Matched-multiphase Grover algorithm for a small number of marked states

Recently, we proposed a multiphase-matching method for the Grover algorithm with a matching rule for multiple phases αj and βj, j=1,…,k, where k is the number of Grover operations. The phases are matched such that αj=−βk−j+1 globally over a sequence of k Grover operations. The success probability P6(λ) for k=6 was found to be almost constant and unity over a wide range of λ, i.e., 0.10777⩽λ⩽1, where λ is the fraction of marked items in a …