Capturing Protein Free Energy Landscape using Efficient Quantum Encoding

TL;DR

This study develops a turn-based encoding scheme for protein backbone prediction on a 3D face-centered cubic (FCC) lattice to enable quantum computation of folding. The method coarse-grains amino acids to Cα-centered beads and builds a Hamiltonian that combines hydrophobic effects with the Miyazawa–Jernigan (MJ) potential, solved via classical simulated annealing and a hybrid quantum-classical variational quantum eigensolver (VQE) approach implemented on IBM hardware. A novel encoding maps lattice moves to qubits, with 5 qubits per turn, and an objective with MJ interactions plus penalties for continuity, overlap, and diagonal crossing, forming a binary-quadratic optimization suitable for quantum solvers. Results over 13 peptides show minimum-RMSD structures in the range $1.22$–$3.11$ Å from experiment on quantum hardware, corroborated by classical MD, indicating the viability of hybrid quantum methods for small-to-medium peptides and laying groundwork for future inclusion of side chains and solvent effects. The work demonstrates scalable qubit requirements ($O(N)$) and $O(N^2)$ growth in Hamiltonian terms, providing a pathway toward more accurate and efficient folding predictions as quantum hardware advances.

Abstract

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 modeled using the Miyazawa Jernigan potential. We constructed a Hamiltonian from the defined objective function that encodes the folding process on a three dimensional face centered cubic 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 implemented on IBM 133 qubit hardware. The predicted structures are validated against experimental data using root mean square deviation as a metric and compared against classical simulated annealing and molecular dynamics simulation results. Our findings highlight the promise of hybrid classical and quantum approaches in advancing protein folding predictions, particularly for sequences with low homology.

Figures (7)

• Figure 1: The workflow for predicting the structure of protein by solving the optimization problem using Variational Quantum Eigensolver.
• Figure 2: An illustration of turn encoding in FCC lattice. Starting with the red bead at the centre, the 18 possible positions in the first turn have been split into 3 planes, i.e., 6 beads parallel to x-y plane (orange beads), 6 beads parallel to y-z plane (green beads), and 6 beads parallel to z-x plane (purple beads)
• Figure 3: Basis matrix structure for 3-qubit system
• Figure 4: Scaling of our encoding scheme: Qubit requirements (blue) and number of Pauli string in the Hamiltonian (red) scale up as $\mathcal{O}(N)$ and $\mathcal{O}(N^2)$ respectively.
• Figure 5: Convergence plot from the VQE iterations for Angiotensin (DRVYIHPFHL). These are run on the simulator and the final hardware runs are initiated with these converged parameters.