发表机构
Universidad de Valladolid（巴利亚多利德大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究利用量子线性光学对循环群进行对称测试，提出确定输入光子态在特定循环群作用下是否不变的方法，推广了相关测试，提供新测试及搜索本征态方法，还讨论了其用于哈达玛测试的场景。
AI 中文摘要
测试量子态的对称性在量子态比较中有多种应用，或是更复杂量子算法的基础。我们提出一种方法，可确定输入光子态在由算子\(\hat{S}\)定义的循环群作用下是否不变，其特征值为单位根。结果推广了先前与傅里叶干涉仪中抑制定律相关的圆和SWAP测试，为二元移位定义的置换提供了新测试及在多光子态中搜索本征态的方法。最后讨论了该测量可用于执行哈达玛测试的场景，这是变分和量子机器学习算法中的基本要素。
英文摘要
Testing quantum states for symmetries has multiple applications in quantum state comparison or as a primitive in more complex quantum algorithms. We present a method that determines whether an input photonic state is invariant under the action of a cyclic group defined by an operator $\hat{S}$ with eigenvalues which are roots of unity. The results generalize previously known circle and SWAP tests related to suppression laws in Fourier interferometers and offer a new test for permutations defined by a binary shift and a way to search for eigenstates in multiphoton states. Finally, we discuss the scenarios where this measurement can be used to perform Hadamard test, a fundamental primitive in variational and quantum machine-learning algorithms.
