Minor demo fixes (#24)

demos/qiskit_patterns/2_qiskit_patterns.ipynb

@@ -7,8 +7,7 @@
    "source": [
     "# Scaling Quantum Optimization with Qiskit Patterns\n",
     "\n",
-    "In this how-to we will learn about Qiskit Patterns and quantum approximate optimization. Qiskit Patterns define a four-step process for running algorithms on a quantum computer:\n",
-    "\n",
+    "In this how-to we will learn about Qiskit Patterns and quantum approximate optimization. A Qiskit Pattern is an intuitive, repeatable set of steps for implementing a quantum computing workflow: \n",
     "\n",
     "<img src=\"imgs/patterns.png\" alt=\"Drawing\" style=\"float: left; width: 200px;\"/>\n",
     "\n",
@@ -48,7 +47,7 @@
    "id": "74b92ba5-c48a-405c-9c4b-04e985a7afbc",
    "metadata": {},
    "source": [
-    "Max-Cut is a hard to solve optimization problem with applications in clustering, network science, and statistical physics. The goal of this problem is to partition the nodes of a graph into to sets such that the number of edges traversed by this cut is maximum.\n",
+    "Max-Cut is a hard to solve optimization problem with applications in clustering, network science, and statistical physics. The goal of this problem is to partition the nodes of a graph into two sets such that the number of edges traversed by this cut is maximum.\n",
     "\n",
     "<img src=\"imgs/max-cut.png\" alt=\"Max-Cut\"/>"
    ]
@@ -171,7 +170,6 @@
     "H_C=\\sum_{ij}Q_{ij}Z_iZ_j + \\sum_i b_iZ_i.\n",
     "\\end{align}\n",
     "\n",
-    "<div class=\"alert alert-block alert-info\">\n",
     "First, a variable change, we convert the binary variables $x_i$ to variables $z_i\\in\\{-1, 1\\}$ by doing\n",
     "\n",
     "\\begin{align}\n",
@@ -195,10 +193,11 @@
     "\\begin{align}\n",
     "H_C=\\sum_{ij}Q_{ij}Z_iZ_j + \\sum_i b_iZ_i.\n",
     "\\end{align}\n",
-    "</div>\n",
     "\n",
-    "We refer to this Hamiltonian as the **cost function Hamiltonian**. It has the property that its gound state corresponds to the solution that **minimizes the cost function $f(x)$**.\n",
-    "Therefore, to solve our optimization problem we now need to prepare the ground state of $H_C$ (or a state with a high overlap with it) on the quantum computer. Then, sampling from this state will, with a high probability, yield the solution to $min f(x)$."
+    "<div class=\"alert alert-block alert-info\">\n",
+    "We refer to this Hamiltonian as the <b>cost function Hamiltonian</b>. It has the property that its gound state corresponds to the solution that <b>minimizes the cost function $f(x)$</b>.\n",
+    "Therefore, to solve our optimization problem we now need to prepare the ground state of $H_C$ (or a state with a high overlap with it) on the quantum computer. Then, sampling from this state will, with a high probability, yield the solution to $min~f(x)$.\n",
+    "</div>"
    ]
   },
   {
@@ -1362,7 +1361,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.9.7"
+   "version": "3.10.0"
   }
  },
  "nbformat": 4,