Add tutorial: Compilation methods for Hamiltonian simulation circuits

[henryzou50]

Add tutorial: Compilation methods for Hamiltonian simulation circuits

This PR adds a new tutorial to the Qiskit documentation titled "Compilation methods for Hamiltonian simulation circuits" and addresses issue #3552

The notebook provides a comparative overview of three compilation methods in Qiskit for Hamiltonian simulation workloads:

• SABRE transpiler: Efficient routing and layout optimization.
• AI Transpiler: Intelligent, automated transpilation and synthesis for Pauli networks.
• Rustiq plugin: Precise and low-depth synthesis for PauliEvolutionGate operations used in Trotterized dynamics.

What the tutorial covers

• Compilation strategies for circuits relevant to quantum simulation.
• Depth and gate count comparisons across methods.
• Circuit examples created from Qiskit’s Patterns module.

Files added

• docs/tutorials/100_representative.json
• docs/tutorials/compilation-methods-for-hamiltonian-simulation-circuits.ipynb

Note: The location of 100_representative.json will likely need to be changed, as week as the notebook's reference of it. This json file is used as the file that contains the benchmarking circuits for Hamlib. What is the best location / most appropriate for this file?

Before finalizing this tutorial

• Add a survey link to the end of the notebook (support appreciated).
• Update notebook metadata and JSON headers to follow Qiskit documentation conventions (support appreciated).

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1 out of 2 committers have signed the CLA.

✅ abbycross
❌ henryzou50
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[qiskit-bot]

One or more of the following people are relevant to this code:

• @annaliese-estes
• @miamico

[abbycross]

Can we link to the SABRE deep-dive tutorial mentioned in the Compilation methods overview section? Or if it isn't published yet, we can add a note to that effect.