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Journal of Chemical Information and Modeling

Quantum Computing Calculations of Protein–Ligand Binding Energies Using Decomposition Methods on Simulated and Real Quantum Hardware

Hironobu Kitajima, Carlos Bistafa, Takao Kobayashi, Shu Kanno, Okimasa Okada, Kouta Murasaki, Jumpei Koyama, Ryuta Saito, Qi Gao

Published Jul 9, 2026• 0 citations
Publisher

Abstract

We analyzed the performance of quantum algorithms for studying protein-ligand systems, using both simulator and real hardware. To achieve this, we selected thrombin and 5 ligands as a test case and employed a decomposition strategy using density matrix embedded theory, dividing the ligand systems into three fragments each. First, the energy of one of the fragments was calculated using the Variational Quantum Eigensolver (VQE) using a state vector simulator, while the energy of the remaining fragments was calculated using Couple Cluster Singles and Doubles (CCSD), with the protein treated as point charges located at the respective atomic sites. Through these noiseless simulations, we evaluated the results under ideal conditions using the state-of-the-art Unitary CCSD ansatz to validate the efficacy of the strategy in a controlled setting without quantum noise. Subsequently, we evaluated the impact of approximations in the ansatz, optimizer, and active space size, which are necessary to decrease the computational cost, in order to target real hardware during the current Noisy Intermediate-Scale Quantum era. Finally, we performed the VQE calculations using a superconducting quantum computer developed by the RIKEN RQC-Fujitsu Collaboration Center and also analyzed the noise effect through simulations. The results demonstrated that the use of quantum algorithms can enhance the binding energy correlation value, offering potential applications in the workflow of computer-aided drug design.

DOI
10.1021/acs.jcim.6c00544

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We analyzed the performance of quantum algorithms for studying protein-ligand systems, using both simulator and real hardware. To achieve this, we selected thrombin and 5 ligands as a test case and employed a decomposition strategy using density matrix embedded theory, dividing the ligand systems into three fragments each. First, the energy of one of the fragments was calculated using the Variational Quantum Eigensolver (VQE) using a state vector simulator, while the energy of the remaining fragments was calculated using Couple Cluster Singles and Doubles (CCSD), with the protein treated as point charges located at the respective atomic sites. Through these noiseless simulations, we evaluated the results under ideal conditions using the state-of-the-art Unitary CCSD ansatz to validate the efficacy of the strategy in a controlled setting without quantum noise. Subsequently, we evaluated the impact of approximations in the ansatz, optimizer, and active space size, which are necessary to decrease the computational cost, in order to target real hardware during the current Noisy Intermediate-Scale Quantum era. Finally, we performed the VQE calculations using a superconducting quantum computer developed by the RIKEN RQC-Fujitsu Collaboration Center and also analyzed the noise effect through simulations. The results demonstrated that the use of quantum algorithms can enhance the binding energy correlation value, offering potential applications in the workflow of computer-aided drug design.
We develop a workflow decomposing a molecule into fragments via quantum embedding and simulating them with a heterogeneous quantum-classical (HQC) method. We sample fragment electronic configurations on two 156-qubit quantum processors (ibm_\__cleveland, ibm_\__kobe), using up to 94 qubits, running 21,006 circuits for over 239 hours, collecting 3.0⋅1093.0 \cdot 10^93.0⋅109 measurement outcomes -- the most resource-intensive HQC computation for quantum chemistry to date. We compute fragment wavefunctions via optimized subspace diagonalization on supercomputers Fugaku, Miyabi-G, and ROQUO, achieving 72.5%\%% parallel efficiency with scalable distributed linear algebra kernels. We simulate two protein-ligand complexes spanning dispersion- and electrostatics-dominated regimes (11,608, 12,635 atoms), demonstrate >40×>40\times>40× increase in system size and up to 210×210\times210× improvement in accuracy over previous state-of-the-art, with HQC matching coupled-cluster (CCSD) accuracy in fragment energies. We present the first HQC protein-ligand binding prediction using a mixed-basis set and an automated end-to-end workflow enabling practical HQC calculations of large protein systems.
Variational quantum eigensolver (VQE) is a hybrid quantum-classical algorithm designed for noisy intermediate-scale quantum (NISQ) computers. It is promising for quantum chemical calculations (QCC) because it can calculate the ground-state energy of molecules. Although VQE has a theoretical potential to achieve a higher accuracy than classical approximation methods, it is challenging to achieve it on current NISQ computers due to the significant impact of noise. Density matrix embedding theory (DMET) is a well-known technique that can be used to decompose a molecule into multiple fragments, which is available to mitigate the noise impact on VQE. However, our preliminary evaluation shows that the naive combination of DMET and VQE hardly mitigates it. In this work, we present two proposals to mitigate the noise impact on the DMET+VQE combination. (1) The size of quantum circuits used by VQE is decreased by reducing the number of bath orbitals which represent interactions between multiple fragments in DMET. (2) While VQE is executed on a NISQ computer, reduced density matrices (RDMs), which are used to calculate the energy of fragments in DMET, are calculated accurately by executing quantum circuits using a noise-less quantum computer simulator. The evaluation using a noisy quantum computer simulator shows that our proposals improve the accuracy of the DMET+VQE combination by an order of magnitude.
Variational quantum eigensolver (VQE) is a hybrid quantum-classical algorithm designed for noisy intermediate-scale quantum (NISQ) computers. It is promising for quantum chemical calculations (QCC) because it can calculate the ground-state energy of a target molecule. Although VQE has a potential to achieve a higher accuracy than classical approximation methods in QCC, it is challenging to achieve it on current NISQ computers due to the significant impact of noises. Density matrix embedding theory (DMET) is a well-known technique to divide a molecule into multiple fragments, which is available to mitigate the noise impact on VQE. However, our preliminary evaluation shows that the naive combination of DMET and VQE does not outperform a gold standard classical method. In this work, we present three approaches to mitigate the noise impact for the DMET+VQE combination. (1) The size of quantum circuits used by VQE is decreased by reducing the number of bath orbitals which represent interactions between multiple fragments in DMET. (2) Reduced density matrices (RDMs), which are used to calculate a molecular energy in DMET, are calculated accurately based on expectation values obtained by executing quantum circuits using a noise-less quantum computer simulator. (3) The parameters of a quantum circuit optimized by VQE are refined with mathematical post-processing. The evaluation using a noisy quantum computer simulator shows that our approaches significantly improve the accuracy of the DMET+VQE combination. Moreover, we demonstrate that on a real NISQ device, the DMET+VQE combination applying our three approaches achieves a higher accuracy than the gold standard classical method.
Accurate prediction of binding energies between drug candidates and target molecules is essential in computational drug discovery, as stronger (more negative) binding energies suggest higher efficacy. This energy corresponds to the ground state of the molecular system and can be computed using methods such as Full Configuration Interaction (FCI), Hartree-Fock (HF), Variational Quantum Eigensolver (VQE), and Quantum Phase Estimation (QPE). While FCI offers benchmark accuracy, its computational cost renders it impractical for larger systems. HF scales efficiently but at the expense of precision. QPE, though theoretically robust, is currently constrained by hardware limitations. VQE emerges as a practical alternative for Noisy Intermediate-Scale Quantum (NISQ) devices, balancing accuracy and feasibility. Nevertheless, quantum noise significantly affects VQE performance. To address this, we incorporate Zero Noise Extrapolation (ZNE) to mitigate errors and improve energy estimates. This study compares these approaches and demonstrates the efficacy of the VQEZNE framework in generating reliable binding energy calculations for drug design applications.
The Variational Quantum Eigensolver (VQE) is a promising quantum algorithm for applications in chemistry within the Noisy Intermediate-Scale Quantum (NISQ) era. The ability for a quantum computer to simulate electronic structures with high accuracy would have a profound impact on material and biochemical science with potential applications e.g., to the development of new drugs. However, considering the variety of quantum hardware architectures, it is still uncertain which hardware concept is most suited to execute the VQE for e.g., the simulation of molecules. Aspects to consider here are the required connectivity of the quantum circuit used, the size and the depth and thus the susceptibility to noise effects. Besides theo-retical considerations, empirical studies using available quantum hardware may help to clarify the question of which hardware technology might be better suited for a certain given application and algorithm. Going one step into this direction, within this work, we present results using the VQE for the simulation of the hydrogen molecule, comparing superconducting and ion trap quantum computers. The experiments are carried out with a standardized setup of ansatz and optimizer, selected to reduce the number of required iterations. The findings are analyzed considering different quantum processor types, calibration data as well as the depth and gate counts of the circuits required for the different hardware concepts after transpilation.
Background: Understanding electronic interactions in protein active sites is fundamental to drug discovery and enzyme engineering, but remains computationally challenging due to exponential scaling of quantum mechanical calculations. Results: We present a quantum-classical hybrid framework for simulating protein fragment electronic structure using variational quantum algorithms. We construct fermionic Hamiltonians from experimentally determined protein structures, map them to qubits via Jordan-Wigner transformation, and optimize ground state energies using the Variational Quantum Eigensolver implemented in pure Python. For a 4-orbital serine protease fragment, we achieve chemical accuracy (< 1.6 mHartree) with 95.3% correlation energy recovery. Systematic analysis reveals three-phase convergence behaviour with exponential decay (α = 0.95), power law optimization (γ = 1.21), and asymptotic approach. Application to SARS-CoV-2 protease inhibition demonstrates predictive accuracy (MAE=0.25 kcal/mol), while cytochrome P450 metabolism predictions achieve 85% site accuracy. Conclusions: This work establishes a pathway for quantum-enhanced biomolecular simulations on near-term quantum hardware, bridging quantum algorithm development with practical biological applications.