Capturing Protein Free Energy Landscape using Efficient Quantum Encoding

Protein folding is one of the age-old biological problems that refers to the mechanism of understanding and predicting how a protein’s linear sequence of amino acids folds into its specific three-dimensional structure.This structure is critical, as a protein’s functionality is inherently linked to its final folded form. Misfolding can lead to severe diseases such as Alzheimer’s and cystic fibrosis, highlighting the biological and clinical importance of understanding protein folding mechanisms. This work presents a novel turn-based encoding optimization algorithm for predicting the folded structures of peptides and small proteins. Our approach builds upon our previous research, where our objective function focused on hydrophobic collapse, a fundamental phenomenon underlying the protein folding process. In this work, we extend that framework by not only incorporating hydrophobic interactions but also including all non-bonded interactions, such as van der Waals and electrostatic forces between residues, modeled using the Miyazawa–Jernigan (MJ) potential. We constructed a Hamiltonian from the defined objective function that encodes the folding process on a three-dimensional face-centered cubic (FCC) lattice, offering superior packing efficiency and a realistic representation of protein conformations. This Hamiltonian is then solved using classical and quantum solvers to explore the vast conformational space of proteins. To identify the lowest-energy folded configurations, we utilize the Variational Quantum Eigensolver (VQE), a hybrid quantum-classical algorithm, implemented on IBM’s 133-qubit hardware. The predicted structures are validated against experimental data using root-mean-square deviation (RMSD) as a metric and compared against classical simulated annealing and molecular dynamics simulation results. Our findings highlight the promise of hybrid classical-quantum approaches in advancing protein folding predictions, particularly for sequences with low homology.