论文标题
从量子观点上看
On the Walsh and Fourier-Hadamard Supports of Boolean Functions From a Quantum Viewpoint
论文作者
论文摘要
在本文中，我们关注布尔函数理论与量子计算之间的联系。特别是，我们研究了我们所谓的完全平衡功能的概念，并分析了具有这种属性的功能的傅立叶和沃尔什支持。我们使用所谓的平衡集研究其他相关功能类别的WALSH和傅立叶支持。这导致我们重新审视并完成某些经典结果并提出新结果。 我们通过将先前的结果扩展到伪树状功能（与矢量功能有关），并深入了解其在分析某个量子算法可以提供的可能性时的应用中，从而深入了解其研究。
In this paper, we focus on the links between Boolean function theory and quantum computing. In particular, we study the notion of what we call fully-balanced functions and analyse the Fourier--Hadamard and Walsh supports of those functions having such property. We study the Walsh and Fourier supports of other relevant classes of functions, using what we call balancing sets. This leads us to revisit and complete certain classic results and to propose new ones. We complete our study by extending the previous results to pseudo-Boolean functions (in relation to vectorial functions) and giving an insight on its applications in the analysis of the possibilities that a certain family of quantum algorithms can offer.
