Update notebook for consistency with website presentation

examples/16_FQAOA_example.ipynb

@@ -29,10 +29,10 @@
     "\n",
     "- Broad Applicability: The Hamiltonian design guideline benefits QAOA and extends to other algorithms like Grover adaptive search and quantum phase estimation, making it a versatile tool for solving constrained combinatorial optimization problems.\n",
     "\n",
-    "This notebook describes the implementation of FQAOA, illustrates its application through various examples, and provides insight into FQAOA's superior performance in constrained combinatorial optimization tasks.\n",
+    "This notebook describes the implementation of FQAOA, illustrates its application through an example portfolio optimization problem, and provides insight into FQAOA's superior performance in constrained combinatorial optimization tasks.\n",
     "\n",
     "### Quadratic Constrained Binary Optimization Problems\n",
-    "The constrained combinatorial optimization problem for a quadratic binary cost function　$C_{\\boldsymbol x}$ can be written in the following form：\n",
+    "The constrained combinatorial optimization problem for a quadratic binary cost function $C_{\\boldsymbol x}$ can be written in the following form：\n",
     "$${\\boldsymbol x}^* = \\arg \\min_{\\boldsymbol x} C_{\\boldsymbol x}\\qquad {\\rm s.t.} \\quad\\sum_{i=1}^{N} x_i = M,$$\n",
     "with bit string ${\\boldsymbol x}\\in \\{0,1\\}^N$, where ${\\boldsymbol x}^*$ is the optimal solution.\n",
     "This problem can be replaced by the minimum eigenvalue problem in the following steps.\n",
@@ -135,8 +135,8 @@
    "source": [
     "## Portfolio Optimization\n",
     "\n",
-    "In the following, the [portfolio optimization problem](https://en.wikipedia.org/wiki/Portfolio_optimization) is taken as a constrained quadratic optimisation problem.\n",
-    "Start by creating an instance of the portfolio optimisation problem, using the `random_instance` method of the `PortfolioOptimisation`."
+    "In the following, the [portfolio optimization problem](https://en.wikipedia.org/wiki/Portfolio_optimization) is taken as a constrained quadratic optimization problem.\n",
+    "Start by creating an instance of the portfolio optimization problem, using the `random_instance` method of the `PortfolioOptimization`."
    ]
   },
   {

examples/17_FQAOA_advanced_parameterization.ipynb

@@ -36,7 +36,7 @@
    "id": "bb6a05c9-82f7-431b-b60f-de61cd71d3cf",
    "metadata": {},
    "source": [
-    "Start by creating an instance of the portfolio optimisation problem, using the `random_instance` method of `the PortfolioOptimisation` class."
+    "Start by creating an instance of the portfolio optimization problem, using the `random_instance` method of the `PortfolioOptimization` class."
    ]
   },
   {
@@ -59,7 +59,7 @@
    "source": [
     "## Quantum Annealing with FQAOA\n",
     "\n",
-    "The framework of Fermionic QAOA (FQAOA) covers the Quantum Annealing (QA) framework [[1]](https://journals.aps.org/prresearch/pdf/10.1103/PhysRevResearch.5.023071). In this note, we demonstrate that QA with FQAOA works for constrained combinatorial optimisation problems in practice and compare its performance with QA with conventional QAOA [[2]](https://arxiv.org/pdf/quant-ph/0001106)."
+    "The framework of Fermionic QAOA (FQAOA) covers the Quantum Annealing (QA) framework [[1]](https://journals.aps.org/prresearch/pdf/10.1103/PhysRevResearch.5.023071). In this note, we demonstrate that QA with FQAOA works for constrained combinatorial optimization problems in practice and compare its performance with QA with conventional QAOA [[2]](https://arxiv.org/pdf/quant-ph/0001106)."
    ]
   },
   {