# Resource-Efficient Quantum Algorithm for Protein Folding

## TL;DR

This paper introduces a resource-efficient quantum algorithm for protein folding, using a variational approach on NISQ devices to simulate small peptide structures with promising accuracy and scalability.

## Contribution

It presents a novel quantum variational algorithm with an $ ext{O}(N^4)$ model Hamiltonian for protein folding, bridging coarse-grained models and lattice representations on NISQ hardware.

## Key findings

- Successfully simulated 10 amino acid peptide folding on 22 qubits.
- Applied the method to a 7 amino acid neuropeptide on a 9-qubit IBM Q device.
- Demonstrated the potential of hybrid quantum-classical algorithms for biological problems.

## Abstract

Predicting the three-dimensional (3D) structure of a protein from its primary sequence of amino acids is known as the protein folding (PF) problem. Due to the central role of proteins' 3D structures in chemistry, biology and medicine applications (e.g., in drug discovery) this subject has been intensively studied for over half a century. Although classical algorithms provide practical solutions, sampling the conformation space of small proteins, they cannot tackle the intrinsic NP-hard complexity of the problem, even reduced to its simplest Hydrophobic-Polar model. While fault-tolerant quantum computers are still beyond reach for state-of-the-art quantum technologies, there is evidence that quantum algorithms can be successfully used on Noisy Intermediate-Scale Quantum (NISQ) 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 tetrahedral lattice. The model reflects many physico-chemical properties of the protein, reducing the gap between coarse-grained representations and mere lattice models. We use a robust and versatile optimisation scheme, bringing together variational quantum algorithms specifically adapted to classical cost functions and evolutionary strategies (genetic algorithms), to simulate the folding of the 10 amino acid Angiotensin peptide 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 Q 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.