Resource-efficient quantum algorithm for protein folding

Anton Robert,Stefan Woerner,Ivano Tavernelli,Panagiotis Kl Barkoutsos

doi:10.1038/s41534-021-00368-4

Abstract

Predicting the three-dimensional structure of a protein from its primary sequence of amino acids is known as the protein folding problem. Due to the central role of proteins’ structures in chemistry, biology and medicine applications, this subject has been intensively studied for over half a century. Although classical algorithms provide practical solutions for the sampling of the conformation space of small proteins, they cannot tackle the intrinsic NP-hard complexity of the problem, even when reduced to the simplest Hydrophobic-Polar model. On the other hand, while fault-tolerant quantum computers are beyond reach for state-of-the-art quantum technologies, there is evidence that quantum algorithms can be successfully used in noisy state-of-the-art quantum computers to accelerate energy optimization in frustrated systems. In this work, we present a model Hamiltonian with {mathcal{O}}({N}^{4}) scaling and a corresponding quantum variational algorithm for the folding of a polymer chain with N monomers on a lattice. The model reflects many physico-chemical properties of the protein, reducing the gap between coarse-grained representations and mere lattice models. In addition, we use a robust and versatile optimization scheme, bringing together variational quantum algorithms specifically adapted to classical cost functions and evolutionary strategies to simulate the folding of the 10 amino acid Angiotensin on 22 qubits. The same method is also successfully applied to the study of the folding of a 7 amino acid neuropeptide using 9 qubits on an IBM 20-qubit quantum computer. Bringing together recent advances in building gate-based quantum computers with noise-tolerant hybrid quantum-classical algorithms, this work paves the way towards accessible and relevant scientific experiments on real quantum processors.

Highlights

The solution of Levinthal’s paradox[1] through a bias search in the protein configuration space[2] demands a very fine description of the amino acids interactions in their natural environment to correctly drive the optimization in the rugged protein energy landscape[3,4,5]
Fingerhuth and coworkers proposed another approach based on the Quantum Approximate Optimization Algorithm (QAOA)[15] using a problem-specific alternating operator ansatz to model protein folding[16]
As for the previous models in literature, a polymer configuration is grown on the lattice by adding the different beads one after the other and encoding, in the qubit register the different "turn” ti that defines the position of the bead i + 1 relatively to the previous bead i

Summary

Introduction

The solution of Levinthal’s paradox[1] through a bias search in the protein configuration space[2] demands a very fine description of the amino acids interactions in their natural environment to correctly drive the optimization in the rugged protein energy landscape[3,4,5]. The amount of resources needed for the simulation of polymer lattice models was reduced, still maintaining an exponential cost in terms of number of qubits and gates needed[12,13]. These methods were used to fold a coarsegrained protein model with 6 and 8 amino acid sequences on 2D and 3D lattices, respectively, using a quantum annealer[14]. These experiments required 81 and 200 qubits and led to a final population of 0.13% and 0.024% for the corresponding ground state structures, using divide and conquer strategies. Employing the same model proposed in[13] they succeeded in folding a 4 amino acid protein model on a

Methods

Results

Conclusion