A comprehensive framework for quantum state estimation in multi-dimensional discrete-time quantum walks is developed, focusing on d-dimensional space. The coin evolution unitary operator is decomposed to characterize the evolution path of the quantum walk, yielding an explicit computational formula for the particle’s position probability distribution. Spectral decomposition of the evolution path establishes rigorous upper and lower bounds for the position probability distribution, demonstrating convergence within a well-defined range regardless of the initial quantum state. Building on these spectral bounds, an inverse problem is addressed: given a target position probability distribution, efficient algorithms are proposed for reconstructing the corresponding quantum initial state. This work overcomes the limitations of conventional forward-simulation methods.