2.12 - Implementation Details – invQFT & Phase Kickback

The lecture slides are available here Download here.

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Phase estimation allows us to determine the eigenphase associated with a specific eigenstate, and while it's typically used when we know the eigenstate, its real power lies in working with superpositions of eigenstates. We can extract a superposition of their associated eigenphases by inputting a superposition of eigenstates.

The lecture highlights the importance of the inverse Quantum Fourier Transform (invQFT) in reading out eigenphases, as it transforms phase differences into readable amplitudes.

It also covers the concept of conditional rotation and phase kick-back, which enables multiple rotations based on the binary representation of a chosen integer, enhancing the precision of eigenphase extraction. In conclusion, QPE leverages phase kickback, controlled unitaries, and invQFT to extract global phase information from a quantum register and present it in a readable format.