Protein Structure Prediction with Quantum Algorithms (Part 1/2)

Predicting protein structures from amino acid sequences is a key challenge in computational biology with implications for drug discovery. In this work, we present the first implementation of the face-centered cubic (FCC) lattice model for protein structure prediction with a quantum algorithm. The FCC lattice offers a more realistic representation of protein conformations compared to simpler cubic or tetrahedral lattice models studied previously, especially in modeling secondary structures. When it comes to encoding the geometric constraints on this lattice, we utilize two novel methods to solve the problem without incurring additional ancilla qubits: a polynomial fitting approach (PolyFit) and Variational Quantum Eigensolver with Constraints (VQEC) based on the Lagrangian duality principle. As a proof of principle, we demonstrate the effectiveness of both methods through numerical simulations and experiments on IBM quantum hardware for a small 6-amino acid sequence. This work paves the way for performing quantum-based protein structure prediction with more complex lattice structures on near-term quantum devices.