Fix/turtorials typo and bugs

[ahao27]

Description:

This pull request introduces a series of corrections of typo and clarifications to the documentation. These changes aim to enhance readability and accuracy across the documentation.

Changes:

1. Supported Quantum Circuit SDKs

• Added a note suggesting the inclusion of qutip as an additional quantum circuit SDK for broader coverage.

2. Building Quantum Circuits

• Updated section heading.

3. Hamiltonian Representation

• Clarified that Hamiltonians should be expressed algebraically by updating phrasing in the section.
  Capitalized "algebraically" for consistency.

4. Spelling Mistake

• Corrected typo: "exiternal" to "external."

5. In Quantum Alternating Operator Ansatz (QAOA) for Maxcut problem tutorial

• Added missing references: [1] and [2].
• Revised code comment for accuracy:
  Updated # Get exp(-i beta H_C) circuit without mixer circuit to # Get exp(-i gamma H_P) circuit without mixer circuit.

6. In QAOA for Graph Partitioning tutorial

• Fix the convergence issues with the minimize function in qiskit and quri-parts.

7. Quantum Approximation for the Vertex Cover

• Corrected comments in the code block within the section "Creating Problem Model using JijModeling" to focus on the vertex cover problem, removing references about coloring.
• Updated title: Changed "Vertex Cover Coloring" to "Vertex Cover Problem".

[Jacomichi]

Can you also add $i$ to the operators on this page?
$e^{-\beta H_M} \to e^{-i\beta H_M}$

[Jacomichi]

Can you also update the title to "Write Hamiltonian Algebraically"?

[ahao27]

Fixed

[Jacomichi]

Can you also add the link to the paper?

[ahao27]

Added

[ahao27]

Change

1. convergence of quick start
2. add 'pip install "qamomile[qutip]"' to the optional dependencies quickstart.html
3. Change command from 'pip install qamomile[qiskit]' to 'pip install "qamomile[qiskit]"'.
4. Can you remove -[Advanced Topic] in index.html

[Jacomichi]

I guess you might just have forgottten to commit the change.

[Jacomichi]

Can you update this part to pip install "qamomile[qiskit]"?

[Jacomichi]

I missed the convergence in the quickstart; however, @ahao27 fixed it.