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I would like to know more about quantum simulations, so as to start on a few standard physical models (maybe particle in a box, harmonic oscillator, etc.) and then build up on more complex things. But I find that the literature on this subject seems a bit scattered all over the place. I only know some guide lines, I know that I have to look into trotterization, VQE and (maybe?) QAOA. But is there a "place" or book that compiles all of it?

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This is somewhat late, but the Wikipedia page has aggregated some of the main techniques for quantum Hamiltonian simulation.

If you're looking for a bit more of a walkthrough (over scientific papers), Microsoft provides a good overview of both Trotteriation / Qubitization. IBM also talks about VQEs.

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