Symmetry tests for cyclic groups with quantum linear optics

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.

arXiv:2607.11393 [quant-ph]

(or arXiv:2607.11393v2 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2607.11393 Focus to learn more arXiv-issued DOI via DataCite

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