Update Hamiltonian simulation compilation tutorial to new template

[henryzou50]

Summary

Revised compilation-methods-for-hamiltonian-simulation-circuits.ipynb to follow the Tutorial_Template structure, focusing exclusively on benchmarking SABRE, AI transpiler, and Rustiq compilation methods on Hamiltonian simulation circuits from the Hamlib collection.

Key changes from the old notebook:

• Removed EfficientSU2 section: The old notebook started with a separate Part 1 using efficient_su2 circuits. The revised version focuses entirely on Hamlib Hamiltonian simulation circuits built with PauliEvolutionGate
• Split benchmarks by scale: Circuits are now grouped into small-scale (<20 qubits) and large-scale (>=20 qubits) with separate analysis for each
• Added circuit filtering: Filters out circuits exceeding backend qubit count or 5000 decomposed gates to keep benchmarks practical
• Added execution and fidelity testing: The old notebook had no execution ("focused on the transpilation process"). The revised version uses mirror circuits to measure survival probability on both an Aer simulator (small-scale) and real hardware (large-scale)
• Improved visualizations: Line charts by circuit index, % improvement over SABRE bar charts, and grouped bar charts for best-performing method with tie tracking
• Added quantitative analysis: Styled summary tables with mean/stdev and per-circuit comparison tables with best-value highlighting
• Updated dependencies: Bumped to Qiskit SDK v2.0+, added Qiskit Aer dependency, switched backend from ibm_torino to least_busy()
• Template compliance: Added learning outcomes, prerequisites, and structured background sections following the standard tutorial template

Tutorial structure:

• Small-scale example (<20 qubits): Full walkthrough with Aer simulator noise evaluation using mirror circuits and survival probability
• Large-scale example (>=20 qubits): Compressed workflow with real hardware submission and fidelity comparison across all three compilation methods

[qiskit-bot]

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

• @henryzou50
• @nathanearnestnoble

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