A polynomial quantum computing algorithm for solving the dualization problem

• URL: http://arxiv.org/abs/2308.14819v1
• Date: Mon, 28 Aug 2023 18:12:54 GMT
• Title: A polynomial quantum computing algorithm for solving the dualization problem
• Authors: Mauro Mezzini, Fernando Cuartero Gomez, Fernando Pelayo, Jose Javier Paulet Gonzales, Hernan Indibil de la Cruz Calvo, Vicente Pascual
• Abstract summary: Given two monotone prime functions $f:0,1n to 0,1$ and $g:0,1n to 0,1$ the dualization problem consists in determining if $g$ is the dual of $f$. We present a quantum computing algorithm that solves the decision version of the dualization problem in time.
• Score: 75.38606213726906
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Given two prime monotone boolean functions $f:\{0,1\}^n \to \{0,1\}$ and $g:\{0,1\}^n \to \{0,1\}$ the dualization problem consists in determining if $g$ is the dual of $f$, that is if $f(x_1, \dots, x_n)= \overline{g}(\overline{x_1}, \dots \overline{x_n})$ for all $(x_1, \dots x_n) \in \{0,1\}^n$. Associated to the dualization problem there is the corresponding decision problem: given two monotone prime boolean functions $f$ and $g$ is $g$ the dual of $f$? In this paper we present a quantum computing algorithm that solves the decision version of the dualization problem in polynomial time.

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