copy edits of DC_QAOA and fixed broken link (#2467)

DCO Remediation Commit for Monica VanDieren <[email protected]>

I, Monica VanDieren <[email protected]>, hereby add my Signed-off-by to this commit: ab2cb59
I, Monica VanDieren <[email protected]>, hereby add my Signed-off-by to this commit: c2d0311

Signed-off-by: Monica VanDieren <[email protected]>

docs/sphinx/applications/python/digitized_counterdiabatic_qaoa.ipynb

@@ -8,7 +8,7 @@
     "\n",
     "Drugs often work by binding to an active site of a protein, inhibiting or activating its function for some therapeutic purpose. Finding new candidate drugs is extremely difficult. The study of molecular docking helps guide this search and involves the prediction of how strongly a certain ligand (drug) will bind to its target (usually a protein).  \n",
     "\n",
-    "One of the primary challenges to molecular docking arises from the many geometric degrees of freedom present in proteins and ligands, making it difficult to predict the optimal orientation and assess if the drug is a good candidate or not. One solution is to formulate the problem as a mathematical optimization problem where the optimal solution corresponds to the most likely ligand-protein configuration. This optimization problem can be solved on a quantum computer using methods like the Quantum Approximate Optimization Algorithm (QAOA). This tutorial demonstrates how this [paper](https://arxiv.org/pdf/2308.04098) used digitized-counteradiabatic (DC) QAOA to study molecular docking.  This tutorial assumes you have an understanding of QAOA, if not, please see the CUDA-Q MaxCut tutorial found [here](https://nvidia.github.io/cuda-quantum/latest/examples/python/tutorials/qaoa.html)\n",
+    "One of the primary challenges to molecular docking arises from the many geometric degrees of freedom present in proteins and ligands, making it difficult to predict the optimal orientation and assess if the drug is a good candidate or not. One solution is to formulate the problem as a mathematical optimization problem where the optimal solution corresponds to the most likely ligand-protein configuration. This optimization problem can be solved on a quantum computer using methods like the Quantum Approximate Optimization Algorithm (QAOA). This tutorial demonstrates how this [paper](https://arxiv.org/pdf/2308.04098) used digitized-counteradiabatic (DC) QAOA to study molecular docking.  This tutorial assumes you have an understanding of QAOA, if not, please see the CUDA-Q MaxCut tutorial found [here](https://nvidia.github.io/cuda-quantum/latest/applications/python/qaoa.html).\n",
     "\n",
     "The next section provides more detail on the problem setup followed by CUDA-Q implementations below."
    ]
@@ -25,10 +25,10 @@
     "\n",
     "\n",
     "There are 6 key steps:\n",
-    "1.  The experimental protein and ligand structures are determined and used to select pharmacores, or an important chemical group that will govern the chemical interactions,\n",
-    "2. T wo labeled distance graphs (LAGs) of size $N$ and $M$ represent the protein and the ligand, respectively. Each node corresponds to a pharmacore and each edge weight corresponds to the distance between pharmacores.\n",
+    "1.  The experimental protein and ligand structures are determined and used to select pharmacores, or an important chemical group that will govern the chemical interactions.\n",
+    "2. Two labeled distance graphs (LAGs) of size $N$ and $M$ represent the protein and the ligand, respectively. Each node corresponds to a pharmacore and each edge weight corresponds to the distance between pharmacores.\n",
     "3.  A $M*N$ node binding interaction graph (BIG) is created from the LAGs. Each node in the BIG graph corresponds to a pair of pharmacores, one from the ligand and the other from the protein. The existence of edges between nodes in the BIG graph are determined from the LAGs and correspond to interactions that can feesibly coexist. Therefore, cliques in the graph correspond to mutually possible interactions. \n",
-    "4. The problem is mapped to a QAOA circuit and corresponding Hamiltonian, and the ground state solution is determined.\n",
+    "4. The problem is mapped to a QAOA circuit and corresponding Hamiltonian. From there, the ground state solution is determined.\n",
     "5.  The ground state will produce the maximum weighted clique which corresponds to the best (most strongly bound) orientation of the ligand and protein.\n",
     "6.  The predicted docking structure is interpreted from the QAOA result and is used for further analysis.\n"
    ]
@@ -44,27 +44,28 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 1,
+   "execution_count": null,
    "metadata": {},
    "outputs": [],
    "source": [
     "import cudaq\n",
     "from cudaq import spin\n",
     "import numpy as np\n",
     "\n",
-    "# cudaq.set_target('nvidia')"
+    "cudaq.set_target('nvidia')\n",
+    "# cudaq.set_target('qpp-cpu') # Uncomment this line if no GPUs are available"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "The block below defines two of the BIG data sets from the paper. The first is a smaller example, but it can be swapped with the commented out example below at your discretion. The weights are specified for each node based on the nature of the ligand and protein pharmacores represented by the node"
+    "The block below defines two of the BIG data sets from the paper. The first is a smaller example, but it can be swapped with the commented out example below at your discretion. The weights are specified for each node based on the nature of the ligand and protein pharmacores represented by the node."
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 2,
+   "execution_count": null,
    "metadata": {},
    "outputs": [
     {
@@ -77,7 +78,7 @@
     }
    ],
    "source": [
-    "# The two graphs input from the paper\n",
+    "# The two graph inputs from the paper\n",
     "\n",
     "# BIG 1\n",
     "\n",
@@ -113,12 +114,12 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "Next, the Hamiltonian is constructed. \n",
+    "Next, the Hamiltonian is constructed: \n",
     "\n",
     "$$H = \\frac{1}{2}\\sum_{i \\in V}w_i(\\sigma^z_i - 1) + \\frac{P}{4} \\sum_{(i,j) \\notin E, i \\neq j} (\\sigma^z_i -1)(\\sigma^z_j - 1) $$\n",
     "\n",
     "\n",
-    "The first term concerns the vertices and the weights of the given pharmacores.  The second term is a penalty term that penalizes edges of the graph with no interactions.  The penalty $P$ is set by the user and is defined as 6 in the cell above. The function below returns the Hamiltonina as a CUDA-Q `spin_op` object.\n",
+    "The first term concerns the vertices and the weights of the given pharmacores.  The second term is a penalty term that penalizes edges of the graph with no interactions.  The penalty $P$ is set by the user and is defined as 6 in the cell above. The function below returns the Hamiltonian as a CUDA-Q `spin_op` object.\n",
     "\n"
    ]
   },
@@ -208,7 +209,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "The kernel below defines a DC-QAOA circuit.  What makes the approach \"DC\" is the inclusion of additional counteradiabatic terms to better drive the optimization to the ground state. These terms are digitized and applied as additional operations following each QAOA layer.  The increase in parameters is hopefully offset by requiring fewer layers. In this example, the DC terms are additional parameterized $Y$ operations applied to each qubit. These can be commented out to run conventional QAOA."
+    "The kernel below defines a DC-QAOA circuit.  What makes the approach \"DC\" is the inclusion of additional counteradiabatic terms to better drive the optimization to the ground state. These terms are digitized and applied as additional operations following each QAOA layer.  The increase in parameters is hopefully offset by requiring fewer layers. In this example, the DC terms are the additional parameterized $Y$ operations applied to each qubit. These can be commented out to run conventional QAOA."
    ]
   },
   {
@@ -246,7 +247,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "The classical optimizer for the QAOA procedure can be specified as one of the build in CUDA-Q optimizers, in this case Nelder Mead. The parameter count is defined for DC-QAOA, but can be swapped with the commented line below for conventional QAOA."
+    "The classical optimizer for the QAOA procedure can be specified as one of the built-in CUDA-Q optimizers, in this case Nelder Mead. The parameter count is defined for DC-QAOA, but can be swapped with the commented line below for conventional QAOA."
    ]
   },
   {