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- W2024588775 abstract "Abstract We prove that, to compute a total Boolean function f on N variables with bounded error probability, any quantum black-box algorithm has to query at least Ω(ρ f N)=Ω( S f ) times, where ρ f is the average influence of variables in f , and S f is the average sensitivity. It is interesting to contrast this result with the known lower bound of Ω( S f ) , where S f is the sensitivity. This lower bound is tight for some functions. We also show for any polynomial f that approximates f , deg ( f )=Ω(ρ f N)=Ω( S f ) . For some functions, this bound is better than the previously known lower bound of Ω( BS f ) , where BS f is the block sensitivity. Our technique may be of interest in itself: by applying Fourier analysis to functions mapping {0,1} N to unit vectors in a Hilbert space, we can write the state of the quantum computer at step t as ∑ s∈{0,1} N , |s|≤t φ s (−1) s·x , which is handy for lower bound analysis." @default.
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- W2024588775 date "2000-07-01" @default.
- W2024588775 modified "2023-10-18" @default.
- W2024588775 title "Lower bounds of quantum black-box complexity and degree of approximating polynomials by influence of Boolean variables" @default.
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- W2024588775 doi "https://doi.org/10.1016/s0020-0190(00)00069-7" @default.
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