbNfZcLVwlUp7XYy6IHpJtNDe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\nmz9xvl9KQMGgHxQKCqKVQAD4P/lO6j4JLd3Z5+5rWRuvNhj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t47chpEWIzFWJJ7ptNAK9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\nCLGgUCCEEGJBoUAIIcTi/wG6p0LzvTs2dwAAAABJRU5ErkJggg==\n",
        "text": [
-        "<matplotlib.figure.Figure at 0x3ca2410>"
+        "<matplotlib.figure.Figure at 0x3a8c2d0>"
        ]
       }
      ],
-     "prompt_number": 65
+     "prompt_number": 67
     },
     {
      "cell_type": "markdown",