Abstract
Quantum gates are crucial for processing quantum information, but implementing them in a photonic platform poses unique challenges due to the peculiar way photons propagate and interfere. Here, we examine quantum photonic gates that utilize continuous time two-dimensional random walking photons. These gates can be implemented using the inverse design method, where photons randomly walk in a two-dimensional silicon host medium embedded with silicon dioxide scatterers. We propose a C-NOT gate as a multiqubit gate and an X-gate as a single qubit gate. In addition, we provide studying the non-trivial spatial correlations of random walking photons by utilizing the quantum correlation function. The results demonstrate high-fidelity probabilistic quantum gates. Further work is required to address error-correction. This work advances the practical implementation photonic elements in linear optics quantum computation schemes.