Photonic simulation of localization phenomena using boson sampling

Quantum simulation in its current state faces experimental overhead in terms of physical space and cooling. We propose boson sampling as an alternative compact synthetic platform performing at room temperature. Identifying the capability of estimating matrix permanents, we explore the applicability of boson sampling for tackling the dynamics of quantum systems without having access to information about the full state vector. By mapping the time-evolution unitary of a Hamiltonian onto an interferometer via continuous-variable gate decompositions, we present proof-of-principle results of localization characteristics of a single particle. We study the dynamics of one-dimensional tight-binding systems in the clean and quasiperiodic-disordered limits to observe Bloch oscillations and dynamical localization, and the delocalization-to-localization phase transition in the Aubry-Andr\'e-Harper model, respectively. Our computational results obtained using boson sampling are in complete agreement with the dynamical and static results of noninteracting tight-binding systems obtained using conventional numerical calculations. Additionally, our study highlights the role of the number of sampling measurements or ``shots'' for simulation accuracy.