title: Optimal quantum circuits for general phase estimation.
abstract: We address the problem of estimating the phase phi given N copies of the phase-rotation gate uphi. We consider, for the first time, the optimization of the general case where the circuit consists of an arbitrary input state, followed by any arrangement of the N phase rotations interspersed with arbitrary quantum operations, and ending with a general measurement. Using the polynomial method, we show that, in all cases where the measure of quality of the estimate phi for phi depends only on the difference phi-phi, the optimal scheme has a very simple fixed form. This implies that an optimal general phase estimation procedure can be found by just optimizing the amplitudes of the initial state.
authors.affiliation: Departments of Computer Science and Physics, University of California, Santa Barbara, Santa Barbara, California 93106-5110, USA.
authors.forename: Wim
authors.initials: W
authors.lastname: van Dam
authors.forename: G Mauro
authors.initials: GM
authors.lastname: D'Ariano
authors.forename: Artur
authors.initials: A
authors.lastname: Ekert
authors.forename: Chiara
authors.initials: C
authors.lastname: Macchiavello
authors.forename: Michele
authors.initials: M
authors.lastname: Mosca