论文标题
MERMIN多项式用于Grover算法和量子傅立叶变换中的纠缠评估
Mermin Polynomials for Entanglement Evaluation in Grover's algorithm and Quantum Fourier Transform
论文作者
论文摘要
量子系统的纠缠可以使用Mermin多项式进行评估。这为我们提供了一种在执行量子算法期间研究纠缠演变的方法。我们首先考虑Grover的量子搜索算法，注意到该算法期间的状态朝着单个常数状态的方向最大化，这使我们能够搜索单个最佳的Mermin运算符，并使用它通过Grover算法的整个执行来评估纠缠。然后，还用Mermin多项式研究了量子傅立叶变换。在每个执行步骤中搜索了另一个最佳的Mermin运算符，因为在这种情况下，没有一个进化方向。将量子傅里叶变换的结果与先前对Cayley高度确定性纠缠的研究结果进行了比较。由于我们提供的结构化和记录的开源代码，我们所有的计算都可以重播。
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.
