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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.

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I encountered this topic while reading this (arXiv:2012.05460) paper, where it is mentioned just above lemma 7; shown below.

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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!

epelaez
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chois3
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1 Answers1

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Block encoding is the framework or tool for developing a variety of quantum algorithms by encoding a matrix as a block of a unitary.There are various ways to implement the same as per requirement,one of the ways is by decomposing the matrices into linear combinations of displacement matrices.

Abhiprada Bera
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