Classical Post-processing for Low-Depth Phase Estimation Circuits

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Traditionally, we use the quantum Fourier transform circuit (QFT) in order to perform quantum phase estimation, which has a number of useful applications.  The QFT circuit for a binary field generally consists controlled-rotation gates which, when removed, yields the lower-depth approximate QFT circuit.  It is known that a logarithmic-depth approximate QFT circuit is sufficient to perform phase estimation with a degree of accuracy negligibly lower than that of the full QFT.  However, when the depth of the AQFT circuit becomes even lower, the phase estimation procedure no longer produces results that are immediately correlated to the desired phase.  In this talk, I will explore the possibility of retrieving this information with classical analysis and with computer post-processing of the measured results of a low-depth AQFT circuit in a phase estimation algorithm.