Non-Hermitian extensions of the Aubry-André-Harper (AAH) model reveal a rich variety of phase transitions arising from the interplay of quasiperiodicity and nonhermiticity. Despite their theoretical significance, experimental explorations remain challenging due to intricacies in realizing controlled nonhermiticity. Here, we present the first experimental realization of the unitary almost-Mathieu operator that simulates the AAH model by employing single-photon quantum walks. We systematically observe a phase transition between localized and delocalized regimes in the Hermitian limit. Subsequently, by introducing a nonreciprocal hopping, we experimentally probe the parity-time symmetry-breaking transition that is characterized by the emergence of complex quasienergies. Moreover, we identify a novel spectral transition exclusive to discrete-time settings, beyond which the real parts of all quasienergies vanish. These results clarify the interplay between localization, symmetry breaking, and topology in non-Hermitian quasicrystals, thereby paving the way for future exploration of synthetic quantum matter.

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• Localization
• Quantum simulation
• Topological effects in photonic systems
• Topological phase transition
• Non-Hermitian systems