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arxiv: 2511.22158 · v3 · submitted 2025-11-27 · 🪐 quant-ph · physics.chem-ph

Quantum Simulation of Ligand-like Molecules through Sample-based Quantum Diagonalization in Density Matrix Embedding Framework

Ashish Kumar Patra , Anurag K. S. V. , Sai Shankar P. , Ruchika Bhat , Raghavendra V. , Rahul Maitra , Jaiganesh G This is my paper

Pith reviewed 2026-05-17 05:08 UTC · model grok-4.3

classification 🪐 quant-ph physics.chem-ph
keywords density matrix embeddingsample-based quantum diagonalizationquantum simulationground-state energychemical accuracyligand-like moleculessuperconducting hardware
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The pith

Density matrix embedding combined with quantum sampling computes ground-state energies to chemical accuracy for low-symmetry ligand-like molecules on superconducting hardware.

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

The paper tests a hybrid method that breaks larger molecules into fragments using density matrix embedding theory and then applies sample-based quantum diagonalization to solve the resulting smaller problems on actual quantum hardware. It focuses on molecules with irregular shapes and mixed bonding types, which create uneven entanglement between each fragment and its surrounding environment. Quantum sampling on the device identifies the most important electron configurations, allowing the calculation to avoid the full exponential cost of classical diagonalization. Across the systems examined, the computed energies stay within 1 kcal/mol of reference values obtained from full configuration interaction inside the same embedding framework. This outcome points toward practical ways to run quantum electronic structure calculations on molecules closer to those used in real chemistry and materials applications.

Core claim

The DMET-SQD framework yields ground-state energies in strong agreement with DMET-FCI benchmarks, achieving chemical accuracy (1 kcal/mol) across all systems studied, by using the entanglement structure across embedding subsystems to construct bath orbitals and impurity Hamiltonians and then performing quantum sampling with iterative configuration recovery on IBM Eagle R3 hardware.

What carries the argument

The DMET-SQD framework, in which density matrix embedding fragments the molecule according to entanglement variations and sample-based quantum diagonalization builds and solves reduced configuration spaces through hardware sampling and recovery.

If this is right

  • Ground-state energies of chemically realistic, low-symmetry molecules become accessible on present-day quantum devices without solving the full embedded Hamiltonian classically.
  • Entanglement differences between subsystems can be turned into an advantage for selecting efficient bath orbitals and sampling spaces.
  • Hybrid quantum-classical electronic structure methods gain a route to treat molecules with diverse bonding motifs beyond highly symmetric test cases.
  • Chemical accuracy on hardware supports moving from model systems toward ligand and catalyst simulations within the same framework.

Where Pith is reading between the lines

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

  • The same embedding-plus-sampling strategy could be tested on catalytic reaction intermediates or drug-like compounds to check scalability.
  • Pairing SQD with additional error mitigation or larger numbers of bath orbitals might further reduce remaining discrepancies.
  • Direct comparison with other quantum solvers inside DMET would clarify whether the sampling approach offers unique advantages for noisy hardware.

Load-bearing premise

The entanglement variations between fragments and baths in these low-symmetry molecules still allow quantum sampling to recover the important configurations before hardware noise dominates the signal for the chosen fragment sizes.

What would settle it

Repeating the DMET-SQD calculations on the same ligand-like molecules but with larger fragments or on a different quantum processor and finding deviations greater than 1 kcal/mol from the corresponding DMET-FCI reference energies would falsify the claim of consistent chemical accuracy.

Figures

Figures reproduced from arXiv: 2511.22158 by Anurag K. S. V., Ashish Kumar Patra, Jaiganesh G, Raghavendra V., Rahul Maitra, Ruchika Bhat, Sai Shankar P..

Figure 1
Figure 1. Figure 1: Quantum Circuit Diagram for performing Sample-based Quantum Diagonalization. The initial state is prepared as the Hartree-Fock configuration, and is acted upon by an LUCJ ansatz which is pre-initialized with t a i and t ab i j parameters obtained through CCSD calculation. Finally, measurement is performed in the σˆz basis. Quantum sampling is performed in the computational basis, and a set Ssamp is obtaine… view at source ↗
Figure 2
Figure 2. Figure 2: Illustrative example of bath-orbital construction for the H2O molecule in the STO-3G basis. The system is fragmented so that the orbital localized on a single hydrogen atom constitutes the fragment. (a) shows an iso-surface of this fragment orbital; (b) shows the corresponding bath orbital obtained via DMET, which is a linear combination of the remaining localized spatial orbitals in the molecular orbital … view at source ↗
Figure 3
Figure 3. Figure 3: A simplified workflow for DMET-SQD For DMET-SQD and DMET-FCI, Tangelo v0.4.357 was used. LUCJ circuits were generated using ffsim v0.10.058 , and quantum circuits were constructed and transpiled with Qiskit v1.4.259 and Qiskit IBM Runtime v0.36.1. All quantum-chemistry tasks (HF, CCSD, and SCI) were carried out using PySCF v2.10.055. The root-finding method used was the Newton–Secant method from scipy v1.1… view at source ↗
Figure 4
Figure 4. Figure 4: Comparison of the DMET-SQD energies obtained for the set of studied molecules on IBM Sherbrooke Quantum Hardware (4th −5 th June, 2025) with DMET-FCI. All the energies obtained are within the chemical accuracy criterion (1 kcal/mol ≈ 0.001594 Ha), which is marked with the red-dashed line. The x-axis denotes the name of the studied molecule, the molecular formula and the molecular weight. The y-axis denotes… view at source ↗
read the original abstract

The accurate treatment of electron correlation in extended molecular systems remains computationally challenging using classical electronic structure methods. Hybrid quantum-classical algorithms offer a potential route to overcome these limitations; however, their practical deployment on existing quantum computers requires strategies that both reduce problem size and mitigate hardware noise. In this work, we investigate ground-state energy calculations of ligand-like molecules using Sample-based Quantum Diagonalization (SQD) within the Density Matrix Embedding Theory (DMET) framework, focusing on low-symmetry systems with diverse bonding motifs that exhibit subsystem-dependent variations in fragment-environment entanglement. These entanglement-based variations directly influence bath orbital construction, impurity sizes, and the structure of the embedded Hamiltonians, posing nontrivial challenges for both embedding and quantum sampling. By combining DMET fragmentation with SQD-based construction of reduced configuration spaces through quantum sampling and iterative configuration recovery, we perform quantum simulations on IBM's Eagle R3 superconducting quantum hardware (IBM Sherbrooke), thereby showing that the entanglement structure across embedding subsystems plays a central role in determining the efficiency and accuracy of the simulations. Despite these complexities, we show that the DMET-SQD framework yields ground-state energies in strong agreement with DMET-FCI benchmarks, achieving chemical accuracy (1~kcal/mol) across all systems studied. These results demonstrate that SQD-based quantum simulations can be robustly extended to low-symmetry, chemically realistic, industry-relevant molecules and highlight the importance of entanglement-aware embedding strategies for scalable quantum electronic structure calculations.

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 / 2 minor

Summary. The manuscript investigates ground-state energy calculations for low-symmetry ligand-like molecules using Sample-based Quantum Diagonalization (SQD) embedded within the Density Matrix Embedding Theory (DMET) framework. It performs these simulations on IBM Eagle R3 superconducting hardware (Sherbrooke) and reports that the resulting energies agree with independent DMET-FCI benchmarks to within chemical accuracy (1 kcal/mol) for all systems studied, while emphasizing that subsystem-dependent entanglement variations affect bath orbital construction, impurity sizes, and embedded Hamiltonians.

Significance. If the central claims are substantiated, the work would demonstrate a viable route for extending near-term quantum simulations to chemically realistic, low-symmetry molecules with diverse bonding motifs. The explicit hardware implementation on IBM Sherbrooke together with the focus on entanglement-aware embedding strategies constitutes a concrete strength; the reported chemical-accuracy agreement, if shown to be robust, would support broader applicability of hybrid quantum-classical methods to industry-relevant systems.

major comments (2)
  1. [Results] Results section: The headline claim that DMET-SQD achieves chemical accuracy across all studied systems rests on the robustness of quantum sampling plus iterative configuration recovery. Although the abstract states that entanglement variations across fragments directly influence bath orbitals, impurity sizes, and Hamiltonian structure, no systematic scans of fragment size, bath-selection threshold, or entanglement cutoff are presented to verify that accuracy is preserved when these parameters are varied by amounts typical for low-symmetry ligands.
  2. [Methods] Methods and Results sections: The abstract reports agreement to chemical accuracy, yet the manuscript does not supply quantitative details on error bars, the number of configuration-recovery iterations performed, or the post-selection criteria applied to the sampled configurations. These omissions prevent independent verification that the reported <1 kcal/mol deviations are statistically meaningful rather than artifacts of the chosen recovery protocol.
minor comments (2)
  1. [Figures] Figure captions and legends should explicitly list the molecular systems, fragment sizes, and bath-orbital counts corresponding to each data point to improve traceability between the embedding choices and the plotted energies.
  2. Ensure consistent use of units (kcal/mol versus hartree) when comparing DMET-SQD and DMET-FCI results throughout the text and tables.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive and detailed review. The comments help clarify how to better present the robustness of the DMET-SQD results for low-symmetry systems. We address each major comment below and indicate the changes we will make in the revised manuscript.

read point-by-point responses

  1. Referee: [Results] Results section: The headline claim that DMET-SQD achieves chemical accuracy across all studied systems rests on the robustness of quantum sampling plus iterative configuration recovery. Although the abstract states that entanglement variations across fragments directly influence bath orbitals, impurity sizes, and Hamiltonian structure, no systematic scans of fragment size, bath-selection threshold, or entanglement cutoff are presented to verify that accuracy is preserved when these parameters are varied by amounts typical for low-symmetry ligands.

    Authors: We agree that systematic parameter scans would strengthen the claim of robustness. Our study demonstrates chemical accuracy for the specific low-symmetry ligand-like molecules, with fragment sizes, bath orbitals, and impurity Hamiltonians determined by the entanglement-aware DMET procedure described in the Methods. To address the referee's concern, we will add in the revised manuscript a new subsection (or supplementary figures) showing the dependence of the SQD energies on modest variations in fragment size and bath-selection threshold for two representative systems. These additional results will confirm that the energies remain within chemical accuracy for parameter choices typical of low-symmetry ligands, thereby supporting the broader applicability of the framework. revision: yes

  2. Referee: [Methods] Methods and Results sections: The abstract reports agreement to chemical accuracy, yet the manuscript does not supply quantitative details on error bars, the number of configuration-recovery iterations performed, or the post-selection criteria applied to the sampled configurations. These omissions prevent independent verification that the reported <1 kcal/mol deviations are statistically meaningful rather than artifacts of the chosen recovery protocol.

    Authors: We concur that explicit quantitative details on the sampling protocol are required for reproducibility and statistical assessment. In the revised manuscript we will expand the Methods and Results sections to report: (i) the error bars obtained from the quantum sampling statistics for each system, (ii) the exact number of configuration-recovery iterations performed, and (iii) the post-selection criteria applied to the sampled bitstrings. These additions will allow readers to verify that the reported deviations from the DMET-FCI benchmarks are statistically meaningful and not sensitive to the particular recovery protocol employed. revision: yes

Circularity Check

0 steps flagged

No circularity: DMET-SQD energies benchmarked against independent DMET-FCI calculations with no reduction to fitted parameters or self-referential steps

full rationale

The paper's central claim is that DMET-SQD produces ground-state energies in agreement with DMET-FCI benchmarks to chemical accuracy across the studied ligand-like molecules. The abstract and reader's summary explicitly position the results as validated against separate classical DMET-FCI computations rather than derived from the same fitted quantities or self-citations. No equations, fragmentation choices, or sampling procedures are described as being defined in terms of the target energies or as predictions forced by prior fits within the same work. The entanglement-aware embedding and SQD sampling are presented as methodological choices whose outputs are then compared externally, satisfying the criterion for a self-contained derivation against independent benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on standard assumptions of DMET validity for the chosen fragments and on the ability of SQD sampling to recover sufficient configurations for chemical accuracy; no new entities or fitted parameters are introduced in the abstract.

axioms (2)
  • domain assumption DMET fragmentation accurately captures subsystem-environment entanglement for the studied low-symmetry molecules
    Invoked to justify bath orbital construction and impurity sizes
  • domain assumption SQD sampling plus iterative configuration recovery converges to the embedded ground state within chemical accuracy
    Central to claiming agreement with DMET-FCI

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Forward citations

Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Hybrid Quantum-Classical Density Functional Theory: A Structured Framework

    quant-ph 2026-05 unverdicted novelty 6.0

    The paper proposes a three-axis framework to organize hybrid quantum-classical DFT approaches and shows embedding methods suit current noisy hardware better than linear algebra speedups.

  2. Sample-Based Quantum Diagonalization with Amplitude Amplification

    quant-ph 2026-05 conditional novelty 6.0

    SQD-AA reduces total query complexity by more than 100x on model distributions and achieves the lowest T-gate counts with 3-4 orders shallower circuits than iQPE for molecular examples.

Reference graph

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