Hamiltonian simulation guide

[alexandre-ricardo]

Adding a first draft for the Hamiltonian Simulation guide. Not yet finished.

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[EdenSchirmanClassiq]

@alexandre-ricardo Great tutorial! Super insightful and concise, well done!

A few notes that we will speak in our meeting:

• At the beggining, add: Additiona methods of QSVT and ... are briefley stated and referenced.
• Trotterization
• 1st order general, 2nd order example - I would go with the general and the simplest example in both. Or just general, and the in the example to cover the 1st and 2nd order examples.
• Evolution coefficient - explanation, how to choose
• Exponentiation with depth constraint
• depth of the circuit?
• can we extract the order?
• qdrift
• The 3 dots I would explain the algorithm a bit more
• Block encoded HAmiltonians
• A bit more explanations. Why necessity?
• qubitization: why only walk operator?
• Example
• Why '11' different case? add comment..
• qdrift - haven't you said something statistical?
• Exercise, I'm not sure I understood - to apply the methods for the tutorial?
• I like the idea of a molecule, I would do estimation of some interesting operator at different times.