Peptide Design with Quantum Approximate Optimization Algorithm

A protein is a long chain of amino acids that folds into a well-defined three-dimensional structure. The amino acid sequence determines the folded structure, which in turn determines the protein's function. Computational tools allow the design of new amino acid sequences, giving rise to new folds and new functions, and permitting the creation of large and small proteins (peptides) with applications in industrial manufacturing, medicine, and agriculture. The protein design problem is NP-complete, with the search space scaling exponentially with the number of amino acids. There is no known efficient classical algorithm able to find optimal sequences. In this work, we propose a formulation of the protein design problem amenable to the quantum approximate optimization algorithm (QAOA). By taking advantage of the qubit-efficient mapping, we design several small peptides on a trapped-ion quantum processor, demonstrating the feasibility and favourable scalability of the approach. This work establishes the utility of near-term universal quantum computers for protein design.