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arxiv: 2605.01138 · v1 · submitted 2026-05-01 · 🪐 quant-ph · physics.chem-ph· physics.comp-ph

Recognition: unknown

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

Kenneth M. Merz , Jr. , Akhil Shajan , Danil Kaliakin , Fangchun Liang , Yuichi Otsuka , Tomonori Shirakawa , Lukas Broers
show 16 more authors
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
Authors on Pith no claims yet

Pith reviewed 2026-05-09 18:45 UTC · model grok-4.3

classification 🪐 quant-ph physics.chem-phphysics.comp-ph
keywords quantum embeddingheterogeneous quantum-classical computingprotein-ligand complexesab initio quantum chemistryquantum processorssupercomputingmolecular simulation
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The pith

A hybrid quantum-classical method simulates protein-ligand complexes with over 12,000 atoms while matching coupled-cluster accuracy.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper establishes a workflow that decomposes large molecules into fragments via quantum embedding, then computes each fragment's wavefunction by sampling on quantum processors and diagonalizing subspaces on classical supercomputers. This combination handles two protein-ligand systems of 11,608 and 12,635 atoms, more than 40 times larger than earlier quantum chemistry efforts, and yields fragment energies that match CCSD accuracy. A sympathetic reader would care because it demonstrates a concrete route to first-principles calculations on realistic biomolecular sizes that classical methods alone cannot reach at this scale.

Core claim

The authors show that quantum embedding allows a large molecule to be split into fragments whose electronic configurations can be sampled on 156-qubit processors and whose wavefunctions can be obtained via optimized subspace diagonalization on distributed classical hardware, producing accurate energies for dispersion- and electrostatics-dominated protein-ligand complexes at 11,608 and 12,635 atoms with over 40-fold size increase and up to 210-fold accuracy gain over prior state-of-the-art while reproducing CCSD fragment energies.

What carries the argument

Quantum embedding decomposition into fragments combined with heterogeneous sampling on quantum processors and subspace diagonalization on supercomputers, which lets independent fragment calculations reconstruct the full system's properties.

If this is right

  • Protein-ligand binding energies become computable at near-CCSD quality for systems previously limited to much smaller sizes.
  • The approach supplies a scalable route to systematically improvable ab initio simulations of biomolecular complexes.
  • Fragment energies from the hybrid method can be used to benchmark or replace less accurate classical force fields in drug-design pipelines.
  • The demonstrated parallel efficiency on supercomputers indicates that further increases in atom count remain feasible with additional hardware.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same decomposition could be applied to molecular dynamics trajectories to obtain time-averaged energies without simulating every snapshot at full quantum cost.
  • Extending the fragment size or adding more quantum processors might reduce the embedding error further, tightening agreement with experiment.
  • The workflow creates a testbed for comparing quantum hardware performance against classical methods on chemically relevant, non-trivial Hamiltonians.

Load-bearing premise

The embedding step splits the molecule such that interactions between fragments are preserved with only negligible error, so separate simulations of the pieces can be added back together accurately.

What would settle it

Running a full coupled-cluster calculation on one of the smaller fragments or measuring an experimental observable such as binding free energy for the 11,608-atom complex and comparing it directly to the reported HQC result would show whether the claimed accuracy holds.

Figures

Figures reproduced from arXiv: 2605.01138 by Akhil Shajan, Danil Kaliakin, Ella Fejer, Fangchun Liang, Han Xu, Hiroshi Horii, Javier Robledo Moreno, Jr., Jun Doi, Kenneth M. Merz, Kevin J. Sung, Lukas Broers, Mario Motta, Mitsuhisa Sato, Miwako Tsuji, Robert Walkup, Ryo Wakizaka, Seetharami Seelam, Seiji Yunoki, Thaddeus Pellegrini, Tomonori Shirakawa, Toshinari Itoko, Yuichi Otsuka, Yukio Kawashima.

Figure 1
Figure 1. Figure 1: Systems investigated (A), overarching algorithmic scheme adopted, (B), representation of a fragment (C), details of the lower-scaling fragment view at source ↗
Figure 2
Figure 2. Figure 2: The workflow of ExtSQD (left) and TrimSQD (middle), with central view at source ↗
Figure 3
Figure 3. Figure 3: Strong scaling of TrimSQD with baseline threshold view at source ↗
Figure 4
Figure 4. Figure 4: Strong scaling of matrix–vector multiplication ( view at source ↗
Figure 5
Figure 5. Figure 5: Accuracy improvement of TrimSQD over ExtSQD. view at source ↗
Figure 6
Figure 6. Figure 6: Accuracy-time tradeoffs. ExtSQD and TrimSQD used 128 GPU nodes. view at source ↗
read the original 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 $1.3 \cdot 10^9$ 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.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 0 minor

Summary. The manuscript presents a heterogeneous quantum-classical (HQC) workflow that uses quantum embedding to decompose protein-ligand complexes into fragments, simulates the fragments on IBM quantum processors (up to 94 qubits, 9200 circuits, 1.3e9 measurements) and classical supercomputers (Fugaku, Miyabi-G) via optimized subspace diagonalization, and applies this to two systems of 11608 and 12635 atoms. It reports >40x larger systems and up to 210x accuracy gains over prior SOTA, with HQC fragment energies matching CCSD accuracy, while achieving 72.5% parallel efficiency.

Significance. If the embedding reconstruction of total energies is shown to be accurate, this constitutes a major advance in scaling wavefunction-based quantum chemistry to realistic biomolecular sizes, combining current quantum hardware with classical resources at record scale. The empirical benchmarking against independent CCSD calculations and the reported parallel efficiency on distributed linear algebra kernels are concrete strengths that support the demonstration of feasibility.

major comments (2)
  1. Abstract: The central claim is that the HQC method enables accurate simulation of the full 11k-12k atom protein-ligand complexes (spanning dispersion- and electrostatics-dominated regimes) with substantial accuracy gains. However, accuracy is only reported for individual fragment energies matching CCSD; no section quantifies the embedding error on the reconstructed total energy, nor demonstrates convergence with fragment size or bath depth. For long-range interactions, truncation of the fragment environment or approximate bath orbitals risks non-negligible many-body errors that do not cancel upon summation, which is load-bearing for the overall accuracy and size claims.
  2. Results and methods sections: The abstract states matching CCSD accuracy and large size gains but provides no details on validation protocols, error bars or statistical uncertainty on the 1.3e9 measurement outcomes, or explicit handling of hardware noise in the quantum runs. Without these, the robustness of the fragment-level CCSD matching and the claimed 210x accuracy improvement cannot be assessed.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive feedback and positive assessment of the work's significance. We address the two major comments point-by-point below, committing to revisions that strengthen the manuscript without altering its core claims.

read point-by-point responses

  1. Referee: Abstract: The central claim is that the HQC method enables accurate simulation of the full 11k-12k atom protein-ligand complexes (spanning dispersion- and electrostatics-dominated regimes) with substantial accuracy gains. However, accuracy is only reported for individual fragment energies matching CCSD; no section quantifies the embedding error on the reconstructed total energy, nor demonstrates convergence with fragment size or bath depth. For long-range interactions, truncation of the fragment environment or approximate bath orbitals risks non-negligible many-body errors that do not cancel upon summation, which is load-bearing for the overall accuracy and size claims.

    Authors: We agree that explicit validation of the reconstructed total energy is important for fully supporting the size and accuracy claims. The original manuscript reports fragment energies matching CCSD because the HQC simulation and accuracy benchmarks are performed at the fragment level, with the total energy obtained by summing embedded fragment contributions. To address the referee's concern regarding potential non-cancellation of long-range embedding errors, we will add a new subsection in Results that (i) describes the total-energy reconstruction formula, (ii) provides convergence data with fragment size and bath depth on representative subsystems, and (iii) reports estimated embedding errors on the total energy for the two target complexes. These additions will be based on additional post-processing of existing data and will not change the reported fragment-level results. revision: yes

  2. Referee: Results and methods sections: The abstract states matching CCSD accuracy and large size gains but provides no details on validation protocols, error bars or statistical uncertainty on the 1.3e9 measurement outcomes, or explicit handling of hardware noise in the quantum runs. Without these, the robustness of the fragment-level CCSD matching and the claimed 210x accuracy improvement cannot be assessed.

    Authors: The referee correctly identifies that the original text is insufficiently detailed on these points. The 1.3e9 shots were collected with standard mitigation (readout-error correction and dynamical decoupling) and statistical uncertainties were computed from binomial shot noise, but these protocols were only summarized. We will expand the Methods section with a dedicated subsection titled 'Quantum Measurement Protocol and Error Analysis' that (i) specifies the validation protocol (direct comparison of each fragment energy to classical CCSD on the same active space), (ii) reports per-fragment error bars derived from the measurement statistics, and (iii) quantifies residual hardware noise after mitigation. This will allow independent assessment of the 210x accuracy claim. revision: yes

Circularity Check

0 steps flagged

No circularity: empirical hardware demonstration benchmarked externally

full rationale

The paper reports a computational workflow applying quantum embedding decomposition followed by HQC simulation on real quantum processors and supercomputers for two large protein-ligand systems. Accuracy is established by direct comparison of fragment energies to independent CCSD calculations, with reported speedups and size increases as empirical outcomes. No derivation chain reduces a claimed result to fitted parameters, self-citations, or ansatzes by construction; the embedding error bound is treated as an assumption validated by the benchmarks rather than proven via internal equivalence. The work is self-contained against external references and does not rename known results or import uniqueness from prior author work in a load-bearing way.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the standard assumption that fragment-based quantum embedding can be applied to protein-ligand systems without introducing uncontrolled errors in inter-fragment coupling; no new entities or fitted parameters are introduced in the abstract.

axioms (1)
  • domain assumption Quantum embedding accurately decomposes the full electronic Hamiltonian into weakly coupled fragments
    Invoked to justify independent fragment simulations on quantum hardware

pith-pipeline@v0.9.0 · 5630 in / 1270 out tokens · 36559 ms · 2026-05-09T18:45:15.975328+00:00 · methodology

discussion (0)

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