Monte Carlo particle transport codes are well established on classical hardware and are considered as the reference tool for nuclear applications. In a growing number of domains, the design of algorithms is progressively shifting towards the field of quantum computing, where theoretical speedups over their classical counterparts are expected. In some of these domains, Monte Carlo methods have already been converted to a quantum computing friendly setup where the expected and observed gain in complexity is quadratic. In this work, we address the particle transport problem in view of a first implementation on these architectures. We propose a quantum algorithm to model the particle transport based on discrete-time quantum walks and compare our approach to Monte Carlo and deterministic classical numerical schemes. The proof-of-concept algorithm is applied to a 10-qubit small-size problem by simulating its behavior on both ideal and noisy quantum computers based on the qiskit framework in view of reproducing classical results.