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arXiv:2607.09737

Q-Score: A Quantum-Native Scoring Function for Molecular Docking

Kangyu Zheng, Yidong Zhou, Ruihao Li, Zixin Ding, Zhiding Liang, Shaohua Li

Published Jul 2, 2026• 0 citations
arXivHTMLPDF

Abstract

Molecular docking predicts how a small molecule binds to a protein and is a key bottleneck in drug discovery. Classical scoring functions sum empirical pairwise contacts, blind to quantum-mechanical effects like orbital charge transfer that govern binding specificity. We introduce Q-Score, encoding GNN-predicted orbital donor-acceptor energies into a weighted graph and scoring binding by solving a maximum-weight vertex clique problem via Digitized-Counterdiabatic QAOA. Each interaction anchor maps to one qubit and compatibility constraints become edges. Across 11 protein targets, DC-QAOA recovers the exact optimum on 8 at 10 qubits. On 1000 AI-generated molecules, Q-Score is orthogonal to classical scoring with Spearman rho of 0.05, driven by orbital quality with rho of 0.90, and free of molecular-weight bias, enriching for strong orbital interactions at twice the random rate. DC-QAOA achieves a mean approximation ratio of 0.94 with 52 percent exact. Execution of 1000 circuits on IBM Eagle confirms 6-qubit solvability on NISQ hardware.

DOI
10.48550/arxiv.2607.09737

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Molecular docking predicts how a small molecule binds to a protein and is a key bottleneck in drug discovery. Classical scoring functions sum empirical pairwise contacts, blind to quantum-mechanical effects like orbital charge transfer that govern binding specificity. We introduce Q-Score, encoding GNN-predicted orbital donor-acceptor energies into a weighted graph and scoring binding by solving a maximum-weight vertex clique problem via Digitized-Counterdiabatic QAOA. Each interaction anchor maps to one qubit and compatibility constraints become edges. Across 11 protein targets, DC-QAOA recovers the exact optimum on 8 at 10 qubits. On 1000 AI-generated molecules, Q-Score is orthogonal to classical scoring with Spearman rho of 0.05, driven by orbital quality with rho of 0.90, and free of molecular-weight bias, enriching for strong orbital interactions at twice the random rate. DC-QAOA achieves a mean approximation ratio of 0.94 with 52 percent exact. Execution of 1000 circuits on IBM Eagle confirms 6-qubit solvability on NISQ hardware.
Molecular docking is a critical process for drug discovery and challenging due to the complexity and size of biomolecular systems, where the optimal binding configuration of a drug to a target protein is determined. Hybrid classical-quantum computing techniques offer a novel approach to address these challenges. The Quantum Approximate Optimization Algorithm (QAOA) and its variations are hybrid classical-quantum techniques, and a promising tool for combinatorial optimization challenges. This paper presents a Digitized Counterdiabatic QAOA (DC-QAOA) approach to molecular docking. Simulated quantum runs were conducted on a GPU cluster. We examined 14 and 17 nodes instances - to the best of our knowledge the biggest published instance is 12-node at Ding et al. and we present the results. Based on computational results, we conclude that binding interactions represent the anticipated exact solution. Additionally, as the size of the examined instance increases, the computational times exhibit a significant escalation.
Molecular docking plays a pivotal role in drug discovery and precision medicine, furnishing insights into protein functionalities and fostering the development of therapeutics. Here, we introduce a potential alternative solution to this problem using a quantum approximate optimization algorithm (QAOA) based algorithm. Our method was applied to analyze diverse biological systems, including the SARS-CoV-2 Mpro{\mathrm{M}}^{\text{pro}}Mpro complex with PM-2-020B, the DPP-4 complex with piperidine fused imidazopyridine 34, and the HIV-1 gp120 complex with JP-III-048. We found that the digitized-counterdiabatic QAOA (DCQAOA), which integrates the concept of counterdiabatic driving, surpasses the conventional QAOA in terms of quantum circuit depth and optimization efficiency. This is particularly evident in complex molecular-docking challenges, where DCQAOA delivers more accurate and biologically relevant results. Our research highlights the promising role of quantum computing in drug discovery and contributes significant insights towards the optimization of protein-ligand docking methodologies.
Molecular docking is a vital computational task in drug discovery, wherein the objective is to efficiently identify optimal binding poses between a ligand and a target receptor protein. Due to the combinatorial explosion of possible binding configurations, docking of large and flexible molecules remains a computationally intensive problem, especially at scale. Early studies have revealed that the molecular docking can be re-cast as a maximum vertex-weighted clique problem (MVWCP) problem on a compatibility graph to be solved classically. In this work, we proposed a hybrid quantum-classical approach for molecular docking leveraging the MVWCP formalism with a variational full-basis encoding (FBE) strategy, which enables efficient encoding of classical binary variables with Bloch sphere vectors. We further prove that a global minimizer of the FBE objective can always be chosen to be a pure product state, thereby providing a rigorous justification for its optimization using a unitary variational circuit. The molecular docking problem is first mapped to a cost Hamiltonian that is minimized within a variational framework, optimized via a randomized imaginary time evolution (ITE)-inspired warm start, and gradient-based techniques. Finally, we also executed the circuit on an IBM quantum computer, underlying the feasibility and of quantum-assisted optimization for structure-based drug design and point towards the broader utility of advanced encoding techniques in quantum optimization for computational biology.
The large search space and the challenge of accurately simulating quantum-level molecular interactions are the fundamental causes of the delayed, complicated, and costly process of discovering new medications. The effectiveness of conventional computational techniques, including molecular docking and molecular dynamics, to assess molecular characteristics and provide highly accurate drug candidate predictions is constrained. This paper presents a Quantum-Assisted Drug Discovery Simulation framework that combines cutting-edge quantum computing algorithms, specifically the Quantum Approximate Optimization Algorithm (QAOA) and the Variational Quantum Eigensolver (VQE), with traditional molecular docking tools like RDKit and AutoDock. The system uses these quantum algorithms to perform very accurate Quantum Refinement on the most potential therapeutic protein poses found by classical identification. This hybrid approach seeks to optimize drug-protein interactions more quickly, speed up early-stage drug discovery, and create opportunities for less costly, more accurate medical research, even though a combination of quantum and classical calculations allows more accurate prediction of molecular energies and binding affinities.
New computational strategies, such as molecular docking, are emerging to speed up the drug discovery process. This method predicts the activity of molecules at the binding site of proteins, helping to select the ones that exhibit desirable behavior and rejecting the rest. However, for large chemical libraries, it is essential to search and score configurations using fewer computational resources while maintaining high precision. In this work, we map the molecular docking problem to a graph problem, a maximum-weight independent set problem on a unit-disk graph in a physical neutral atom quantum processor. Here, each vertex represents an atom trapped by optical tweezers. The Variational Quantum Adiabatic Algorithm (VQAA) approach is used to solve the generic graph problem with two optimization methods, Scipy and Hyperopt. Additionally, a machine learning method is explored using the adiabatic algorithm. Results for multiple graphs are presented, and a small instance of the molecular docking problem is solved, demonstrating the potential for near-term quantum applications.
Molecular docking, a critical task in drug discovery, represents a highly promising application domain for quantum computing. While the Quantum Approximate Optimization Algorithm (QAOA) shows potential, its performance on near-term quantum devices is limited by noise susceptibility and optimization challenges such as barren plateaus. To address these limitations, we apply Adaptive Bias Fields QAOA (ABF-QAOA) to solve molecular docking problems mapped to Ising Hamiltonians. Our results demonstrate that ABF-QAOA achieves accelerated convergence and higher solution accuracy compared to standard QAOA. In addition, under simulated quantum noise conditions, ABF-QAOA maintains higher solution quality, showcasing significantly enhanced noise resilience. This work establishes ABF-QAOA as a robust quantum approach for molecular docking on noisy intermediate-scale quantum (NISQ) hardware.