An approach to solve the coarse-grained Protein folding problem in a Quantum Computer

Abstract

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. This limitation highlights the significance of investigating the thermodynamic landscape of proteins by sampling the diverse conformations they can adopt and identifying the global minimum energy structure. 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. 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. The optimization problem gives us a formulation that can go up to sixth order, but, with suitable modifications and assumptions, can be brought down to a second order formulation, making it a QUBO problem. 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. Details of the VQE algorithm that was used for solving this problem is presented. We also present results obtained from IBM quantum simulators and real machines, and compare them with the ones obtained from PyQUBO (simulated annealing) and CPLEX.