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We realize quasi-periodic dynamics of a quantum walker over 2.5 quasi-periodsby realizing the walker as a single photon passing through a quantum-walkoptical-interferometer network. We introduce fully controllablepolarization-independent phase shifters in each optical path to realizearbitrary site-dependent phase shifts, and we employ large clear-aperture beamdisplacers, while maintaining high-visibility interference, to enable reaching10 quantum-walk steps. By varying the half-wave-plate setting, we control thequantum-coin bias thereby observing a transition from quasi-periodic dynamicsto ballistic diffusion.

Observation of quasiperiodic dynamics in a one-dimensional quantum walk of single photons in space