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A Quantum Circuit Framework for Protein Ensemble-Level Energetics

Bhushan K. Bonde, Pratik Patil, Bhaskar Choubey

Published Aug 7, 2026• 0 citations
Publisher

Abstract

Abstract Proteins occupy heterogeneous free-energy landscapes, where broad, high-entropy ensembles converge toward compact, low-energy basins containing multiple sub-states. Molecular dynamics can capture these landscapes at atomic resolution, but exhaustively sampling rare transitions remains computationally demanding. Furthermore, most quantum approaches to protein modelling target only a single optimal structure, leaving the energetic heterogeneity of the full ensemble largely unexplored. We introduce a residue-level, gate-based quantum circuit framework for coarse-graining protein thermodynamics. Each amino acid is represented as a two-state qubit with stabilised and excited solvation states, initialised from solvation energetics. Following this, a structure-informed entanglement block of parametrised controlled gates encodes covalent bonds and non-covalent contacts across the residue network. The circuit is then measured approx 10 6 times, yielding an ensemble of binary thermodynamic microstates, from which we compute energy distributions, residue-level statistical couplings, energetic sensitivities, and information gain relative to total free energy. We showcase the comparative results for Trp-cage miniprotein (PDB:1L2Y) and the disulfide-stabilised chimera (PDB:9GDL), which comprises a structured, folding-funnel-like energy distribution for 1L2Y. Moreover, comparison with 9GDL reveals clear shifts in global energy and residue-level profiles, localising the residues driving stabilisation and ensemble reorganisation. Additionally, dimer- and trimer-level couplings resolve both direct and interaction-mediated dependencies, showing the circuit captures network-level, not just isolated, correlations. The framework moves quantum protein modelling beyond single-structure optimisation toward interpretable, ensemble-level characterisation.

DOI
10.21203/rs.3.rs-10608214/v1

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Abstract Proteins occupy heterogeneous free-energy landscapes, where broad, high-entropy ensembles converge toward compact, low-energy basins containing multiple sub-states. Molecular dynamics can capture these landscapes at atomic resolution, but exhaustively sampling rare transitions remains computationally demanding. Furthermore, most quantum approaches to protein modelling target only a single optimal structure, leaving the energetic heterogeneity of the full ensemble largely unexplored. We introduce a residue-level, gate-based quantum circuit framework for coarse-graining protein thermodynamics. Each amino acid is represented as a two-state qubit with stabilised and excited solvation states, initialised from solvation energetics. Following this, a structure-informed entanglement block of parametrised controlled gates encodes covalent bonds and non-covalent contacts across the residue network. The circuit is then measured approx 10 6 times, yielding an ensemble of binary thermodynamic microstates, from which we compute energy distributions, residue-level statistical couplings, energetic sensitivities, and information gain relative to total free energy. We showcase the comparative results for Trp-cage miniprotein (PDB:1L2Y) and the disulfide-stabilised chimera (PDB:9GDL), which comprises a structured, folding-funnel-like energy distribution for 1L2Y. Moreover, comparison with 9GDL reveals clear shifts in global energy and residue-level profiles, localising the residues driving stabilisation and ensemble reorganisation. Additionally, dimer- and trimer-level couplings resolve both direct and interaction-mediated dependencies, showing the circuit captures network-level, not just isolated, correlations. The framework moves quantum protein modelling beyond single-structure optimisation toward interpretable, ensemble-level characterisation.
Proteins occupy heterogeneous free-energy landscapes in which high-entropy ensembles converge toward compact, low-energy basins with multiple sub-states. Molecular dynamics can access these landscapes at atomic resolution, but exhaustive sampling remains computationally demanding. Meanwhile, most quantum approaches target only single optimal structures, leaving full ensemble energetic heterogeneity unexplored. We introduce a residue-level, gate-based quantum circuit framework for coarse-graining protein thermodynamics. Each amino acid is represented as a two-state qubit (stabilised vs. excited solvation state) based on residue solvation energetics. A structure-informed entanglement block then encodes covalent and non-covalent contacts using parameterised controlled gates, embedding correlations across the residue-interaction network. Sampling the circuit (∼106\sim 10^6∼106 measurements) yields binary thermodynamic microstates used to compute protein energy distributions, residue-level statistical couplings, energetic sensitivities, and information gains relative to total free energy. We showcase the framework on the benchmark Trp-cage miniprotein 1L2Y (TC5b) and 9GDL, a disulfide-stabilised Trp-cage-fortified exenatide chimera. For 1L2Y, the circuit reproduces a structured, folding-funnel-like energy distribution. Comparative analysis with 9GDL reveals shifts in global energy distributions and residue-level stability profiles. Coupling and information-theoretic analyses localise residues associated with ensemble reorganisation, while multi-body couplings show the circuit resolves both direct and indirect statistical correlations. This framework expands quantum protein modelling beyond single-structure optimisation toward ensemble-level characterisation, capturing key features of rugged energy landscapes to guide protein design, mutation mapping, and allosteric pathway identification.
Protein structure prediction remains central to computational biology and drug discovery. While deep learning models such as AlphaFold have achieved remarkable accuracy for known fold families, they struggle with novel folds, intrinsically disordered regions, and conformational dynamics, and they do not explicitly optimize physics-based energy functions. We present a quantum-assisted approach to protein conformation optimization that uses parameterized quantum circuits within a variational framework to explore the energy landscape of small proteins and fragments from first-principles or coarse-grained physics. Our method encodes backbone torsion angles (ϕ, ψ) and selected side-chain degrees of freedom into qubit registers and employs a variational quantum eigensolver (VQE)-inspired optimization to minimize an approximate Hamiltonian incorporating bonded interactions, sterics, hydrogen bonding, and hydrophobic contacts. We introduce problem-inspired ansätze that respect chain connectivity and secondary-structure motifs (helices, beta-sheets) and propose hierarchical circuit growth strategies for scaling from peptides to larger domains. Through classical simulations of small peptides and secondary-structure motifs, we demonstrate that quantum variational optimization can identify low-energy conformations consistent with experimentally determined structures. We provide explicit resource estimates for NISQ and early fault-tolerant quantum computers and discuss hybrid classical-quantum strategies for refining quantum solutions with classical molecular dynamics and machinelearning priors. While full protein-folding quantum advantage remains distant, we identify concrete subproblems where nearterm quantum devices offer complementary physics-based insight beyond data-driven approaches, opening pathways toward practical quantum-classical protein structure and drug discovery pipelines.
Variational quantum algorithms provide a direct, physics-based approach to protein structure prediction, but their accuracy is limited by the coarse resolution of the energy landscapes generated on current noisy devices. We propose a hybrid framework that combines quantum computation with deep learning, formulating structure prediction as a problem of energy fusion. Candidate conformations are obtained through the Variational Quantum Eigensolver (VQE) executed on IBM’s 127 qubit superconducting processor, which defines a global yet low resolution quantum energy surface. To refine these basins, secondary structure probabilities and dihedral angle distributions predicted by the NSP3 neural network are incorporated as statistical potentials. These additional terms sharpen the valleys of the quantum landscape, resulting in a fused energy function that enhances effective resolution and better distinguishes native like structures. Evaluation on 375 conformations from 75 protein fragments shows that, on this short fragment-only benchmark (10–14 residues without surrounding chain context), the hybrid pipeline achieves a mean RMSD of 4.9 Å with statistical significance ( p < 0.001), outperforming both quantum-only re-rankings and fragment-level runs of AlphaFold3 and ColabFold. We caution that this conclusion is restricted to the fragment-scale regime accessible to current quantum hardware and does not extend to the full-chain regime in which AlphaFold3 and ColabFold are usually evaluated. The findings demonstrate that energy fusion offers a systematic method for combining data driven models with quantum algorithms, improving the practical applicability of near term quantum computing to molecular and structural biology.
Predicting the structure of short peptides in protein binding pockets remains difficult because this regime requires physics-based conformational search, yet existing methods do not provide a practical way to carry out that search on current hardware. We present QSAD, a quantum-classical framework that reformulates peptide structure prediction as amino-acid-level Hamiltonian sampling and replaces iterative optimization with non-iterative Hamiltonian evolution. Executed entirely on IBM Heron R2 across 101 binding-pocket peptides (5-18 residues), QSAD improves prediction accuracy by 27-71% over all evaluated AI and quantum baselines while maintaining the lowest variance across tested lengths. QSAD also tolerates noise levels 3-5x beyond typical hardware error rates, where iterative methods fail, and reduces mean quantum execution time by 27x relative to VQE. The sampled ensemble further supports approximate reconstruction of protein energy landscapes. These results establish coarse-grained quantum sampling as a practical computational path for structure prediction in regimes where data-driven methods lack sufficient signal.
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.
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.