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I’m trying to understand and implement the amplitude amplification algorithm described in the HHL paper. I’m using the cirq implementation of the HHL algorithm as my starting point.

I have a couple of doubts with regard to this:

  1. The paper says the number of times the amplitude amplification procedure has to be applied to the HHL algorithm is and .

I’m unsure about how to calculate p˜ with regard to the cirq implementation. I’m also unclear as to how to find the functions f and g and the parameter λ˜. Could someone please help me understand this?

  1. With regard to the exact procedure to be used for amplitude amplification, the paper defines two new operators and

From what I understand, I need to loop over the HHL subroutine constantly applying an operator P = - RsuccRinit to it.

Could someone please explain how Rsucc and Rinit are described with respect to the cirq code? Can the P operator be expressed as another oracle?

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