Quantum algorithms and approximating polynomials for composed functions with shared inputs

SODA '19: Symposium on Discrete Algorithms San Diego California January, 2019, pp. 662-678, 2018.

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Abstract:

We give new quantum algorithms for evaluating composed functions whose inputs may be shared between bottom-level gates. Let f be a Boolean function and consider a function F obtained by applying f to conjunctions of possibly overlapping subsets of n variables. If f has quantum query complexity Q(f), we give an algorithm for evaluating F u...More

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