Crossing the 12,000-atom barrier with heterogeneous quantum-classical supercomputing: quantum chemistry of protein-ligand complexes

Abstract: Ab initio wavefunction methods provide accurate molecular simulations but their computational scaling restricts applications to small systems. We develop a workflow combining quantum embedding to decompose a molecule into fragments with a heterogeneous quantum-classical (HQC) method to simulate fragments. We sample fragment electronic configurations on two 156-qubit quantum processors (ibm$_$cleveland, ibm$_$kobe), using up to 94 qubits, running 9,200 circuits for over 100 hours, collecting $1.3 \cdot 10<sup>9$ measurement outcomes - the most resource-intensive HQC computation for quantum chemistry to date. We compute fragment wavefunctions via optimized subspace diagonalization on two supercomputers (Fugaku, Miyabi-G), 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 and 12,635 atoms), demonstrate $&gt;40\times$ increase in system size and up to $210\times$ improvement in accuracy over the previous state-of-the-art, with HQC matching coupled-cluster (CCSD) accuracy in fragment energies, and establish a scalable pathway for systematically improvable biomolecular simulations.

• The paper presents a quantum-classical workflow that overcomes the 12,000-atom barrier in protein-ligand complex simulations using advanced quantum embedding techniques.
• It introduces the TrimSQD fragment solver that uses spatially localized orbital truncation and configuration trimming to reduce computation costs significantly.
• The method achieves up to 210× improved fragment accuracy with near-peak supercomputing efficiency, setting a new benchmark for scalable quantum chemistry.

Crossing the 12,000-Atom Barrier in Quantum Chemistry of Protein-Ligand Complexes via Heterogeneous Quantum-Classical Supercomputing

Introduction

Ab initio wavefunction-based quantum chemistry offers a path to exact modeling of molecular electronic structure, yet its exponential scaling restricts practical application to small molecules. This paper presents an algorithmic and computational advance, crossing the 12,000-atom barrier for electronic structure calculations of protein-ligand complexes. The workflow combines quantum embedding, fragment decomposition, and heterogeneous quantum-classical (HQC) simulation, exploiting pre-fault-tolerant quantum processors alongside exascale supercomputing resources. The reported platform achieves simulation sizes and accuracies unattainable with conventional methods, demonstrating a $>40\times$ increase in size and up to $210\times$ improvement in fragment accuracy relative to previous state-of-the-art HQC approaches.

Algorithmic Innovations

The core of the workflow leverages quantum embedding via the Embedded WaveFunction (EWF) formalism to partition large biomolecules into fragments—each treated independently under high-level wavefunction methods. The major algorithmic advances are:

• Spatially Localized Orbital Truncation and ERI Localization: Fragment construction formerly required $O(M^5)$ scaling for two-electron repulsion integral (ERI) evaluation and full-system MP2 calculations. This bottleneck is eliminated by spatially restricting MP2 and ERI computation to localized neighborhoods of each fragment, reducing construction cost to $O(1)$ per fragment and enabling embarrassingly parallel execution on HPC resources.

Figure 1: Schematic visualization of investigated systems, hierarchical algorithmic flow, fragment representation, and localized fragment construction that underpins scalable HQC embedding.

• TrimSQD Fragment Solver: TrimSQD is introduced as an advanced HQC fragment solver—building on sample-based quantum diagonalization (SQD) and its ExtSQD variant. TrimSQD improves fragment accuracy by integrating configuration trimming based on diagonalization results and optimizing configuration selection via subgroup interaction. The workflow incorporates distributed, GPU-accelerated Selected-Basis Diagonalization (SBD-G), supporting scalable execution across thousands of fragments.

Figure 2: Comparison of ExtSQD and TrimSQD workflows, highlighting configuration selection and parallelization innovations.

Computational Implementation and Resource Utilization

Quantum sampling is accomplished on two 156-qubit Heron r2 QPUs ("cleveland" and "kobe"), with up to 94 qubits sampled per circuit, over 100 hours and 9,200 circuit executions—yielding $1.3 \cdot 10^9$ measurement outcomes. Fragment diagonalization is performed on the Fugaku (CPU-based) and Miyabi-G (GPU-based) supercomputers, achieving near-peak node utilization and 72.5% parallel efficiency in subspace diagonalization.

Performance Scaling

Strong scaling of TrimSQD and its dominant computational kernel, matrix-vector multiplication, is validated on large fragments ($N_{\mathrm{sub}}=2^{32}$). Increasing HPC node counts yields high parallel efficiency, with sublinear scaling at extreme node counts reflecting diminishing returns due to communication overhead.

Figure 3: Strong scaling characterization of TrimSQD for a large fragment, displaying parallel efficiency across node counts.

Figure 4: Strong scaling of matrix-vector multiplication, the dominant operation in subspace diagonalization for HQC fragment solvers.

Accuracy and Tradeoffs

TrimSQD consistently outperforms ExtSQD in fragment energy accuracy, with lower energies especially in larger fragments. Benchmark fragments in trypsin and T4-Lysozyme complexes show that TrimSQD achieves accuracies comparable to DMRG and CCSD.

Figure 5: TrimSQD delivers systematic improvement in fragment energy accuracy over ExtSQD for large fragments.

Time-to-accuracy analysis demonstrates that TrimSQD (with SBD-G) attains high accuracy at substantially reduced runtime relative to classical SCI and DMRG implementations, which are limited in parallelization and memory scaling.

Figure 6: Accuracy–time tradeoff analysis for representative fragments, comparing TrimSQD, ExtSQD, SCI, and DMRG.

Practical and Theoretical Implications

This study fundamentally expands the feasible scope of quantum chemistry simulations in biomolecular contexts, enabling protein-ligand complexes to be treated at scales previously limited to small molecules. Fragment-solving accuracy matches coupled-cluster (CCSD) and DMRG, ensuring chemical reliability. The scalable HQC approach establishes a practical template for harnessing near-term quantum processors as specialized fragment solvers within quantum embedding workflows—anticipated to be a dominant mode in early-fault-tolerant quantum computing.

The methodological advances provide a pathway for systematic improvement (via fragment expansion and tighter thresholds) and are extensible to other scientific domains (e.g., catalysis, materials science) requiring quantum-accurate modeling at large scales.

Future Outlook

Projected development of early-fault-tolerant QPUs (with 200–2,000 logical qubits) will further boost fragment solver capabilities, potentially outpacing classical solvers for intermediate-scale fragments, while HQC frameworks remain essential for tackling full-system biomolecular complexity. Integration of algorithmic and implementation innovations (such as SBD-G) into classical methods will continue to drive performance gains, blurring boundaries between quantum and classical computing in computational chemistry.

Conclusion

The combination of lower-scaling quantum embedding, advanced HQC fragment solvers (TrimSQD), and large-scale supercomputing resources enables electronic structure calculations for biomolecular systems exceeding 12,000 atoms, achieving highly accurate energies and establishing a foundation for scalable, systematic HQC modeling in quantum chemistry. These results underscore the viability of HQC paradigms and quantum embedding for the practical deployment of quantum computing in scientific discovery.