Protein folding, which traces the protein three-dimensional (3D) structure from its amino acid sequence, is a half-a-century-old problem in biology. The function of the protein correlates with its structure, emphasizing the need to study protein folding to understand the cellular and molecular processes better. While recent AI-based methods have shown significant success in protein structure prediction, their accuracy diminishes with proteins of low sequence similarity. Classical simulations face challenges in generating extensive conformational samplings. In this work, we develop a novel turn-based encoding algorithm with more significant degrees of freedom that successfully runs on a gate-based quantum computer and predicts the structure of proteins of varied lengths utilizing up to 114 qubits (IBM hardware). To make the problem tractable in quantum computers, the protein sequences were described with the simplistic HP model (H = hydrophobic residues, P = polar residues). The proposed formulation successfully captures the so-called nucleation step in protein folding, the hydrophobic collapse, that brings the hydrophobic residues to the core of the protein.