The entanglement of a quantum system can be valuated using Mermin polynomials. This gives us a means to study entanglement evolution during the execution of quantum algorithms. We first consider Grover's quantum search algorithm, noticing that states during the algorithm are maximally entangled in the direction of a single constant state, which allows us to search for a single optimal Mermin operator and use it to evaluate entanglement through the whole execution of Grover's algorithm. Then the Quantum Fourier Transform is also studied with Mermin polynomials. A different optimal Mermin operator is searched at each execution step, since in this case there is no single direction of evolution. The results for the Quantum Fourier Transform are compared to results from a previous study of entanglement with Cayley hyperdeterminant. All our computations can be replayed thanks to a structured and documented open-source code that we provide.

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Grover算法和量子傅立叶变换中用于纠缠评估的Mermin多项式

可以使用Mermin多项式来评估量子系统的纠缠。这为我们提供了一种在量子算法执行过程中研究纠缠演化的方法。我们首先考虑Grover的量子搜索算法，注意到算法中的状态在单个恒定状态的方向上最大地纠缠，这使我们可以搜索单个最佳Mermin算子，并使用它来评估整个Grover算法的纠缠度。然后，还使用Mermin多项式研究了量子傅立叶变换。在每个执行步骤中都会搜索不同的最佳Mermin运算符，因为在这种情况下，没有单一的演化方向。将量子傅立叶变换的结果与先前与Cayley高决定簇纠缠的研究结果进行了比较。