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Quantum walks (QWs) have been proposed as powerful tools in a broad range of fields. Discrete-time QW (DTQW) is an extension of the classical random walk, where the walker goes back and forth along a line and the direction at each step depends on the result of a fair coin flip. Continuous-time QW (CTQW) can be shown as a limit of DTQW. Many objects, such as atoms, trapped ions etc., have been used to simulate QW. But photon, with the wave-particle duality, is easy to generate and can be easily manipulated in many platforms, such as space light circuits and integrated optical platforms. Silicon-on-insulator (SOI) integrated optics have been widely used, among these self-collimation photonic crystal shows a great potential. In this paper we propose the simulation of CTQWs and DTQWs with self-collimation photonic crystal chip fabricated on 830 nm thick top silicon SOI. Similarity between theory results and simulations are analyzed.
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