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Crossing the 12,000-atom barrier with heterogeneous quantum-classical supercomputing: quantum chemistry of protein-ligand complexes
Kenneth M. Merz,, Akhil Shajan, Danil Kaliakin, Fangchun Liang, Yuichi Otsuka, Tomonori Shirakawa, Lukas Broers, Han Xu, Miwako Tsuji, Mitsuhisa Sato, Seiji Yunoki, Ryo Wakizaka, Yukio Kawashima, Jun Doi, Toshinari Itoko, Hiroshi Horii, Thaddeus Pellegrini, Javier Robledo Moreno, Kevin J. Sung, Ella Fejer, Robert Walkup, Seetharami Seelam, Mario Motta
TL;DR
Accurate wavefunction simulations are difficult to scale to biomolecular systems because fragment construction and fragment equations remain computationally demanding. The paper combines quantum embedding with HQC fragment solvers and scalable distributed linear algebra to simulate protein-ligand complexes at 12,000-atom scale. The resulting calculations exceed prior HQC system sizes by more than 40× and improve accuracy by up to 210×, while matching CCSD accuracy in fragment energies.
Problem
Wavefunction methods provide accurate, systematically improvable molecular simulations, but biomolecular-scale applications are constrained by costly fragment construction and fragment solutions.
Method
The workflow combines lower-scaling EWF fragment construction with TrimSQD HQC fragment calculations and GPU-accelerated SBD-G distributed linear algebra.
Results
More than 40× larger systems and up to 210× higher accuracy than prior HQC studies were achieved, with HQC fragment solutions matching leading classical solver accuracy.
Takeaways & Limitations
The workflow enables systematically improvable HQC quantum-chemistry calculations for protein-ligand complexes at approximately 12,000-atom scale.
Abstract
from arXiv · showhide
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 $1.3 \cdot 10^9$ 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 $>40\times$ 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.
I. DESCRIPTION
Accurate wavefunction methods remain difficult to scale to biomolecular systems, motivating quantum embedding and heterogeneous quantum-classical workflows. The work combines fragment decomposition, improved fragment solvers, and large-scale classical computing to reach 12,000-atom simulations.
- Motivation: Chemical-accuracy predictions for biomolecules require scalable methods that can treat thousands of atoms while retaining accurate energy differences.This is especially relevant to protein-ligand binding energies and structure-based drug discovery.
- Motivation: Wavefunction methods offer systematically improvable accuracy, but solving the many-electron Schrödinger equation remains computationally costly and limits accessible system sizes.DFT is more scalable but may lack the accuracy required for drug-discovery applications.
- Approach: Quantum embedding partitions a molecule into independently treated fragments, allowing quantum processors to act as specialized co-processors within a classical workflow.The approach exploits spatial locality and coarse-grained parallelism.
- Challenges: Embedding at biomolecular scale requires compact accurate fragment bases and systematically improvable fragment solutions without overwhelming memory bandwidth, accelerators, or inter-node communication.These constraints motivate algorithmic and software advances in the HQC workflow.
IV. INNOVATIONS REALIZED
The workflow addresses conventional EWF bottlenecks in fragment-construction cost, fragment-solver accuracy, and distributed diagonalization, enabling 12,000-atom HQC calculations with improved accuracy.
- Limitations: O(M^5) fragment-construction cost and O(M) fragment growth make biochemical-scale EWF calculations computationally demanding.Conventional EWF also faces inaccurate SQD and ExtSQD fragment solutions and requires GPU-accelerated distributed diagonalization.
- Innovations: The workflow combines lower-scaling EWF with higher-accuracy TrimSQD fragment solutions to improve scalability and accuracy.These innovations target the principal limitations of conventional EWF with HQC fragment solvers.
- Impact: 12,635 atoms represents more than 40× the previous HQC size of 303 atoms.The calculations use quantum embedding and TrimSQD fragment solutions.
- Impact: 0.1 mHa deviation from DMRG for the largest trypsin fragment corresponds to a 210× accuracy improvement.The largest Trp-cage fragment has a 21 mHa deviation.
A. Overarching algorithm
The overarching algorithm combines Hartree–Fock orbital generation, EWF fragment decomposition, parallel fragment solvers, HQC subspace diagonalization, and parallel energy reconstruction.
- Input and decomposition: O(M^3) Hartree–Fock generates molecular orbitals that serve as quantum-embedding inputs.Here, M is the number of orbitals in the full system.
- Input and decomposition: EWF decomposes the molecule into fragments, with construction reduced from O(M^5) to O(1) per fragment and parallelized across fragments.The reduced-scaling construction is described as embarrassingly parallel.
- Fragment solvers: Fragments use FCI for small hydrogen-centered cases, TrimSQD for heavier-atom cases, and CCSD as a classical comparison.TrimSQD is used for fragments with 13 ≤ M_c ≤ 45.
- HQC fragment calculation: Quantum sampling, subspace diagonalization, and subspace extension generate fragment solutions before parallel energy reconstruction.Quantum circuits produce electronic configurations that guide subspace diagonalization.
B. Innovations in EWF fragment construction
EWF fragment construction is made scalable by localizing orbital and integral computations, removing full-system data dependencies and enabling embarrassingly parallel fragment processing.
- Construction strategy: The construction innovations eliminate data dependencies at full-system scale and make fragment processing embarrassingly parallel.They target the cost and memory bottlenecks of conventional EWF construction.
- Localized MP2: O(M^5) MP2 cost is reduced by restricting each fragment calculation to orbitals within a 7 Å radius.The restriction is centered on the atom defining the fragment.
- Localized ERIs: O(M^4) ERI construction and its large memory and I/O requirements are addressed by restricting ERIs to orbitals within Rcut + 3 Å.The buffer is intended to avoid artificial boundary effects while controlling computational cost.
- Impact: Localized orbital truncation and ERI construction reduce fragment-construction cost to O(1) per fragment.The resulting operation is embarrassingly parallel.
1) TrimSQD:
TrimSQD improves configuration selection by combining recovery, subgroup diagonalization, contribution-based trimming, subspace extension, and final thresholded diagonalization.
- TrimSQD workflow: TrimSQD introduces determinant trimming based on diagonalization results into ExtSQD to improve configuration selection.The approach draws on closed-loop SQD and TrimCI.
- Configuration recovery: The configuration-recovery loop merges recovered configurations, partitions them across subgroups, and diagonalizes each subgroup.The loop carries selected configurations between iterations.
- Configuration trimming: Top k1-percent configurations by contribution to |Ψ_x| are retained from subgroup diagonalizations, followed by global retention of the top k2 percent.The global subspace diagonalization spans all MPI ranks.
- Subspace extension: The subspace is extended with configurations coupled to retained configurations by H_xy ≠ 0 and Hamming distance at most two.Final diagonalization retains configurations satisfying |Ψ_x| > ε.
- Subspace extension: The final expanded-subspace diagonalization typically dominates execution time because its dimension becomes very large.It is performed on all MPI ranks using the user-defined threshold ε.
2) Selected-basis diagonalization:
Selected-Basis Diagonalization (SBD) addresses the dominant cost of ExtSQD and TrimSQD through distributed-memory execution, GPU acceleration, and redesigned matrix–vector multiplication. TrimSQD further improves configuration selection by introducing interactions between otherwise independent configuration subgroups.
- Subspace diagonalization dominates ExtSQD and TrimSQD computational cost, motivating an implementation tailored for large-scale parallel execution.
- SBD partitions each vector across computing nodes, reducing per-node memory requirements and enabling scalable large-problem computations.
- GPU acceleration redesigns the dominant matrix–vector multiplication kernel with fine-grained data-parallel primitives and GPU-resident layouts.
- TrimSQD introduces interactions between subgroups of otherwise independent configurations, improving configuration selection and fragment-energy accuracy.
- The experiments benchmark two contrasting protein–ligand complexes to assess the workflow’s portability.
- The trypsin–benzamidine benchmark contains 12,635 atoms and 31,795 molecular orbitals, while T4-Lysozyme–n-butyl-benzene contains 11,608 atoms and 28,844 molecular orbitals.
B. HPC and Quantum computing platforms
The workflow distributes quantum sampling across two 156-qubit QPUs and performs fragment subspace diagonalization on Fugaku and Miyabi-G. Its timing and performance measurements distinguish processor-reported QPU runtime from classical wall-clock time and track hardware quality metrics.
- Quantum sampling is distributed across ibm_cleveland and ibm_kobe, two 156-qubit Heron r2 QPUs.
- ExtSQD and TrimSQD subspace diagonalization run on both Fugaku and Miyabi-G.
- Fugaku provides 158,976 Arm-based nodes with distributed-memory interconnects for large-scale parallel computation.
- Miyabi-G provides 1,120 GH200 nodes, each combining a 72-core Grace CPU with an NVIDIA Hopper H100 GPU.
- Classical timing uses synchronized MPI wall-clock measurements, while QPU runtime includes circuit execution and inter-circuit intervals but excludes compilation and network transmission.
- QPU performance is characterized by qubit coherence times and 1- and 2-qubit gate and measurement error rates.
D. Setting of experiments
Experiments combine in-house and established quantum-chemistry software with platform-specific solver settings, representative fragments, and energy comparisons. The reported binding energies are comparable between classical CCSD and HQC TrimSQD but remain too positive under the chosen basis and fragment parameters.
- The software stack combines ORCA for Hartree–Fock, in-house EWF and diagonalization codes, and PySCF, DICE, and Block2 for classical comparisons.
- Fugaku uses ExtSQD for fragments with Mc ≤26 and TrimSQD for fragments with Mc ≥27, whereas Miyabi-G uses TrimSQD for all fragments.
- Detailed performance and accuracy analyses focus on three representative trypsin fragments.
- EWF-CCSD and EWF-TrimSQD produce comparable ground-state and binding-energy calculations for both benchmark complexes.
- The binding energies are too positive, with the minimal STO-3G basis and selected η values identified as likely causes.
- Future improvements include more realistic compact basis sets and a more flexible η choice to increase computational cost and accuracy selectively in the binding region.
- Reported timing distinguishes total QPU time in hours from GPU-hours on Miyabi-G.
B. QPU capacity
The workflow sustains substantial QPU and supercomputer utilization while using strong-scaling results to select practical node counts. TrimSQD reaches approximately 72.5% parallel efficiency at 64 nodes, balancing time-to-solution with memory constraints.
- Quantum sampling uses up to 94 qubits on ibm_cleveland and sustains performance for 56 h on trypsin and 44 h on T4-Lysozyme across ibm_cleveland and ibm_kobe.
- Fugaku and Miyabi-G sustain 95.7% and 98.6% of their available nodes, respectively, during EWF fragment calculations.
- Using two QPUs and two leadership-class supercomputers demonstrates workflow portability and flexibility across CPU- and GPU-based platforms.
- Parallelization targets subspace diagonalization and its dominant matrix–vector multiplication routine, based on strong-scaling analysis.
- 72.5% parallel efficiency is achieved with Nnode = 64 in the practically relevant production regime.
- Increasing node counts reduces time-to-solution but eventually deviates from ideal linear scaling, making moderate node counts preferable for these problems.
2) Strong scaling of matrix-vector multiplication:
Strong scaling makes large subspace diagonalizations practical by reducing matrix-vector multiplication time across nodes, while TrimSQD preserves fragment accuracy and improves as fragment size grows.
- Strong scaling of matrix-vector multiplication:: ≈11 s or less per matrix-vector operation is achieved for a subspace dimension of 4.29 · 10^9.Increasing node counts eventually yields diminishing time-reduction returns because scaling becomes sublinear.
- Strong scaling of matrix-vector multiplication:: 72.5% parallel efficiency enables scalable distributed execution of EWF fragment calculations across Fugaku and Miyabi-G.Strong scaling determines the optimal parallelization of subspace diagonalizations across these large-scale platforms.
- Strong scaling of matrix-vector multiplication:: SBD-G supports accurate fragment treatment alongside strong scaling, motivating the assessment of EWF fragment energies after performance evaluation.The workflow treats performance gains as meaningful only when the underlying fragments are accurately solved.
- Strong scaling of matrix-vector multiplication:: TrimSQD’s accuracy advantage over ExtSQD becomes more pronounced as fragment size increases, confirming benefits from its subspace-diagonalization innovations.The comparison evaluates energy differences for 403 non-water fragments with large molecular-orbital spaces.
2) Accuracy-time tradeoff in TrimSQD and ExtSQD:
The study combines quantum embedding, optimized fragment solvers, and heterogeneous quantum-classical computing to extend accurate protein-ligand simulations beyond prior size limits. It crosses 12,000 atoms while achieving higher HQC accuracy than previously reported and matching leading classical wavefunction methods.
- Accuracy-time tradeoff in TrimSQD and ExtSQD:: TrimSQD achieves high accuracy with substantially reduced time-to-solution versus ExtSQD and selected CPU-based SCI and DMRG implementations.SBD-G avoids storing the Hxy matrix and distributed Ψx vectors, reducing memory demands for large-scale diagonalization.
- Accuracy-time tradeoff in TrimSQD and ExtSQD:: 12,000 atoms are exceeded in two protein-ligand complex simulations using quantum embedding and heterogeneous quantum-classical fragment solvers.The approach combines lower-scaling fragment construction with algorithmic and implementation advances in fragment solutions.
- Accuracy-time tradeoff in TrimSQD and ExtSQD:: 1.3·10^9 measurement outcomes from 9,200 quantum circuits support the reported large-scale fragment calculations.The circuits include 1,016 runs using 58 to 94 qubits.
- Accuracy-time tradeoff in TrimSQD and ExtSQD:: The study establishes a practical baseline for future HQC applications in biochemistry and other systems with comparable size and chemical intricacy.Proposed applications include covalent-binding drugs, catalytic reactions, transition states, and phase diagrams in quantum liquids and solids.