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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 Ŝ 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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Cite

BibTeXRIS
BibTeX
@misc{navasmerlo2026symmetry,
  title = {{Symmetry tests for cyclic groups with quantum linear optics}},
  author = {Carlos Navas-Merlo and Juan Carlos García Escartín},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2607.11393},
  eprint = {2607.11393},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2607.11393},
}
RIS
TY  - UNPB
TI  - Symmetry tests for cyclic groups with quantum linear optics
AU  - Carlos Navas-Merlo
AU  - Juan Carlos García Escartín
PY  - 2026
DA  - 2026/09/29
PB  - arXiv
DO  - 10.48550/arxiv.2607.11393
UR  - https://arxiv.org/abs/2607.11393
AB  - 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 Ŝ 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.
ER  -