Peptide conformational sampling using the Quantum Approximate Optimization Algorithm

Protein folding has attracted considerable research effort in biochemistry in recent decades. In this work, we explore the potential of quantum computing to solve a simplified version of protein folding. More precisely, we numerically investigate the performance of the Quantum Approximate Optimization Algorithm (QAOA) in sampling low-energy conformations of short peptides. We start by benchmarking the algorithm on an even simpler problem: sampling self-avoiding walks. Motivated by promising results, we then apply the algorithm to a more complete version of protein folding, including a simplified physical potential. In this case, we find less promising results: deep quantum circuits are required to achieve accurate results, and the performance of QAOA can be matched by random sampling up to a small overhead. Overall, these results cast serious doubt on the ability of QAOA to address the protein folding problem in the near term, even in an extremely simplified setting.