Phase kickback is a subtle yet powerful concept that is at the heart of many quantum algorithms. Here we show how it works by way of a simple example: two uses of the quantum phase estimation algorithm, which has phase kickback as an essential subroutine, and the Hadamard test for computing expectation values.
Also included are classical methods using numpy for obtaining the same values using “classical” computations that do not scale to larger system sizes, an issue the quantum solutions do not suffer from.
Image credits: M Reiher et al, PNAS 114, 7555 (2017) & ZY Meng et al, Nature 464, 847 (2010)
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