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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.


After several days of thinking and researching, I decided to answer my own question. N.B. The tensor product symbol $\otimes$ are omitted when there is no risk in confusion, especially when the index is different. In symbol, $$ A_iB_j = A_i \otimes B_j (i \neq j). $$ Firstly, for case $$e^{i \beta B} Z_i Z_j e^{-i \beta B},$$ we only consider qubit $j$, in ...

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