We present a quantum-dynamical framework for identifying structurally important residues in proteins based on continuous time quantum walks (CTQWs) on weighted residue interaction networks constructed from experimentally resolved structures. By mapping the weighted adjacency matrix to a Hamiltonian, residue importance emerges from the long-time averaged occupation probability, confirmed analytically through its spectral decomposition. Across a dataset of approximately 150 proteins spanning diverse structural and functional classes, CTQW centrality exhibits consistently strong agreement with classical eigenvector centrality in identifying central residues, while extending beyond it through incorporating signatures of quantum interference. Analyzing the time-averaged quantum transition matrix reveals consistently larger spectral gaps than the classical random-walk operator. Furthermore, biological relevance is confirmed through recovery of experimentally established functional residues in proteins kinase A and oxytocin. CTQW-derived centrality rankings are accessible on near-term intermediate-scale quantum hardware, as we demonstrate through a proof-of-principle implementation on IBM superconducting quantum hardware. These results establish continuous-time quantum walks as a computationally tractable framework for protein network analysis, that connects network theoretical treatments of protein structural biology to continuous-time quantum walk dynamics.
We present a quantum-dynamical framework for identifying structurally important residues in proteins based on continuous time quantum walks (CTQWs) on weighted residue interaction networks constructed from experimentally resolved structures. By mapping the weighted adjacency matrix to a Hamiltonian, residue importance emerges from the long-time averaged occupation probability, confirmed analytically through its spectral decomposition. Across a dataset of approximately 150 proteins spanning diverse structural and functional classes, CTQW centrality exhibits consistently strong agreement with classical eigenvector centrality in identifying central residues, while extending beyond it through incorporating signatures of quantum interference. Analyzing the time-averaged quantum transition matrix reveals consistently larger spectral gaps than the classical random-walk operator. Furthermore, biological relevance is confirmed through recovery of experimentally established functional residues in proteins kinase A and oxytocin. CTQW-derived centrality rankings are accessible on near-term intermediate-scale quantum hardware, as we demonstrate through a proof-of-principle implementation on IBM superconducting quantum hardware. These results establish continuous-time quantum walks as a computationally tractable framework for protein network analysis, that connects network theoretical treatments of protein structural biology to continuous-time quantum walk dynamics.
We present a quantum-dynamical framework for identifying structurally and functionally important residues in proteins based on continuous-time quantum walks (CTQWs) on weighted residue-interaction networks constructed from experimentally resolved structures. By mapping the weighted adjacency matrix to a Hamiltonian, residue importance emerges from the long-time averaged occupation probability, confirmed analytically through its spectral decomposition. Across a data set of 150 proteins spanning diverse structural and functional classes, CTQW centrality exhibits consistently strong agreement with classical eigenvector centrality in identifying central residues, while extending beyond it through incorporating signatures of quantum interference. Analyzing the time-averaged quantum transition matrix reveals consistently larger spectral gaps than the classical random-walk operator. Furthermore, biological relevance is confirmed through recovery of experimentally established functional residues in proteins kinase A and oxytocin. CTQW-derived centrality rankings are accessible on near-term intermediate-scale quantum hardware, as we demonstrate through a proof-of-principle implementation on IBM superconducting quantum hardware. These results establish continuous-time quantum walks as a computationally tractable framework for protein network analysis, that connects network theoretical treatments of protein structural biology to continuous-time quantum walk dynamics.
Abstract Long-range interactions between residues in proteins underlie diverse biological processes such as signal transmission, conformational regulation, and catalysis. Identifying residues that mediate such communication remains a major challenge. Herein, we introduce a framework based on quantum walks and entropy, and employ it on protein structures to predict important residues participating in long-range interactions. The selected proteins have been well-studied experimentally in literature. Our approach models information flow through protein contact networks using discrete-time quantum walk dynamics, where quantum superposition and interference govern transition amplitudes at the residue level. Normalized time-averaged transition probabilities quantify interaction strength between residues, while Shannon entropy calculations identify residues exhibiting delocalized interaction behavior. We find that the residues identified by us are known to be structurally and functionally important in literature, thereby confirming the predictive capacity of this framework. We experimentally validate our formalism on As LOV2 (PDB: 2V0U) using site-directed mutagenesis, protein purification, and dark-recovery kinetics. The predicted residues are important for understanding the mechanism of photosensing in As LOV2. Significance This study bridges quantum transport theory and structural biology by introducing discrete-time quantum walks as a mechanism to model communication between residues. We provide a scalable and interpretable method to predict key residues, without requiring molecular dynamics or prior functional annotation. The present method, inspired by quantum physics and quantum information, and validated by experiments, offers a broad and robust framework to study communication in biomolecular systems. It further demonstrates how quantum principles such as coherence and interference can enhance our understanding of information flow in biological macromolecules.
Centrality measure is an essential tool in network analysis and widely used in the domain of computer science, biology and sociology. Taking advantage of the speedup offered by quantum computation, various quantum centrality measures have been proposed. However, few work of quantum centrality involves weighted graphs, while the weight of edges should be considered in certain real-world networks. In this work, we extend the centrality measure based on continuous-time quantum walk to weighted graphs. We testify the feasibility and reliability of this quantum centrality using an ensemble of 41,675 graphs with various topologies and comparing with the eigenvector centrality measure. The average Vigna's correlation index of all the tested graphs with all edge weights in [1, 10] is as high as 0.967, indicating the pretty good consistency of rankings by the continuous-time quantum walk centrality and the eigenvector centrality. The intuitive consistency of the top-ranked vertices given by this quantum centrality measure and classical centrality measures is also demonstrated on large-scale weighted graphs. Moreover, the range of the continuous-time quantum walk centrality values is much bigger than that of classical centralities, which exhibits better distinguishing ability to pick the important vertices from the ones with less importance. All these results show that the centrality measure based on continuous-time quantum walk still works well on weighted graphs.
We introduce RinQ, a hybrid quantum-classical framework for identifying functionally critical residues in proteins, utilizing techniques in quantum optimization. To that end, protein structures are modeled as residue interaction networks (RINs), and the centrality detection task is cast as a Quadratic Unconstrained Binary Optimization (QUBO) problem. Solved using D-Wave’s simulated annealing, this approach is applied to a diverse set of proteins, including small peptides and biologically significant regulatory proteins. RinQ consistently finds residues that align with classical centrality benchmarks, underscoring the accuracy and reliability of the approach. This work highlights the promise of near-term quantum and quantum-inspired methods for advancing protein network analysis and lays the groundwork for future extensions to larger systems using real quantum hardware.
Continuous-time quantum walks (CTQWs) exhibit localization phenomena that differ fundamentally from their classical counterparts, yet the precise relationship between network structure, spectral degeneracy, and confined dynamics remains incompletely understood. In this work, we present a complete analytical characterization of localization in CTQWs on two highly symmetric graph families: barbell graphs and star-of-cliques graphs. These networks combine pronounced spectral degeneracy with modular structure, enabling exact diagonalization and explicit computation of both eigenstate and dynamical inverse participation ratios (IPRs). Our analysis reveals that localization is governed by the interplay between degenerate subspaces, which generate families of confined modes, and hybridization between invariant subspaces, which redistributes spectral weight. Notably, the dynamical IPR can exceed expectations based solely on eigenstate IPRs, demonstrating that coherent superposition within degenerate eigenspaces enhances confinement. By connecting IPR values to the effective number of vertices visited, we provide a structural diagnostic for predicting quantum transport outcomes in modular networks, establishing that connectivity alone can determine where and how strongly a quantum walk localizes.
We present RinQ, a hybrid quantum-classical approach for identifying functionally critical residues in proteins by leveraging quantum computing techniques for optimization. Proteins, modeled as residue interaction networks, alongside the task of selecting top central residues, is formulated as a Quadratic Unconstrained Binary Optimization (QUBO) problem, which is then solved using D-Wave’s simulated annealing. Applied across a diverse set of proteins, the presented approach consistently identifies central residues aligned with classically calculated central sites. RinQ thus exemplifies the potential of near-term quantum and quantum-inspired methods to accelerate protein analysis and inform drug discovery. Our findings match classical benchmarks for small peptides and sets the stage for extending QUBO-based centrality detection to larger proteins using real quantum hardware.