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arXiv:2204.01821

Peptide conformational sampling using the Quantum Approximate Optimization Algorithm

Sami Boulebnane, Xavier Lucas, Agnes Meyder, Stanisław Adaszewski, Ashley Montanaro

Published Apr 4, 2022• 2 citations
arXivHTMLPDF

Abstract

Protein folding -- the problem of predicting the spatial structure of a protein given its sequence of amino-acids -- 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 a variational quantum algorithm, 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, which is a necessary condition for a valid protein conformation. Motivated by promising results achieved by QAOA on this problem, we then apply the algorithm to a more complete version of protein folding, including a simplified physical potential. In this case, based on numerical simulations on 20 qubits, 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. We believe that the approach and conclusions presented in this work could offer valuable methodological insights on how to systematically evaluate variational quantum optimization algorithms on real-world problems beyond protein folding.

DOI
10.48550/arxiv.2204.01821

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Protein folding -- the problem of predicting the spatial structure of a protein given its sequence of amino-acids -- 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 a variational quantum algorithm, 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, which is a necessary condition for a valid protein conformation. Motivated by promising results achieved by QAOA on this problem, we then apply the algorithm to a more complete version of protein folding, including a simplified physical potential. In this case, based on numerical simulations on 20 qubits, 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. We believe that the approach and conclusions presented in this work could offer valuable methodological insights on how to systematically evaluate variational quantum optimization algorithms on real-world problems beyond protein folding.
Abstract 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.
Quantum computing has gained a lot of attention recently, and scientists have seen potential applications in this field using quantum computing for Cryptography and Communication to Machine Learning and Healthcare. Protein folding has been one of the most interesting areas to study, and it is also one of the biggest problems of biochemistry. Each protein folds distinctively, and the difficulty of finding its stable shape rapidly increases with an increase in the number of amino acids in the chain. A moderate protein has about 100 amino acids, and the number of combinations one needs to verify to find the stable structure is enormous. At some point, the number of these combinations will be so vast that classical computers cannot even attempt to solve them. In this paper, we examine how this problem can be solved with the help of quantum computing using two different algorithms, Variational Quantum Eigensolver (VQE) and Quantum Approximate optimization Algorithm (QAOA), using Qiskit Nature. We compare the results of different quantum hardware and simulators and check how error mitigation affects the performance. Further, we make comparisons with SoTA algorithms and evaluate the reliability of the method.
Protein folding prediction is a critical challenge in bioinformatics, demanding significant computational resources. This research explores the potential of quantum computing to accelerate and enhance this process. We formulate the protein folding problem as a quantum optimization problem, employing quantum simulation algorithms for efficient solution. The methodology involves mapping the protein's amino acid sequence into a quantum Hamiltonian, followed by simulating the system using quantum algorithms. We investigate the effectiveness of Variational Quantum Eigensolver (VQE) and Quantum Approximate Optimization Algorithm (QAOA) in determining the ground state energy and, consequently, the folded conformation of the protein. The predicted structures are then validated through comparison with known experimental data and integration with classical molecular dynamics simulations. The core claim of this work is to leverage the computational power of quantum computers to drastically reduce the time required for protein folding prediction, leading to improved accuracy and efficiency. The results demonstrate a promising approach for tackling this computationally intensive problem, potentially revolutionizing drug discovery and protein engineering.
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 O(N4){\mathcal{O}}({N}^{4})O(N4) 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.
Abstract Quantum computing in biology is one of the most rapidly evolving field of technology. Protein folding is one of the key challenges which requires accurate and efficient algorithms with a quick computational time. Structural conformations of proteins with disordered regions need colossal amount of computational resource to map its least energy conformation state. In this regard, quantum algorithms like Variational quantum eigensolver (VQE) are applied in the current research work to predict the lowest energy value of 50 peptides of 7 amino acids each. VQE is initially used to calculate the energy values over which Variational Quantum Optimization is applied via Conditional Value at Risk (CVaR) over 100 iterations of 500000 shots each to obtain least ground state energy value. This is compared to the molecular dynamics-based simulations of 50 nanoseconds each to calculate the energy values along with the folding pattern. The results suggest efficient folding outcomes from CvaR-VQE compared to MD based simulations. With the ever-expanding quantum hardware and improving algorithms the problem of protein folding can be resolved to obtain in depth insights on the biological process and drug design.
Identifying minimum-energy structures of lattice proteins is a challenging discrete optimization problem. Quantum approaches such as analog quantum annealing and the gate-based quantum approximate optimization algorithm (QAOA) can address this problem after mapping it to a binary representation, which typically involves introducing penalty terms to enforce valid chain configurations. However, in this and many related problems, the use of quadratic penalty terms can be avoided by restricting the search space to independent sets in a conflict graph and using a QAOA mixer designed for the maximum independent set problem. In this work, we implement and explore this QAOA variant for lattice protein folding. Here, the objective function consists solely of the protein energy together with a simple linear bias term, without quadratic penalties. We validate this approach through classical simulations of the quantum circuits for lattice proteins of lengths N=4N=4N=4 and N=6N=6N=6. To explore larger systems, we further introduce a heuristic iterative local-search scheme, with which we successfully fold lattice proteins with lengths up to N=14N=14N=14 using local subgraphs with at most 26 qubits.