Clean up tutorials

docs/tutorials/01_chemistry_hamiltonian.ipynb

@@ -317,9 +317,9 @@
    "source": [
     "First, we will transform the counts into a bitstring matrix and probability array for post-processing.\n",
     "\n",
-    "Each row in the matrix represents one unique bitstring. Since qubits are normally indexed from the right of a bitstring, column ``0`` represents qubit $N-1$, and column $N-1$ represents qubit ``0``, where $N$ is the number of qubits.\n",
+    "Each row in the matrix represents one unique bitstring. Since qubits are normally indexed from the right of a bitstring, column index ``0`` represents qubit ``N-1``, and column index ``N-1`` represents qubit ``0``, where ``N`` is the number of qubits.\n",
     "\n",
-    "The alpha particles are represented in the column range $[N / 2, N]$, and the beta particles are represented in the column range $[0, N / 2)$."
+    "The alpha particles are represented in the column range ``(N, N/2]``, and the beta particles are represented in the column range ``(N/2, 0]``."
    ]
   },
   {

docs/tutorials/02_qubit_hamiltonian.ipynb

@@ -8,7 +8,7 @@
     "\n",
     "In this tutorial we implement a [Qiskit pattern](https://docs.quantum.ibm.com/guides/intro-to-patterns) showing how to post-process quantum samples to approximate the minimum eigenvalue and spin-spin correlators for a ``22``-site XX-Z spin-1/2 chain. We will follow a sample-based quantum diagonalization approach [[1]](https://arxiv.org/abs/2405.05068).\n",
     "\n",
-    "While a Qiskit pattern typically involves 4 steps, the aim of this tutorial is to focus on the post-processing of the samples obtained from a quantum circuit whose support coincides with that of the ground state. Consequently, we generate a synthetic set of bitstrings to define the subspace and do not design an ansatz nor sample from a quantum circuit in this tutorial.\n",
+    "While a Qiskit pattern typically involves 4 steps, the aim of this tutorial is to focus on the post-processing of the samples obtained from a quantum circuit whose support coincides with that of the eigenstate corresponding to the minimum eigenvalue. Consequently, we generate a synthetic set of bitstrings to define the subspace and do not design an ansatz nor sample from a quantum circuit in this tutorial.\n",
     "\n",
     "The pattern we will implement is as follows:\n",
     "\n",
@@ -20,7 +20,7 @@
     "    - N/A: Will generate synthetic quantum samples\n",
     "4. **Step 4: Post-process results**\n",
     "   - Project the Hamiltonian onto the subspace spanned by the samples\n",
-    "   - Diagonalize the Hamiltonian in the subspace to approximate the ground state\n",
+    "   - Diagonalize the Hamiltonian in the subspace to approximate the minimum eigenstate\n",
     "   - Calculate spin-spin correlators for each site, $l$"
    ]
   },