Symmetry tests for cyclic groups with quantum linear optics

• URL: http://arxiv.org/abs/2607.11393v1
• Date: Mon, 13 Jul 2026 10:58:46 GMT
• Title: Symmetry tests for cyclic groups with quantum linear optics
• Abstract summary: We present a method that determines whether an input photonic state is invariant under the action of a cyclic group defined by an operator.<n>Results generalize previously known circle and SWAP tests related to suppression laws in Fourier interferometers.<n>We discuss the scenarios where this measurement can be used to perform Hadamard test, a fundamental primitive in variational and quantum machine-learning algorithms.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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