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Towards Chemically Accurate and Scalable Quantum Simulations on IQM Quantum Hardware: A Quantum-HPC Hybrid Approach

T0 review · 3 major / 6 minor · reviewed 2026-07-15 · grok-4.5

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Pith's one-line read Sample-based quantum diagonalization on IQM hardware recovers chemical accuracy for molecules up through amantadine, including a full experimental 2D water surface.

desk verdict Solid experimental hardware paper: dense 2D water PES and DMET-SQD on amantadine on IQM Sirius, with transparent sampling limits and no overclaim of advantage. read the letter →

arxiv 2604.01983 v2 pith:ZD6ATKDJ submitted 2026-04-02 quant-ph cs.ETphysics.chem-phphysics.comp-ph

Anurag K. S. V. , Ashish Kumar Patra , Manas Mukherjee , Alok Shukla , Sai Shankar P. , Ruchika Bhat , Radhika T. S. L. , Jaiganesh G This is my paper · ORCID
classification quant-phcs.ETphysics.chem-phphysics.comp-ph
keywords Sample-basedQuantumDiagonalizationLUCJansatzLCNot-UCCSDDensityMatrixEmbeddingTheorypotentialenergysurfaceIQMSiriuschemistrychemicalaccuracy
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper reports a large hardware campaign on a 24-qubit superconducting processor (up to 16 operational qubits) that uses sample-based quantum diagonalization (SQD) rather than variational optimization. A trial circuit prepares a state; the device only samples configurations; classical exact diagonalization inside that sampled subspace returns the energy. With the Local Unitary Cluster Jastrow (LUCJ) ansatz the authors recover full-configuration-interaction (FCI) ground-state energies for H2, LiH, BeH2, H2O and NH3 to chemical accuracy, map one-dimensional dissociation curves, and produce the first experimental 32-by-32 two-dimensional potential-energy surface of water on superconducting hardware. They further embed SQD inside density-matrix embedding theory (DMET) to treat eight ligand-like molecules and the drug amantadine, again matching DMET-CASCI references within chemical accuracy. A second, deeper Linear-CNOT UCCSD ansatz is introduced for comparison: it reduces classical pre-processing but fails for larger systems once circuit depth outruns hardware noise. The work therefore argues that sample-based hybrid workflows already deliver chemically useful energies on present-day devices and that embedding extends their reach to pharmacologically relevant molecules.

What carries the argument

Sample-based Quantum Diagonalization (SQD) with the LUCJ ansatz: the quantum processor only samples a trial wave-function; classical configuration recovery and exact sparse diagonalization inside the recovered subspace produce a variational energy that is noise-free once the subspace is fixed.

What would settle it

Repeat the BeH2 dissociation or the water 2-D surface with the same shot budget and LUCJ initialization but force the post-recovery subspace dimension well below the full symmetry space; if energies then systematically exceed chemical accuracy relative to FCI, the claim that the sampled subspace remains faithful collapses.

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Extended reading notes

Core claim

Across fixed-geometry benchmarks, 1-D and 2-D potential-energy surfaces, and DMET-embedded ligand and amantadine calculations, the majority of SQD(LUCJ) energies obtained on IQM Sirius agree with exact FCI or DMET-CASCI references to within chemical accuracy for the chosen basis sets, establishing that sample-based diagonalization plus classical embedding is already a practical route to chemically accurate molecular energies on current superconducting hardware.

Load-bearing premise

That a shallow LUCJ (or deeper LCNot-UCCSD) circuit, started from single-reference amplitudes and sampled with ten thousand shots, still yields a configuration pool whose recovered subspace overlaps the true ground state after hardware noise, especially near multi-reference geometries or when circuit depth becomes large.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 6 minor

Summary. The manuscript reports an extensive experimental campaign of Sample-based Quantum Diagonalization (SQD) on IQM’s Sirius 24-qubit superconducting processor (up to 16 operational qubits). Using the Local Unitary Cluster Jastrow (LUCJ) ansatz (CCSD-initialized) and a newly introduced Linear-CNOT UCCSD (LCNot-UCCSD) ansatz (MP2-initialized), the authors compute ground-state energies for H2, LiH, BeH2, H2O and NH3, perform 1D potential-energy scans for H2, HeH+, LiH and BeH2 (STO-3G and, for the two-electron systems, 6-31G), and map a 32×32 2D PES for H2O in STO-3G. They further couple SQD(LUCJ) to Density Matrix Embedding Theory (DMET) for eight ligand-like molecules and for amantadine, reporting active-space energies that largely agree with FCI or DMET-CASCI to within chemical accuracy for the chosen basis sets. Circuit resources, subspace-coverage metrics (ηpost-cr, ηsub), and the effects of the sampling parameter εs are systematically tabulated and plotted.

Significance. If the numerical claims hold, the work is a substantial experimental contribution to near-term quantum chemistry. It provides one of the most complete hardware demonstrations of sample-based diagonalization to date: multi-molecule benchmarks, two ansätze with explicit resource and accuracy trade-offs, the first experimental 32×32 2D PES of water on a superconducting device, and DMET-SQD energies for a pharmacologically relevant molecule (amantadine) on IQM hardware. Strengths include transparent reporting of failures (LCNot recovery on H2O/NH3), controlled degradation under reduced εs, and direct comparison to independent classical FCI/CASCI/CCSD references with no fitted energy parameters. The data establish a practical baseline for hybrid SQD–embedding workflows on current superconducting platforms.

major comments (3)
  1. §4.1.2 and Table 6: LCNot-UCCSD configuration recovery fails entirely for H2O and NH3 (no samples in the symmetry sector S). The abstract and conclusion still present LCNot-UCCSD as a demonstrated alternative within the SQD workflow. The manuscript should state more sharply that LCNot is only validated for H2, LiH and BeH2 on this hardware, and that the depth-induced failure mode is a hard limit of the present demonstration rather than a minor caveat.
  2. §4.2.1 (BeH2, εs=√|S|) and §4.3 (2D H2O, εs=21): under reduced subsampling, isolated geometries exceed chemical accuracy (≈1.6 mHa), especially where multireference character grows. The abstract’s claim that “the majority” of energies lie within chemical accuracy is supported by the tables, but the paper should quantify the fraction of grid points / runs that fail the threshold (e.g., for the 32×32 surface and for stretched BeH2) so that the qualifier “majority” is numerically precise rather than qualitative.
  3. §3.3 and §4.4: all DMET impurities are truncated to a 4-HOMO–4-LUMO active space (≤16 qubits). The reported chemical accuracy is therefore relative to DMET-CASCI in the same truncated space, not to full-system FCI or larger active spaces. This is methodologically consistent, but the abstract and §5 should make explicit that the embedding results demonstrate accuracy of the SQD impurity solver inside a fixed, hardware-limited active space, not recovery of the untruncated molecular correlation energy.
minor comments (6)
  1. Table 1 is a useful algorithm comparison but is long; consider moving part of it to the SI or tightening the “Key limitations” column for readability.
  2. Notation: ηsym, ηpost-cr and ηsub are defined in Eq. (28); ensure every figure caption that uses them points back to that definition (some 1D/2D captions omit it).
  3. §2.3 / Fig. 2: the LCNot-UCCSD single- and double-excitation circuits are shown, but a short statement that no parity-relaxing approximations were used (as claimed later) would help readers who only skim the methods.
  4. Appendix references (B–D) for geometries, calibration and QPU runtimes are essential for reproducibility; confirm that the Zenodo deposit includes the raw bitstring counts and the exact geometry JSON used for the 2D grid.
  5. A few typographical inconsistencies appear (e.g., “Nitrosyl” vs “Nitrocyl” in Fig. 35 labels; “post–configuration-recovery” hyphenation). A light copy-edit pass would clean these.
  6. The claim of “first experimental 2D-PES on superconducting hardware” is carefully hedged in the text; keep that hedging in the abstract so it is not over-read as absolute priority over all platforms.

Circularity Check

1 steps flagged · score 2.0 of 10

Mild self-definitional exactness when ηsub=1 (full symmetry space); core experimental claims otherwise independent of inputs and benchmarked externally.

  1. self definitional [Section 4.1.1 (and analogous statements in 4.2, 4.3, 4.4); Table 4; Eq. (18)]
    "For εs=10^8, the SQD(LUCJ) workflow recovers the FCI ground-state energy to within sub-nanohartree precision for all five molecules across all three independent runs, with no run-to-run variance observed. This is primarily due to |Ssub| spanning the complete |S|, as reflected by ηsub. ... EQSCI=mineig(Hsub)≥Eexact"

    When the chosen εs forces |Ssub|=|S|, the SQD energy is defined as the lowest eigenvalue of the full symmetry-adapted Hamiltonian matrix, which is exactly the FCI energy by construction. The reported sub-nanohartree 'agreement' is therefore an identity, not an independent quantum prediction. The paper discloses the ηsub=1 values, so the circularity is transparent and limited to the non-factor-subsampling regime.

full rationale

The paper is an experimental hardware demonstration of SQD(LUCJ/LCNot-UCCSD) + optional DMET, not a first-principles derivation of a new physical law. Final energies are obtained by classical exact diagonalization of a (recovered) configuration subspace and are compared to independent PySCF FCI/CASCI/CCSD references. No parameters are fitted to the target energies and then re-predicted. When the user-chosen εs is large enough that |Ssub|=|S| (ηsub=1), ESQD equals EFCI (or DMET-CASCI) by construction of the algorithm; the paper itself states this explicitly and reports the corresponding ηsub values. That identity is a minor self-definitional step, not a hidden circular prediction. For the reduced-εs, multi-reference, and LCNot-failure cases the paper quantifies genuine deviations and limitations. Self-citations are to prior algorithmic literature (SQD, LUCJ, DMET, qubit-excitation gates) that are externally published and not uniqueness theorems load-bearing for the present experimental numbers. Overall circularity is therefore low and non-central.

Assumptions & free parameters 4 free parameters · 4 assumptions · 1 invented entities

The central accuracy claims rest on standard quantum-chemistry approximations (Born–Oppenheimer, finite basis sets, RHF reference, single-reference CCSD/MP2 initialization) plus a handful of algorithmic hyperparameters (shot count, recovery iterations, εs, active-space truncation) that are chosen by the authors and whose effect is partially ablated. No new physical entities are postulated; the LCNot-UCCSD ansatz is a circuit-construction variant of known UCCSD.

free parameters (4)
  • Nshots = 10000 (default)
    Fixed at 10 000 (or varied 500–10 000 for amantadine); controls sampling completeness of the configuration pool.
  • εs (samples per batch) = 1e8 or sqrt(|S|)
    User-chosen; either 1e8 (non-factor) or sqrt(|S|); directly sets diagonalization subspace size and therefore accuracy.
  • Imax (recovery iterations) = 10
    Fixed at 10; controls how many times configuration recovery is applied.
  • Active-space truncation (4 HOMO–4 LUMO) = (8,8) max
    Hardware-driven cut to ≤16 qubits for DMET impurities; not variationally optimized.
assumptions (4)
  • domain assumption Born–Oppenheimer approximation and non-relativistic electronic Hamiltonian
    Standard starting point for all ab-initio calculations in the paper (Section 2.1).
  • domain assumption Finite Gaussian basis sets (STO-3G, 6-31G) adequately represent the electronic structure for the claimed chemical accuracy
    All energies and PES are reported inside these bases; basis-set incompleteness is not corrected.
  • domain assumption Single-reference CCSD or MP2 amplitudes provide a sufficiently good initialization for the LUCJ/LCNot trial state
    Used throughout; known to degrade for multi-reference geometries (explicitly noted for stretched BeH2).
  • domain assumption Configuration recovery + SCI proliferation yields a subspace whose lowest eigenvalue is a reliable upper bound to the true ground-state energy
    Core of the SQD method (Section 2.5); variational only inside the selected subspace.
invented entities (1)
  • LCNot-UCCSD ansatz (Linear-CNOT Unitary Coupled-Cluster Singles and Doubles)
    purpose: Reduce classical pre-computation (MP2 instead of CCSD) at the cost of deeper circuits while preserving UCCSD structure.
    Introduced and implemented for the first time inside the SQD workflow; circuit construction given in Section 2.3 and Figure 2.

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Cite this review

Pith. "Pith review of Towards Chemically Accurate and Scalable Quantum Simulations on IQM Quantum Hardware: A Quantum-HPC Hybrid Approach." pith.science (2026). https://pith.science/paper/ZD6ATKDJ

@misc{pith2026260401983,
  author       = {Pith},
  title        = {Pith review of: Towards Chemically Accurate and Scalable Quantum Simulations on IQM Quantum Hardware: A Quantum-HPC Hybrid Approach},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/ZD6ATKDJ}},
  note         = {Machine review of arXiv:2604.01983}
}
abstract

We present a large-scale experimental study of quantum-computing-based molecular simulation carried out on IQM's Sirius 24-qubit superconducting processor, utilizing up to 16 operational qubits. The work employs Sample-based Quantum Diagonalization (SQD) together with the Local Unitary Cluster Jastrow (LUCJ) ansatz to estimate ground-state energies for a set of benchmark molecules, including H$_2$, LiH, BeH$_2$, H$_2$O, and NH$_3$. In addition, we introduce a Linear-CNOT variant of the Unitary Coupled-Cluster Singles and Doubles (LCNot-UCCSD) ansatz within the SQD workflow, trading higher circuit depth for reduced classical preprocessing. A comparison between these ans\"atze is provided, clarifying their respective strengths, limitations, and suitability for near-term quantum hardware. We further explore potential energy landscapes through 1D scans for H$_2$ and HeH$^+$ using both STO-3G and 6-31G basis sets, and for LiH and BeH$_2$ in STO-3G. Extending beyond this, we demonstrate the experimental construction of a full 2D potential energy surface for the water molecule on quantum hardware, mapped over a 32 $\times$ 32 grid in bond length and bond angle. To move beyond small benchmark systems, we combine SQD(LUCJ) with Density Matrix Embedding Theory (DMET) to compute active-space energies for a set of ligand-like molecules, as well as the pharmacologically relevant amantadine system. Across all studies, the majority of quantum-computed energies agree with reference FCI results, as well as with DMET-CASCI energies for embedded systems, to within chemical accuracy for the chosen basis sets. These results demonstrate the reliability of sample-based diagonalization approaches and underscore the potential of hybrid embedding strategies for extending quantum simulations to increasingly complex molecular systems, while also highlighting their practicality on current IQM quantum hardware.

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Forward citations

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Pith tools

Reviewed July 15, 2026 · model on record in the stance chip above.