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arXiv · 2607.11393

Symmetry tests for cyclic groups with quantum linear optics

Carlos Navas-Merlo·Juan Carlos García Escartín
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Abstract

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.

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Carlos Navas-Merlo, Juan Carlos García Escartín. 2026-07-13. Symmetry tests for cyclic groups with quantum linear optics. https://arxiv.org/abs/2607.11393

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