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The quantum query complexity of approximating the median and related statistics
[article]
1998
arXiv
pre-print
Let X = (x_0,...,x_n-1) be a sequence of n numbers. For ϵ > 0, we say that x_i is an ϵ-approximate median if the number of elements strictly less than x_i, and the number of elements strictly greater than x_i are each less than (1+ϵ)n/2. We consider the quantum query complexity of computing an ϵ-approximate median, given the sequence X as an oracle. We prove a lower bound of Ω(1/ϵ,n) queries for any quantum algorithm that computes an ϵ-approximate median with any constant probability greater
arXiv:quant-ph/9804066v2
fatcat:sjur2nsdhjccbcdkgh6abaqd6e