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Russian Microelectronics

Protein Folding Quantum Circuit for Bio Material Modelling Compression

Marina Lisnichenko, Stanislav Protasov

Published Dec 1, 2022• 2 citations
Publisher

Abstract

Abstract Computational material science aims to simulate substances to understand their physical properties. Bioelectronics is an interdisciplinary field that studies biological material from the conductivity point of view. In case of proteins, the folding is an important feature that directly influences physical and chemical properties. The folding modelling is a hard task. The enormous number of degrees of freedom makes modelling impossible for classical computation due to resource limits. Quantum computations aim to process multidimensional data with logarithmic growth of quantum bits. Quantum operators, gates, form quantum programs, known as circuits, which process the input data. When talking about real quantum computers, the gates are noisy and expensive to execute. Thus, it is essential to reduce the number of quantum gates both for the quality of the result and the cost of computations. This work describes an approach to decrease the number of quantum gates based on their mathematical property.

DOI
10.1134/s1063739722080182

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Quantum computing has progressed from a theoretical concept to a practical experimental technology. By processing information according to quantum mechanics rather than classical rules, quantum computers may offer advantages for certain problems. Although a few algorithms have proven speedups, it remains unclear where quantum computers will be practically useful, especially since current devices are noisy, small, and not yet fault tolerant. This thesis explores quantum computing for biophysically motivated combinatorial problems, with a focus on lattice protein models. In these simplified models, a protein is represented as a chain on a discrete lattice. Despite their simplicity, lattice proteins retain important features of real proteins, such as such as the folding of a chain with exponentially many possible shapes to a unique minimum-energy structure and steric constraints.To run lattice protein problems on quantum hardware, they must first be formulated using binary variables and objective functions. The latter typically contain soft constraints needed to ensure physical solutions. In Papers~\I--\II, we developed and extended a coordinate-based mapping for lattice protein folding, enabling D-Wave's hybrid quantum-classical annealer to fold both $2$D hydrophobic-polar and $3$D Miyazawa-Jernigan lattice proteins. In Paper~\III, we adapted the approach to the gate-based paradigm and showed how quadratic soft constraints could be removed by a mixer developed for the maximum-independent-set problem. Papers~\IV--\V addressed lattice protein design using quantum annealing, quantum approximate optimization algorithm, quantum alternating operator ansatz and hardware-efficient ansatz, while Paper~\VI extended the framework to multi-chain thermodynamics and the reconstruction of densities of states and heat-capacity features.Together, these papers show how folding, design, and multi-chain thermodynamics can be formulated, implemented, and analyzed using present-day quantum and hybrid hardware. A recurring limitation is the treatment of soft constraints. In quantum annealing, their high connectivity leads to error accumulation. On gate-based hardware, they increase circuit depth and sensitivity to noise. At the same time, temporary constraint violations can provide useful freedom during optimization. Further progress will therefore require improved formulations, algorithms and hardware that reduce the cost of enforcing physical solutions while retaining this flexibility.

•Jan 1, 2026•0 citations
Abstract Computational material science aims to simulate substances to understand their physical properties. Bioelectronics is an interdisciplinary field that studies biological material from the conductivity point of view. In case of proteins, the folding is an important feature that directly influences physical and chemical properties. The folding modelling is a hard task. The enormous number of degrees of freedom makes modelling impossible for classical computation due to resource limits. Quantum computations aim to process multidimensional data with logarithmic growth of quantum bits. Quantum operators, gates, form quantum programs, known as circuits, which process the input data. When talking about real quantum computers, the gates are noisy and expensive to execute. Thus, it is essential to reduce the number of quantum gates both for the quality of the result and the cost of computations. This work describes an approach to decrease the number of quantum gates based on their mathematical property.
Computational material science aims to simulate substances to understand their physical properties. Bioelectronics is an interdisciplinary field that studies biological material from the conductivity point of view. In case of proteins, the folding is an important feature that directly influences physical and chemical properties. The folding modelling is a hard task. The enormous number of degrees of freedom makes modelling impossible for classical computation due to resource limits. Quantum computations aim to process multidimensional data with logarithmic growth of quantum bits. Quantum operators (gates) form quantum programs, known as circuits that process the input data. In real quantum computers, the gates are noisy and expensive to execute. Thus, it is essential to reduce the number of quantum gates both for the quality of the result and the cost of computations. This work describes an approach to decrease the number of quantum gates based on their mathematical property. The matrix properties form the first optimization technique. In this case, the optimized quantum circuit predicts precisely the same protein folding as the not optimized circuit predicts. This happens because both of the circuits are mathematically equivalent. The removal of weakly-parametrized gates forms the second optimization technique. In such case the optimized quantum circuit calculates the approximate protein folding. The error depends on parameter’s amplitude of the gates. The first technique allows to decrease the circuit depth from 631 to 629 gates while modelling the part of Azurin peptide. The second technique allows to decrease the depth to 314 gates with the threshold parameter value 0.4 radians.
Bioelectronics is a perspective future of electronics. The modelling of the protein is an important part that allows to search the appropriate folding structure with applicable conductivity properties. The classical computers struggle from modelling large structures because of number degrees of freedom. The mathematical modelling inside the quantum programming paradigm is a possible way to overcome this factor. This work describes a simplification algorithm of bio material (protein) model used in bioelectronics
Protein folding processes are a vital aspect of molecular biology that is hard to simulate with conventional computers. Quantum algorithms have been proven superior for certain problems and may help tackle this complex life science challenge. We analyze the resource requirements for simulating simplified yet computationally challenging protein folding models on a quantum computer, assessing the feasibility of these existing approaches in the current and near-future technological landscape. We calculate the minimum number of qubits, interactions, and two-qubit gates necessary to build a heuristic quantum algorithm with the specific information of a folding problem. Particularly, we focus on the resources needed to build quantum operations based on the Hamiltonian linked to the protein folding models for a given amino acid count. Such operations are a fundamental component of these quantum algorithms, guiding the evolution of the quantum state for efficient computations. Specifically, we study coarse-grained folding models on the lattice and the fixed backbone side-chain conformation model and assess their compatibility with the constraints of existing quantum hardware given different bit encodings. We conclude that the number of qubits required falls within current technological capabilities. However, the limiting factor is the high number of interactions in the Hamiltonian, resulting in a quantum gate count unavailable today.
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.
In computational biology, protein folding continues to be a key challenge with important implications for drug design and biological function comprehension. Using both classical and quantum computing methods, this paper provides an in-depth analysis of various possible lattice configurations and how theyare used in protein folding. To assess the protein design, we investigate classic models including the more intricate Miyazawa-Jernigan (MJ) interaction matrix and the hydrophobic-hydrophilic (HP) lattice model. Furthermore, we use integer programming methods to protein folding problems on lattices, addressing their NP-hardness and proving their effectiveness in obtaining optimal solutions. Expanding upon these conventional techniques, we present sophisticated graph neural network (GNN) models, particularly the RG-MPNN, which integrate pharmacophore ideas to predict chemical properties by using task-related representations. In the latter section of our paper, we examine how protein folding simulations on lattice structures could be transformed using quantum algorithms. Compared to classical methods, quantum computational techniques promise to be more accurate and efficient at handling the enormous diversity and complexity of protein folding.
Quantum computing has progressed from a theoretical concept to a practical experimental technology. By processing information according to quantum mechanics rather than classical rules, quantum computers may offer advantages for certain problems. Although a few algorithms have proven speedups, it remains unclear where quantum computers will be practically useful, especially since current devices are noisy, small, and not yet fault tolerant. This thesis explores quantum computing for biophysically motivated combinatorial problems, with a focus on lattice protein models. In these simplified models, a protein is represented as a chain on a discrete lattice. Despite their simplicity, lattice proteins retain important features of real proteins, such as such as the folding of a chain with exponentially many possible shapes to a unique minimum-energy structure and steric constraints.To run lattice protein problems on quantum hardware, they must first be formulated using binary variables and objective functions. The latter typically contain soft constraints needed to ensure physical solutions. In Papers~\I--\II, we developed and extended a coordinate-based mapping for lattice protein folding, enabling D-Wave's hybrid quantum-classical annealer to fold both 222D hydrophobic-polar and 333D Miyazawa-Jernigan lattice proteins. In Paper~\III, we adapted the approach to the gate-based paradigm and showed how quadratic soft constraints could be removed by a mixer developed for the maximum-independent-set problem. Papers~\IV--\V addressed lattice protein design using quantum annealing, quantum approximate optimization algorithm, quantum alternating operator ansatz and hardware-efficient ansatz, while Paper~\VI extended the framework to multi-chain thermodynamics and the reconstruction of densities of states and heat-capacity features.Together, these papers show how folding, design, and multi-chain thermodynamics can be formulated, implemented, and analyzed using present-day quantum and hybrid hardware. A recurring limitation is the treatment of soft constraints. In quantum annealing, their high connectivity leads to error accumulation. On gate-based hardware, they increase circuit depth and sensitivity to noise. At the same time, temporary constraint violations can provide useful freedom during optimization. Further progress will therefore require improved formulations, algorithms and hardware that reduce the cost of enforcing physical solutions while retaining this flexibility.