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3

HHL is more popular because it is much older (and it was the first in its category). The CKS algorithm (which you've been calling the Childs algorithm, even though the paper had three equally contributing authors in alphabetical order) is simply an improvement to the HHL algorithm in terms of its computational complexity. The reason you haven't seen it being ...

1

After some research I found an illustrating example on how QPE is used for simulation of many-body systems. The idea is the following: Start with a (possibly time dependent) Hamiltonian $H$ of a many-body system, e.g. a molecular system. The evolution operator then reads: $$U = \mathrm{e}^{-{\rm i}Ht}.$$ Use Trotter decomposition so as to break this ...

2

I generally think of it the other way around. Simulating dynamics (ie. evolving a system in time) is used in Quantum Phase Estimation (QPE). That is, the $U$ appearing in QPE is the time-evolution operator $U=e^{-iHt}$, where $H$ is the Hamiltonian of the system. Part of the QPE protocol requires implementing $U^k$ for increasing powers $k$. This reduces to ...

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