Protein folding, which dictates the protein structure from its amino acid sequence, is half a century old problem of biology. The function of the protein correlates with its structure, emphasizing the need of understanding protein folding for studying the cellular and molecular mechanisms that occur within biological systems. Understanding protein structures and enzymes plays a critical role in target based drug designing, elucidating protein-related disease mechanisms, and innovating novel enzymes. While recent advancements in AI based protein structure prediction methods have solved the protein folding problem to an extent, their precision in determining the structure of the protein with low sequence similarity is limited. Classical methods face challenges in generating extensive conformational samplings, making quantum-based approaches advantageous for solving protein folding problems. In this work we developed a novel turn based encoding algorithm that can be run on a gate based quantum computer for predicting the structure of smaller protein sequences using the HP model as an initial framework, which can be extrapolated in its application to larger and more intricate protein systems in future. The HP model best represents a major step in protein folding phenomena - the hydrophobic collapse which brings the hydrophobic amino acid to the interior of a protein. The folding problem is cast in a 3D cubic lattice with degrees of freedom along edges parallel to the orthogonal axes, as well as along diagonals parallel to the axial planes. While, the original formulation with higher order terms can be run on gate based quantum hardwares, the QUBO formulation can give results on both classical softwares employing annealers and IBM CPLEX as well as quantum hardwares.
