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arxiv: 1907.00362 · v1 · pith:BKMYULTMnew · submitted 2019-06-30 · 🪐 quant-ph · cond-mat.mtrl-sci

Computational Chemistry on Quantum Computers: Ground state estimation

V. Armaos , Dimitrios A. Badounas , Paraskevas Deligiannis This is my paper

Pith reviewed 2026-05-25 12:40 UTC · model grok-4.3

classification 🪐 quant-ph cond-mat.mtrl-sci
keywords quantum simulationvariational quantum eigensolverunitary coupled clustermolecular ground statesSTO-3G basisbenchmark datacomputational chemistry
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The pith

UCCSD with VQE on a simulator produces expected ground state energies for 14 small molecules on STO-3G basis.

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

This paper computes the ground state energies of fourteen small molecules by simulating the UCCSD ansatz using the VQE algorithm on a quantum computer simulator. The resulting energies are presented as the values that would be obtained from a real quantum computer for these molecules in the STO-3G basis set. The authors intend this dataset to act as a benchmark for experimental work on actual quantum hardware implementing the same method.

Core claim

Implementing the Unitary Coupled Cluster Singles and Doubles (UCCSD) method through the Variational Quantum Eigensolver (VQE) on a simulator yields ground state energies for the molecules CO, HCl, F2, NH4+, CH4, NH3, H3O+, H2O, BeH2, LiH, OH-, HF, HeH+, and H2 that represent the expected output from a quantum computer on the STO-3G basis.

What carries the argument

The UCCSD ansatz executed via the VQE algorithm on a quantum simulator.

If this is right

  • These energies can serve as reference values to compare against results from physical quantum computers.
  • Any deviations in hardware experiments would point to the effects of noise and decoherence rather than methodological issues.
  • The dataset enables validation of quantum chemistry algorithms on near-term quantum devices for these specific systems.

Where Pith is reading between the lines

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

  • Future work could extend these simulations to larger basis sets or more complex molecules to test scalability.
  • Direct comparison of these values with classical full configuration interaction results would quantify the accuracy of the UCCSD approximation itself.

Load-bearing premise

The VQE implementation of UCCSD on the simulator accurately captures the ground state that an ideal quantum computer would find without noise or errors.

What would settle it

Executing the identical UCCSD circuits on a real quantum computer and obtaining energies that significantly differ from the simulated values, after accounting for hardware noise, would show that the simulator data does not represent expected quantum computer output.

Figures

Figures reproduced from arXiv: 1907.00362 by Dimitrios A. Badounas, Paraskevas Deligiannis, V. Armaos.

Figure 1
Figure 1. Figure 1: Circuit design for quantum chem￾istry. Circuit implementation of the UCC operator e −iθXZY for 3 qubits. θ controls the amplitude of the excitation. The H and Rz( π 2 ) gates facilitate a basis change, so that the applied operator to the selected qubit is X and Y respectively, instead of Z. Serves as an essential circuit for any type of UCC simulation.[18] creation and annihilation operators to qubits, we … view at source ↗
Figure 2
Figure 2. Figure 2: Illustration of geometry parameters of H2O. On the left panel, we present the ground state energy of H2O as a function of the distance between the oxygen atom and any of the two Hydrogen atoms. On the right panel, the energy is a function of the angle between the two OH bonds. In each graph we keep constant one of the geometry variables. The empty circles correspond to the UCCSD ground state energy while t… view at source ↗
Figure 4
Figure 4. Figure 4: Double Excitation Contribution to Energy. In this plot we present the energy contribution of the e θ(α † 13α † 12α5α4−α † 4α † 5α12α13) excitation. For θ = 0, the excitation has no effect on the state and the energy. For θ = ±π, the excitation takes full effect, equivalent to acting with the α † 13α † 12α5α4 operator on the state. As it is expected, the minimum lies close to 0, since the double excitations… view at source ↗
read the original abstract

We present computational chemistry data for small molecules ($CO$, $HCl$, $F_2$, $NH_4^+$, $CH_4$, $NH_{3}$, $H_3O^+$, $H{_2}O$, $BeH_{2}$, $LiH$, $OH^-$, $HF$, $HeH^+$, $H_2$), obtained by implementing the Unitary Coupled Cluster method with Single and Double excitations (UCCSD) on a quantum computer simulator. We have used the Variational Quantum Eigensolver (VQE) algorithm to extract the ground state energies of these molecules. This energy data represents the expected ground state energy that a quantum computer will produce for the given molecules, on the STO-3G basis. Since there is a lot of interest in the implementation of UCCSD on quantum computers, we hope that our work will serve as a benchmark for future experimental implementations.

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

1 major / 1 minor

Summary. The manuscript implements the UCCSD ansatz via the VQE algorithm on a noiseless quantum simulator to compute ground-state energies for 14 small molecules (CO, HCl, F₂, NH₄⁺, CH₄, NH₃, H₃O⁺, H₂O, BeH₂, LiH, OH⁻, HF, HeH⁺, H₂) in the STO-3G basis. It presents these energies as benchmark data and states that they represent the expected ground-state energies a quantum computer will produce.

Significance. If the simulations are correctly executed and documented, the tabulated energies could serve as reproducible ideal-case references for UCCSD/VQE on small molecules. The work does not introduce new algorithms or hardware demonstrations, so its value is primarily as a computational benchmark rather than a methodological advance.

major comments (1)
  1. [Abstract] Abstract: The claim that the reported energies 'represent the expected ground state energy that a quantum computer will produce' is not supported. The manuscript describes only ideal, noiseless classical simulation of the UCCSD/VQE circuit; no noise model, decoherence, gate-error simulation, readout noise, or hardware comparison is provided. Real NISQ hardware shifts variational energies, so the stated equivalence requires additional justification or rephrasing.
minor comments (1)
  1. The manuscript should clarify the simulator backend, convergence criteria for VQE optimization, and any active-space or qubit-mapping details used for each molecule to allow exact reproduction.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful review of our manuscript. We address the single major comment below and agree that a clarification is warranted.

read point-by-point responses

  1. Referee: [Abstract] Abstract: The claim that the reported energies 'represent the expected ground state energy that a quantum computer will produce' is not supported. The manuscript describes only ideal, noiseless classical simulation of the UCCSD/VQE circuit; no noise model, decoherence, gate-error simulation, readout noise, or hardware comparison is provided. Real NISQ hardware shifts variational energies, so the stated equivalence requires additional justification or rephrasing.

    Authors: We agree with the referee that the original phrasing is imprecise. The simulations are performed on a noiseless classical simulator of the VQE algorithm, which yields the exact variational minimum of the UCCSD ansatz (within numerical tolerances). This value is precisely the energy that would be obtained by an ideal, error-free quantum computer executing the same circuit. We did not intend to claim equivalence to noisy NISQ hardware. To address the concern, we will revise the abstract to read: 'This energy data represents the expected ground state energy that an ideal, noiseless quantum computer will produce for the given molecules, on the STO-3G basis.' The remainder of the manuscript already describes the noiseless setting, so no further changes are needed. revision: yes

Circularity Check

0 steps flagged

No circularity; direct implementation of established VQE/UCCSD on simulator

full rationale

The manuscript performs a standard noiseless classical simulation of UCCSD via VQE to obtain ground-state energies for listed molecules in STO-3G and states that these energies represent expected ideal quantum-computer output. This is a direct computational result under the ideal (noiseless) model; the derivation chain consists of the usual VQE variational minimization and does not reduce any claimed prediction or first-principles result to its own fitted inputs by construction. No self-definitional equations, no fitted-input-called-prediction steps, and no load-bearing self-citations appear in the abstract or described content. The work is therefore self-contained against external benchmarks and receives the default non-circularity finding.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on standard assumptions in quantum computational chemistry regarding the basis set and ansatz accuracy, which are not new to this paper.

axioms (1)
  • domain assumption The UCCSD ansatz provides a good approximation to the ground state wavefunction for the listed molecules on STO-3G.
    Implicit in the use of UCCSD for ground state estimation in the abstract.

pith-pipeline@v0.9.0 · 5699 in / 1099 out tokens · 47941 ms · 2026-05-25T12:40:27.580954+00:00 · methodology

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Reference graph

Works this paper leans on

31 extracted references · 31 canonical work pages · 12 internal anchors

  1. [1]

    STO- 3G, 6-31G ,cc-pVDZ)

    An ab-initio computational chemistry program is used (in our case Psi4) to perform a (classically tractable) Hartree-Fock (H-F) geometry optimiza- tion calculation on the chosen molecule for the se- lected computational chemistry basis (e.g. STO- 3G, 6-31G ,cc-pVDZ). The resulting optimal ge- ometry is fed to the next step of the algorithm

    work page

  2. [2]

    Assuming that the H-F geometry is sufficiently close to the UCCSD optimal geometry, we fit a paraboloid to find the actual minimum

    The H-F optimal geometry is used as the ansatz for the UCCSD geometry optimization algorithm. Assuming that the H-F geometry is sufficiently close to the UCCSD optimal geometry, we fit a paraboloid to find the actual minimum. See Fig- ure 3

    work page

  3. [3]

    For each distinct geometry, we run again a classical H-F calculation to obtain the fermionic Hamilto- nian and the ground state energy of the configura- tion

    work page

  4. [4]

    We use the Jordan-Wigner encoding to transform the fermionic Hamiltonian in to the corresponding qubit Hamiltonian and perform the following VQE algorithm

    work page

  5. [5]

    Us- ing circuits similar to the one pictured in Figure 1, we perform double and single excitations on the ini- tial state

    We initialize the quantum computer at the en- coded H-F ground state, |00...0011...11⟩ (N ones andM−N zeros), where N is the number of elec- trons andM the number of orbitals considered. Us- ing circuits similar to the one pictured in Figure 1, we perform double and single excitations on the ini- tial state. We write the resulting state as |Ψ(θθθ)⟩, where...

    work page

  6. [6]

    A classical optimizer is used to find the configu- ration θθθmin that minimizes the energy of the spe- cific geometry. The corresponding state |Ψ(θθθmin)⟩ is the UCCSD ground state for the specific geom- etry and the expectation value of the Hamiltonian ⟨Ψ(θθθmin)| ˆH|Ψ(θθθmin)⟩ is the corresponding ground state energy

    work page

  7. [7]

    Since we are using a statevector simulator, we have the benefit of retrieving the expectation value di- rectly from the wavefunction

    The energy of any |Ψ(θθθ)⟩ can be found by mea- suring the expectation values of the operators that comprise the Hamiltonian (McArdle et al.[18]). Since we are using a statevector simulator, we have the benefit of retrieving the expectation value di- rectly from the wavefunction. In an actual quan- tum computer, we would have to execute the same experiment...

    work page

  8. [8]

    We found that in order to achieve chemical accuracy, three iterations through the list of excitations are usu- ally sufficient

    In our case, in order to perform the classical op- timization part of the algorithm, we just iterate through the excitations and optimize each one se- quentially until the energy converges. We found that in order to achieve chemical accuracy, three iterations through the list of excitations are usu- ally sufficient. Molecule Qubits Energy Distance Angle (Ha...

    work page

  9. [9]

    R. P. Feynman, Quantum mechanical computers (1986), URL https://doi.org/10.1007/BF01886518

    work page doi:10.1007/bf01886518 1986

  10. [10]

    Sugisaki, S

    K. Sugisaki, S. Nakazawa, K. Toyota, K. Sato, D. Sh- iomi, and T. Takui, Quantum chemistry on quantum computers: A method for preparation of multicon- figurational wave functions on quantum computers without performing post-hartreefock calculations (2019), https://doi.org/10.1021/acscentsci.8b00788, URL https://doi.org/10.1021/acscentsci.8b00788

    work page doi:10.1021/acscentsci.8b00788 2019

  11. [11]

    I. M. Georgescu, S. Ashhab, and F. Nori, Quantum sim- ulation (2014), URL https://link.aps.org/doi/10. 1103/RevModPhys.86.153

    work page 2014

  12. [12]

    Maslov, Y

    D. Maslov, Y. Nam, and J. Kim, An outlook for quantum computing [point of view] (2019)

    work page 2019

  13. [13]

    Kelly, Engineering superconducting qubit arrays for Quantum Supremacy (2018), URL https://ui.adsabs

    J. Kelly, Engineering superconducting qubit arrays for Quantum Supremacy (2018), URL https://ui.adsabs. harvard.edu/abs/2018APS..MARA33001K

    work page 2018

  14. [14]

    Full-Stack, Real-System Quantum Computer Studies: Architectural Comparisons and Design Insights

    P. Murali, N. M. Linke, M. Martonosi, A. J. Abhari, N. H. Nguyen, and C. H. Alderete,Full-stack, real-system quantum computer studies: Architectural comparisons and design insights (2019), arXiv:1905.11349

    work page internal anchor Pith review Pith/arXiv arXiv 2019

  15. [15]

    Aspuru-Guzik, A

    A. Aspuru-Guzik, A. D. Dutoi, P. J. Love, and M. Head- Gordon, Simulated quantum computation of molecu- lar energies (2005), URL http://science.sciencemag. org/content/309/5741/1704

    work page 2005

  16. [16]

    Simulating chemistry efficiently on fault-tolerant quantum computers

    N. Cody Jones, J. D. Whitfield, P. L. McMahon, M.- H. Yung, R. Van Meter, A. Aspuru-Guzik, and Y. Ya- mamoto, Faster quantum chemistry simulation on fault- tolerant quantum computers (2012), 1204.0567

    work page internal anchor Pith review Pith/arXiv arXiv 2012

  17. [17]

    M. B. Hastings, D. Wecker, B. Bauer, and M. Troyer, Improving Quantum Algorithms for Quantum Chemistry (2014), 1403.1539

    work page internal anchor Pith review Pith/arXiv arXiv 2014

  18. [18]

    Strategies for quantum computing molecular energies using the unitary coupled cluster ansatz

    J. Romero, R. Babbush, J. R. McClean, C. Hempel, P. Love, and A. Aspuru-Guzik, Strategies for quantum computing molecular energies using the unitary coupled cluster ansatz (2017), 1701.02691

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  19. [19]

    J. Lee, W. J. Huggins, M. Head-Gordon, and K. B. Wha- ley, Generalized Unitary Coupled Cluster Wavefunctions for Quantum Computation (2018), 1810.02327

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  20. [20]

    I. G. Ryabinkin, T.-C. Yen, S. N. Genin, and A. F. Izmaylov, arXiv e-prints arXiv:1809.03827 (2018), 1809.03827

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  21. [21]

    J. R. McClean, J. Romero, R. Babbush, and A. Aspuru- Guzik, The theory of variational hybrid quantum-classical algorithms (2016), 1509.04279

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  22. [22]

    Somma, G

    R. Somma, G. Ortiz, J. E. Gubernatis, E. Knill, and R. Laflamme, Simulating physical phenomena by quan- tum networks (2002), URL https://link.aps.org/doi/ 10.1103/PhysRevA.65.042323

    work page doi:10.1103/physreva.65.042323 2002

  23. [23]

    Jordan and E

    P. Jordan and E. Wigner, ¨Uber das paulische ¨ aquivalenzverbot(1928), URL https://doi.org/10. 1007/BF01331938

    work page 1928

  24. [24]

    J. T. Seeley, M. J. Richard, and P. J. Love, The Bravyi- Kitaev transformation for quantum computation of elec- tronic structure (2012), 1208.5986

    work page internal anchor Pith review Pith/arXiv arXiv 2012

  25. [25]

    S. B. Bravyi and A. Y. Kitaev,Fermionic Quantum Com- putation (2002), quant-ph/0003137

    work page internal anchor Pith review Pith/arXiv arXiv 2002

  26. [26]

    McArdle, S

    S. McArdle, S. Endo, A. Aspuru-Guzik, S. Benjamin, and X. Yuan, Quantum computational chemistry (2018), 1808.10402

    work page arXiv 2018

  27. [27]

    Aleksandrowicz, T

    G. Aleksandrowicz, T. Alexander, P. Barkoutsos, L. Bello, Y. Ben-Haim, D. Bucher, F. J. Cabrera- Hernndez, J. Carballo-Franquis, A. Chen, C.-F. Chen, et al. (2019)

    work page 2019

  28. [28]

    Moseley and M

    B. Moseley and M. A. Osborne, Bayesian optimisation for variational quantum eigensolvers (2018)

    work page 2018

  29. [29]

    A variational eigenvalue solver on a quantum processor

    A. Peruzzo, J. McClean, P. Shadbolt, M.-H. Yung, X.-Q. Zhou, P. J. Love, A. Aspuru-Guzik, and J. L. O’Brien, A variational eigenvalue solver on a photonic quantum processor (2014), 1304.3061

    work page internal anchor Pith review Pith/arXiv arXiv 2014

  30. [30]

    Hardware-efficient Variational Quantum Eigensolver for Small Molecules and Quantum Magnets

    A. Kandala, A. Mezzacapo, K. Temme, M. Takita, M. Brink, J. M. Chow, and J. M. Gambetta, Hardware- efficient variational quantum eigensolver for small molecules and quantum magnets (2017), 1704.05018

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  31. [31]

    Ground-state energy estimation of the water molecule on a trapped ion quantum computer

    Y. Nam, J.-S. Chen, N. C. Pisenti, K. Wright, C. Delaney, D. Maslov, K. R. Brown, S. Allen, J. M. Amini, and J. Apisdorf, Ground-state energy estimation of the wa- ter molecule on a trapped ion quantum computer (2019), 1902.10171

    work page internal anchor Pith review Pith/arXiv arXiv 2019