andrewmusselman commented on code in PR #472:
URL: https://github.com/apache/mahout/pull/472#discussion_r1842930573


##########
examples/Simple_Example.ipynb:
##########
@@ -29,7 +29,7 @@
   {
    "cell_type": "code",
    "source": [
-    "!pip install git+https://github.com/apache/mahout.git@main";
+    "# pip install git+https://github.com/apache/mahout.git@main";

Review Comment:
   Is this supposed to be commented out?



##########
examples/Optimization_Example.ipynb:
##########
@@ -0,0 +1,144 @@
+{

Review Comment:
   Does this need an "Open in Colab" button?



##########
examples/Optimization_Example.ipynb:
##########
@@ -0,0 +1,144 @@
+{
+ "nbformat": 4,
+ "nbformat_minor": 2,
+ "cells": [
+  {
+   "cell_type": "code",
+   "source": [
+    "# pip install git+https://github.com/apache/mahout.git@main";
+   ],
+   "metadata": {
+    "colab": {
+     "base_uri": "https://localhost:8080/";
+    },
+    "id": "lNDTZhztd2dp",
+    "outputId": "ea3b9e41-43a8-44e7-9daf-e62e71d93143"
+   },
+   "execution_count": null,
+   "outputs": []
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# Quantum Circuit Parameterization and Optimization\n",
+    "\n",
+    "In this notebook, we'll explore how to create parameterized quantum 
circuits using the QuMat framework. This feature allows us to bind values to 
parameters at execution time, paving the way for optimization tasks in quantum 
computing.\n",
+    "\n",
+    "## Overview\n",
+    "\n",
+    "1. **Parameter Handling**: We will use symbols to represent parameters in 
quantum gates, allowing these parameters to be updated during optimization.\n",
+    "2. **Circuit Execution with Binding**: We will bind parameter values to a 
circuit prior to its execution, a critical step in parameter optimization 
routines.\n",
+    "3. **Simple Optimization Loop**: We'll implement a basic optimization 
loop that updates parameters based on a cost function.\n"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Step 1: Setting Up\n",
+    "\n",
+    "We start by setting up the backend configuration and initializing the 
QuMat framework. This framework interfaces with quantum computing libraries 
like Qiskit or Cirq to manage the underlying quantum computations.\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "from qumat.qumat import QuMat\n",
+    "\n",
+    "# Configure the backend to use Qiskit with a simulator\n",
+    "backend_config = {\n",
+    "    'backend_name': 'qiskit',\n",
+    "    'backend_options': {'simulator_type': 'qasm_simulator', 'shots': 
1024}\n",
+    "}\n",
+    "\n",
+    "# Create an instance of QuMat\n",
+    "qumat_instance = QuMat(backend_config)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Step 2: Creating a Parameterized Quantum Circuit\n",
+    "\n",
+    "We create a simple quantum circuit with one qubit and apply parameterized 
RX, RY, and RZ gates. The parameters will be defined symbolically, allowing 
them to be replaced with actual values during execution.\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# Create a quantum circuit with 1 qubit\n",
+    "qumat_instance.create_empty_circuit(1)\n",
+    "\n",
+    "# Apply parameterized RX, RY, and RZ gates\n",
+    "qumat_instance.apply_rx_gate(0, 'theta')\n",

Review Comment:
   I don't see where `theta`, `phi`, and `lambda` are defined, should we add 
those definitions?



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