Meeting 2026 06 29

Meeting - June 29, 2026

• Date: Monday, June 29, 2026
• Time: (Slot #2) 7 pm - 8 pm US Eastern Daylight Time (View Meeting Time in Your Timezone)
• Location: Virtual Meeting.
• Meeting Link: openqse.org/captcha

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• Next: Monday, July 6, 2026 (Slot #1) @ 12 pm - 1 pm US Eastern Daylight Time (View Meeting Time in Your Timezone)

Agenda

• Speaker: Luke Bertels (ORNL) - "Large-scale quantum chemistry applications with sample-based quantum diagonalization"

Attendance

Person	Institution
Amir Shehata	ORNL
Luke Bertels	ORNL
Marcelo Amaral	IBM
Doug Oucharek	ORNL
Brandon Neth	HPE
Ryan Landfield	ORNL
Claudio Siqueira de Carvalho	IBM
Jim Garrison	IBM
Jiri Schindler	IonQ
Andy Stone	HPE
Abdelaziz Rahwan	Brightskies
Namit Anand	HPE
Masoud Mohseni	HPE
Josh Moles	IonQ
Aaron Lott	HPE
Michael Ferguson	HPE
Thomas Naughton	ORNL
Neal Erickson	Quantinuum
Mohamed Elgharawy	Brightskies
Vanessa Sochat	External
Christian Heiter	HPE
Hiroshi Horii	IBM
Jeff Heckey	AWS
Smriti Bajaj	Dell Technologies
Ermal Rrapaj	NERSC/LBL
Martin Schulz	TUM

Executive Summary

• Luke Bertels presented two recent quantum chemistry studies using sample-based quantum diagonalization (SQD) and quantum selected configuration interaction ideas for biomolecular-scale problems.
• The central workflow uses a quantum processor as a sampler rather than as a direct Hamiltonian expectation-value estimator:
  • Prepare chemically motivated states on the QPU.
  • Sample electronic configurations.
  • Use classical HPC to recover/correct configurations, build a reduced Hamiltonian, and diagonalize it.
• The first study focused on a TRP-cage mini-protein of roughly 300 atoms and compared folded vs. unfolded conformers.
• The second study scaled the same broad idea to protein-ligand binding systems with more than 11,000 atoms and nearly 30,000 molecular orbitals.
• The discussion repeatedly emphasized that these studies are not claims of quantum advantage:
  • Current classical methods remain faster for the fragment sizes used.
  • Much of the heavy computation is in classical post-processing.
  • The value of the studies is as a resource-intensive demonstration and a marker for what near-term hybrid quantum/HPC workflows can currently do.
• A recurring theme was that practical utility would likely require larger, more strongly correlated fragments where classical fragment solvers such as DMRG or coupled-cluster approaches become inadequate.

Main Presentation

Motivation

• Quantum chemistry remains one of the long-promised applications of quantum computing because electronic structure is naturally a many-body quantum problem.
• Direct simulation of biomolecular-scale systems is not tractable on near-term quantum hardware.
• The presented work therefore combines:
  • Fragmentation or embedding to reduce a large molecule into smaller subproblems.
  • QPU sampling on selected fragments.
  • Classical HPC for post-processing, diagonalization, and reconstruction of full-system properties.
• The methods discussed differ from typical VQE-style workflows:
  • VQE directly estimates Hamiltonian expectation values on the quantum processor.
  • SQD uses the quantum processor to sample important configurations, then performs the expensive diagonalization classically in a reduced subspace.

Core Workflow

• The overall workflow described by Luke:

  • Start from the full molecular geometry.
  • Perform a full-system mean-field calculation, typically Hartree-Fock.
  • Use an embedded wave function (EWF) method to partition the system into atomic fragments with bath orbitals.
  • Solve small fragments classically.
  • Use SQD or extended SQD for larger fragments.
  • Apply configuration recovery to handle noisy bitstrings and enforce the correct electron count.
  • Diagonalize the recovered and expanded subspace on classical hardware.
  • Extract energies and one- and two-particle reduced density matrices.
  • Reconstruct the total system energy from the fragment results.

• The embedding method was described as:

  • Inspired by density matrix embedding theory.
  • Non-iterative in the version discussed.
  • Based on atomic fragments plus bath orbitals.
  • Enhanced with MP2 natural orbitals to include some correlated bath information.

Study 1: TRP-Cage Mini-Protein

System and Goal

• The first paper studied two conformers of a TRP-cage mini-protein.
• The protein was described as roughly 300 atoms.
• The chemistry objective was to estimate the energy difference between folded and unfolded conformations.
• Fragment sizes after embedding were roughly 6 to 33 molecular orbitals.
• Using a Jordan-Wigner mapping, Luke framed this as roughly 12 to 66 qubits before additional mapping overhead.

Fragment Treatment

• Fragments below about 15 molecular orbitals were solved with classical exact diagonalization.
• Fragments in the 15 to 33 molecular orbital range were treated with extended SQD.
• The fragment distribution was roughly:
  • About 150 fragments in the 6 to 14 molecular orbital range.
  • About 150 fragments in the 15 to 33 molecular orbital range.

Quantum Sampling

• The QPU was used only as a sampler.
• The ansatz was described as a local unitary cluster Jastrow (LUCJ) ansatz.
• The ansatz can be seeded from a relatively cheap coupled-cluster calculation on the fragment, reducing the need for expensive parameter optimization on the QPU.
• Sampling was performed on IBM Heron R2 QPUs with a heavy-hex layout.
• The reported sampling scale was about one million shots per fragment.

Classical Post-Processing

• Configuration recovery was used to repair sampled bitstrings that did not have the correct Hamming weight, corresponding to the correct electron count.
• Configuration recovery and subspace diagonalization were described as:
  • The most computationally intensive part of the algorithm.
  • Asynchronous.
  • Highly parallelizable.
• Smaller quantum-treated fragments used Michigan State University HPC resources, reportedly across 80 to 100 nodes.
• Larger cases used Cleveland Clinic Foundation HPC resources with large-memory nodes.
• Extended SQD improved coverage of the ground-state support by adding single excitations around dominant configurations after the initial recovered set.

Results and Interpretation

• SQD reduced the effective Hilbert space by several orders of magnitude in larger fragments.
• The reduction comes from using the LUCJ ansatz to preferentially sample important configurations in the fragment wavefunction.
• Accuracy is not guaranteed a priori for arbitrary systems.
• The argument for why this may work in chemistry relies on:
  • Structure in chemistry Hamiltonians.
  • Locality of correlations.
  • The existence of high-weight determinants near a mean-field solution.
• For cases where exact diagonalization is possible, the authors benchmarked the SQD approach.
• The folded/unfolded energy difference from the quantum-assisted method fell between embedded wave function MP2 and embedded wave function CCSD references.
• Luke characterized this as evidence that the SQD result was not obviously far from the expected chemical behavior, but not as a quantum advantage result.

Study 2: Protein-Ligand Binding at Larger Scale

System and Goal

• The second paper scaled the workflow to protein-ligand binding energies relevant to drug-discovery-style applications.
• Binding energy was described as comparing:
  • The bound protein-ligand system.
  • The unbound protein.
  • The ligand.
• Two large systems were discussed:
  • A trypsin-ligand system, described in the transcript as trypsin-benzamide, with about 12,635 atoms and more than 31,000 molecular orbitals.
  • T4 lysozyme with n-butylbenzene, with about 11,600 atoms and nearly 29,000 molecular orbitals.

Scaling Changes

• The first embedded wave function approach has expensive full-system steps:
  • Full-system Hartree-Fock and orbital localization scale roughly cubically with orbital count.
  • Atomic-orbital to molecular-orbital transformations can scale roughly quartically.
  • Full-system MP2 bath construction scales roughly quintically.
• The scaled-up study kept the full-system Hartree-Fock step but localized the expensive correlated steps:
  • MP2 perturbation-theory excitations were restricted to orbitals within about 7 angstroms of each atomic fragment.
  • Electron-repulsion orbital construction was restricted to about 10 angstroms from each center.
• This relies on a locality assumption:
  • If electronic correlation is sufficiently local, distant orbitals need not be included in every fragment.
  • If correlation lengths grow, larger fragments are needed and the approximation becomes harder to justify.

Trim SQD

• The second paper introduced trim SQD as an improvement over extended SQD.
• Trim SQD adds determinant trimming through a two-level filtering process:
  • Keep configurations above a first weight threshold, K1, during batched subspace diagonalization.
  • Apply a second filtering level with threshold K2.
  • Extend the retained configuration set using one- and two-particle excitations, i.e. singles and doubles.
  • Perform the final diagonalization over the extended subspace.
• The diagonalization was accelerated with an in-house selected basis diagonalization code using:
  • Distributed memory.
  • GPU acceleration.
  • Parallel execution across leadership-class resources.

Quantum Resources

• The study used two 156-qubit IBM Heron R2 systems:
  • IBM Cleveland.
  • IBM Kobe.
• Reported quantum resource use included:
  • About 106 total QPU hours.
  • About 92,000 quantum circuits.
  • About 1.3 billion total shots.
  • About 1,000 larger circuits.
  • Larger circuits mapped to roughly 58 to 94 qubits.
  • Largest circuits had about 252 two-qubit gate depth.
  • Execution time for the largest circuits was about 17 microseconds, below the reported 150 to 200 microsecond T1/T2 scale.

Classical Resources

• Classical post-processing used RIKEN leadership computing resources:
  • Fugaku, described as a 160,000-node system.
  • Miyabi-G, described as a GPU cluster with NVIDIA GH200 Grace Hopper superchips.
• Reported classical processing scale included:
  • About 396,000 Fugaku hours for the trypsin system.
  • About 308,000 Fugaku hours for the T4 system.
  • About 4,281 Miyabi-G hours for one system.
  • About 3,554 Miyabi-G hours for the other system.
• Peak machine utilization was described as very high:
  • Roughly 95.7% of Fugaku.
  • Roughly 98.6% of Miyabi-G.
• The selected basis diagonalization routine achieved about 72.5% parallel efficiency at 64-node parallelization.

Results and Interpretation

• The embedded wave function trim SQD results were compared with embedded wave function coupled-cluster references.
• The computed binding energies were positive, meaning the systems were not predicted to be bound at that level of theory.
• Luke noted several possible reasons:
  • Minimal basis set limitations.
  • No counterpoise correction.
  • Potential embedding artifacts.
  • Other accumulated sources of approximation error.
• The rough agreement between the quantum-assisted and classical reference calculations suggested the quantum component was not producing obviously inconsistent results.
• On selected fragments, trim SQD approached the accuracy of DMRG and improved substantially over extended SQD.
• The study was framed as the most quantum-resource-intensive quantum chemistry study to date, not as a demonstration of advantage.

Discussion and Questions

Origin and Validity of the Hilbert-Space Reduction

• Namit Anand asked what causes the apparent reduction in Hilbert-space dimension.
• Luke explained that the LUCJ ansatz preferentially samples important configurations, reducing the classical subspace that must be diagonalized.
• Namit pressed on whether the reduction preserves energy accuracy.
• Luke answered that:
  • It is not known a priori for arbitrary systems.
  • The method relies on structure and locality in chemistry Hamiltonians.
  • The authors validated the approach on smaller exactly diagonalizable cases.
• Namit noted that the flatness of the sampled subspace scaling is non-trivial and should imply some trade-off elsewhere, such as circuit depth, shot count, or classical SQD runtime.
• Luke agreed and suggested the observed behavior may reflect the limits of finite shot count and finite circuit depth.

Role of Classical Post-Processing

• Namit emphasized that these workflows may be trading one classical computation for another:
  • QPU sampling is only one part of the workflow.
  • Configuration recovery, spin restoration, and subspace diagonalization can perform much of the heavy lifting.
• He suggested separating baselines such as:
  • Hartree-Fock alone.
  • Hartree-Fock plus LUCJ.
  • LUCJ plus SQD.
  • SQD with post-processing.
• Luke did not have the Hartree-Fock-only energy available during the meeting.

Memory, Runtime, and Shot Count

• Jiri Schindler asked whether the SQD variants trade memory for runtime and accuracy.
• Luke agreed with that interpretation:
  • Batching can reduce one-shot memory requirements.
  • Extended SQD can improve accuracy but at higher memory cost.
• Jiri also asked why one million shots per fragment was needed.
• Luke said the likely reason is to obtain enough configuration diversity for configuration recovery and subspace diagonalization.
• The group noted that this is also tied to NISQ noise and that, in principle, more samples could be better.

Fragment Molecular Orbital Methods and Scaling

• Namit asked how the EWF approach compares with fragment molecular orbital methods that can show favorable scaling.
• Luke said he did not have a firm accuracy estimate for the specific embedding method in the papers.
• He noted that most embedding approaches still require a mean-field calculation, creating a practical floor around cubic scaling.
• Namit suggested that FMO-style methods may be important to investigate in the near term because quantum resources remain expensive.
• Luke said related approaches are being actively investigated.

Utility, Advantage, and Classical Comparisons

• Amir Shehata asked whether systems with 12,000 atoms are useful from a chemistry perspective.
• Luke answered that this is already a useful scale for small to medium protein systems and drug/protein binding benchmarks.
• Amir asked whether the classical counterpart can handle the same scale faster.
• Luke answered that, for the current fragment sizes and embedding scheme, the classical approach is significantly faster.
• Michael Ferguson asked whether the hybrid quantum/classical method is more accurate than known classical techniques.
• Luke clarified:
  • It is not better than all known classical techniques.
  • DMRG is a strong classical reference for the fragment sizes used.
  • The coupled-cluster comparison used the same fragmentation approach.
  • Full MP2 or full coupled-cluster at the full biomolecular scale would be infeasible due to scaling.
• Namit explicitly asked whether there is any quantum-advantage claim.
• Luke confirmed there is no quantum-advantage claim.

Qubit Counts, Fault Tolerance, and Strong Correlation

• Amir asked what would be needed for this kind of method to become useful.
• Luke said utility would likely require scaling to larger fragment active spaces where classical methods degrade.
• He mentioned a rough speculative range of 100 to 200 logical qubits for transformative chemistry results, later clarifying that he was assuming ideal or perfect qubits in that statement.
• Ermal Rrapaj asked what error rate was assumed and raised the relevance of DMRG bond dimension.
• Luke did not have a specific error rate or DMRG bond dimension available.
• Ermal noted that DMRG bond dimension can inform the circuit depth required to reproduce DMRG-like states on a quantum computer, and that the corresponding circuits may be too deep for early fault-tolerant devices.
• The group discussed why larger fragments may become necessary:
  • Fragmentation assumes relatively local correlations.
  • In strongly correlated systems, correlation lengths can grow.
  • Larger correlation lengths force larger fragments to avoid embedding/truncation error.
• Namit connected this to condensed-matter and many-body localization examples:
  • Effective length scales determine how easily systems can be fragmented.
  • Strongly correlated regions may remain large even if the correlation scale is finite.
  • Such regions may require direct quantum simulation rather than further fragmentation.

Conclusions

• The meeting highlighted a realistic near-term quantum/HPC pattern:
  • Quantum processors provide samples.
  • Classical leadership computing performs most of the recovery, filtering, and diagonalization.
  • The workflow is currently asynchronous rather than tightly coupled.
• The demonstrated systems are impressive in size and resource use, but not yet evidence of practical quantum advantage.
• The strongest potential path to utility is not simply increasing the number of atoms in the full biomolecule, but increasing the chemically meaningful fragment sizes beyond what classical solvers can handle reliably.
• Accuracy and resource accounting need to be separated carefully:
  • QPU time and circuit depth.
  • Shot count.
  • Classical configuration recovery.
  • Classical diagonalization.
  • Embedding and basis-set errors.

Open Questions and Follow-Ups

• No formal action items were assigned during the meeting.
• Useful follow-up topics raised implicitly by the discussion:
  • Collect Hartree-Fock, Hartree-Fock plus LUCJ, SQD, and fully post-processed SQD baselines for the same fragments.
  • Quantify how much accuracy comes from the QPU sampling vs. classical configuration recovery and diagonalization.
  • Compare EWF against fragment molecular orbital methods for similar protein-scale workloads.
  • Track resource scaling separately for QPU sampling, shot count, memory, and classical diagonalization.
  • Clarify DMRG bond dimensions for benchmark fragments and translate them into approximate quantum circuit requirements.
  • Define sharper criteria for "utility" in this workflow, distinct from quantum advantage.

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