MÖBIUS TRANSFORMATIONS IN QUANTUM AMPLITUDE AMPLIFICATION WITH GENERALIZED PHASES
César Bautista-Ramos, Nora Castillo-Tépox · International Journal of Quantum Information · 2010
The iteration of the operators employed in quantum amplitude amplification with generalized phases is analyzed by using elementary properties (geometric and algebraic) of the Möbius transformations (fractional linear transformations). It is shown that, for a given quantum algorithm without measurement, which produces a good state with probability a of success, if the phase angles φ and ϕ which mark the good and initial states respectively satisfy φ = ϕ with a small enough, then, for a number n of iterations with [Formula: see text] we get an error probability that is at most O(aϕ2).