Hidden shift problem for complex functions
Serge Adonsou, Peter Bruin, Maris Ozols, Joppe Stokvis
TL;DR
This paper investigates quantum algorithms for the hidden shift problem in complex functions over finite abelian groups, analyzing success probabilities and highlighting perfect success for bent functions.
Contribution
It introduces quantum algorithms for the hidden shift problem and analyzes their success probabilities based on function properties.
Findings
Quantum algorithms succeed with probability 1 for bent functions.
Success probability varies with the 'bentness' of the function.
Analysis of constant-query success probabilities for complex functions.
Abstract
We study quantum algorithms for the hidden shift problem of complex scalar- and vector-valued functions on finite abelian groups. Given oracle access to a shifted function and the Fourier transform of the unshifted function, the goal is to find the hidden shift. We analyze the success probability of our algorithms when using a constant number of queries. For bent functions, they succeed with probability 1, while for arbitrary functions the success probability depends on the `bentness' of the function.
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Taxonomy
TopicsQuantum Computing Algorithms and Architecture · Complexity and Algorithms in Graphs · Mathematical Approximation and Integration