I was wondering if someone could explain to me what this technique called "block encoding" does, and what it is used for at a high level, found in arXiv:1806.01838.
It is in section 4.1, definition 43; shown below.
I encountered this topic while reading this (arXiv:2012.05460) paper, where it is mentioned just above lemma 7; shown below.
I am told that block encoding is used to reduce the 3D circuit down to a 2D circuit, by applying block encoding k times, to get the leading schmidt vector of this circuit. However, I'm not sure if this is the correct intuition, and I certainly don't understand the symbols in the definition of block encoding. If my question isn't really clear I'm happy to elaborate!