1：Experimental Design and Method Selection:

The experiment uses a linear optical setup to emulate quantum computation with classical light. It involves preparing input states, applying cyclic permutation operations via a black box, and detecting output states to determine permutation parity. Theoretical models include quantum state representations and optical transformations.

2：Sample Selection and Data Sources:

A laser beam with specific polarization and orbital angular momentum modes is used as the input. No external datasets are involved; data is generated from optical measurements.

3：List of Experimental Equipment and Materials:

Includes a He-Ne laser, polarizers, q plate, quarter-wave plates, half-wave plates, polarizing beam splitters, mirrors, Dove prisms, piezo transmitter, power detectors, and potentially a spatial light modulator and CCD camera for higher-dimensional cases.

4：Experimental Procedures and Operational Workflow:

The setup has three parts: input state preparation (using polarizer, q plate, PBS, QWP), black box for permutations (using HWP, Mach-Zehnder interferometer with PBSs, mirrors, DPs), and output detection (using QWP, PBS, power detectors). Specific settings for HWP and DPs are adjusted to realize different permutations.

5：Data Analysis Methods:

Intensities from detectors are normalized and compared to theoretical predictions to determine parity. Errors are analyzed using standard deviations.