Digital quantum simulation is the process of simulating the dynamics of a physical system by a programmable quantum computer. The universality of quantum computers makes it possible to simulate any quantum system, whether fermionic or bosonic. In this work, we discuss the application of digital quantum simulations to simulate a ubiquitous bosonic system, a beam splitter. To perform the boson-to-qubit mapping, we used the gray code, whose superiority over other encoding schemes has been shown recently. We validated our quantum circuit that mimics the action of a beam splitter by simulating the Hong-Ou-Mandel interference experiment. We simulated the experiment in both quantum simulators and actual quantum backends and were able to observe the HOM interference.