Quantum transport remains a central yet experimentally challenging problem in condensed matter and quantum physics. Here we report the first complete experimental characterization of the full spectrum of quantum transport behaviors in a one-dimensional Fibonacci chain—the paradigmatic quasicrystalline model—spanning localization, subdiffusion, normal and superdiffusion, and ballistic transport. Using a tunable photonic quantum-walk platform, these regimes are unambiguously resolved through their distinct power-law scalings of the mean square displacement and smooth autocorrelation function, together with pronounced oscillatory dynamical structures. These signatures arise from the intrinsic multifractal spectra and hyperuniform order of the Fibonacci quasicrystal, long predicted but never before experimentally resolved. Beyond mapping a comprehensive transport regime diagram, our highly controllable platform provides a powerful and versatile framework for exploring quasiperiodicity, multifractal criticality, and emergent quantum transport phenomena.

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• Quantum control
• Quantum engineering
• Quantum simulation
• Quantum transport
• Quantum walks