Better accuracy with fewer qubits: Single-particle basis set optimization for quantum chemistry on quantum computers

Subimal Deb; V. S. Prasannaa

REVIEW 5 major objections 5 minor 59 references

Better accuracy with fewer qubits: Single-particle basis set optimization for quantum chemistry on quantum computers

T0 review · 5 major / 5 minor · reviewed 2026-08-15 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read The paper claims that re-optimized minimal STO-kG basis sets reach or beat 6-31G-quality atomic energies with only 10 spin orbitals, and for lithium exceed cc-pVQZ.

desk verdict Useful basis-optimization pipeline and open-source data, but the headline accuracy claims rest on Dunning table columns that are plain copy-paste errors. read the letter →

arxiv 2608.02119 v1 pith:AP6DUHGO submitted 2026-08-03 quant-ph physics.atom-phphysics.chem-ph

Subimal Deb , V. S. Prasannaa This is my paper · ORCID

classification quant-phphysics.atom-phphysics.chem-ph

keywords modifiedminimalbasissetssetoptimizationquantumchemistrycomputingvariationaleigensolverphaseestimationcontractedGaussiancorrelationenergy

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 argues that re-optimizing the exponents and contraction coefficients of minimal STO-kG basis sets gives atomic ground-state energies comparable to or better than the much larger 6-31G basis while using the same 10 spin orbitals as the minimal basis, and for lithium even surpassing cc-pVQZ. Because contracted minimal bases keep the spin-orbital count fixed as the number of Gaussians k grows, the improvement costs no extra qubits in a quantum algorithm. The authors generate MSTO-kG bases (k=2 through 11) for H through F with a genetic-algorithm-plus-refinement scheme and benchmark FCI energies, plus VQE, QPE, and HHL resource counts for lithium. If correct, the approach gives near-term quantum chemistry a better accuracy-per-qubit trade-off than choosing a standard larger basis and truncating its active space.

What carries the argument

The load-bearing object is the contracted Gaussian minimal basis: each atomic orbital is a fixed linear combination of k zero-centered Gaussians, so the number of contracted functions, and hence the number of spin orbitals and qubits, is independent of k. The memetic algorithm—a genetic algorithm with elitist selection, interpolative mutation, and discrete-parameter crossover, followed by parallel aggressive refinement—tunes the k exponents and k contraction coefficients against the CISD ground-state energy. Because k can grow to 11 without enlarging the orbital space, the same qubit footprint yields progressively lower energies, which is the mechanism behind the claim of better accuracy at a fixed quantum-resource budget.

What would settle it

Repeat the Li FCI calculation with the full cc-pVQZ basis, with all spin orbitals active, and compare against the MSTO-11G result of $-7.452345\,\mathrm{Ha}$; if the full cc-pVQZ FCI energy is lower, the paper's claim that MSTO surpasses cc-pVQZ fails. Likewise, run full 6-31G FCI for B, C, N, O, and F and check whether MSTO energies remain below the untruncated 6-31G values.

Watch

Extended reading notes

Core claim

The paper constructs modified minimal Slater-type-orbital basis sets, MSTO-kG for k=2 through 11, for the atoms H through F, excluding He, by memetic optimization of Gaussian exponents and contraction coefficients against CISD energies. At the FCI level these bases yield ground-state energies that are comparable to or lower than 6-31G for all the atoms studied, and for Li the MSTO-11G energy of $-7.452345\,\mathrm{Ha}$ falls below the truncated cc-pVQZ value of $-7.431554\,\mathrm{Ha}$, while using only 10 spin orbitals compared with 18 for 6-31G and 28 for cc-pVDZ. For molecules, the FCI results from MSTO bases are comparable to or better than 6-31G for Li$_2$, LiH, BeH, and BeH$_2$, and for C$_2$ at the CISD level, whereas H$_2$ is a known failure. Resource estimates for VQE-UCCSD, QPE-CASCI, and HHL-LCCSD on Li show far fewer qubits and CX gates with MSTO bases than with 6-31G or cc-pVDZ along with lower FCI energies.

Load-bearing premise

The comparisons to 6-31G and Dunning bases are made with those larger bases truncated to the same 10 spin orbitals; if one instead compares full active-space FCI in each basis, the larger bases recover much more correlation energy and the apparent advantage of MSTO bases may disappear.

Editorial extensions

If this is right

With MSTO bases, a quantum computation for these atoms uses 10 qubits instead of 18 or 28 while targeting lower energies, directly expanding what is feasible on near-term hardware.
The VQE-UCCSD gate count for Li drops from 17,420 CX gates with 6-31G to 2,246 with MSTO-11G, and QPE and HHL logical T-gate counts fall because gate estimates scale polynomially with spin-orbital count.
One-time classical basis-set optimization can be reused for any quantum-chemical calculation on molecules built from H through F atoms, including hybrid STO/MSTO combinations.
For N, O, and F the MSTO bases still lack sufficient virtual orbitals, so FCI correlation energy is near zero and a quantum computer gains nothing over Hartree-Fock there.
H$_2$ is a counterexample where MSTO underperforms both STO-6G and 6-31G, so the method is not universally better for molecules.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

Editorial inference: The same memetic recipe could be applied to polarization or split-valence bases to push the accuracy-per-qubit frontier further; the paper notes 6-31G is already near-optimal, so gains there would be smaller.
Editorial inference: The near-parity with cc-pVQZ for Li hints that re-optimized contracted bases may be systematically beneficial for one- and two-valence-electron atoms; extending to Na, K, or Mg would test this without new methodology.
Editorial inference: Because contracted basis size and qubit footprint are decoupled from k, basis-set optimization can be composed with qubit tapering and orbital-selection heuristics, potentially stacking resource savings.
Editorial inference: If the truncated-active-space benchmark is replaced by a full-basis comparison, MSTO's margin will shrink or invert; the practical claim is best read as 'best accuracy within a fixed small active space.'

Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

The useful core here is real: a memetic optimization of STO-kG exponents and contraction coefficients up to k=11 for H–F, with open-source code and basis parameters released. That is a concrete extension of Andrade et al. and a legitimate tool for qubit-limited quantum chemistry. But you can't trust the abstract as written.

What is genuinely new: the systematic extension to k=11, the resource accounting for VQE, QPE, and HHL, and the molecular PECs. The H2 failure is honestly flagged and consistent with earlier work. The Li example—same qubits as STO-6G, better FCI energy than 6-31G in the 10-orbital space—is a meaningful demonstration of the core idea. The code being public is real evidence and deserves credit.

The soft spots are serious but fixable. First, the cc-pVTZ and cc-pVQZ columns in every table are numerically identical to the 6-31G entries. No physical basis gives Li cc-pVQZ FCI = -7.431554; the exact nonrelativistic energy is -7.478060, and the paper's own Hylleraas line shows MSTO-11G is 25.7 mHa above exact. So the abstract's claim that MSTO 'surpasses cc-pVQZ' for Li is unsupported by the paper's own data. Second, the abstract says FCI energies for H–F are comparable to or lower than 6-31G, but the tables show C, N, O, F are 16–56 mHa higher, and the conclusion later concedes N, O, F are higher. The abstract and conclusion contradict each other. Third, Appendix A lists only s-type exponents and contraction coefficients for every element. If p functions were left at their STO values, that should be stated; if they were optimized, the tables are missing data. Either way, reproducing the B–F results is not possible from the released basis parameters as presented. The active-space truncation issue in Table I also shows the 'fewer qubits' advantage is a trade-off for B–F, not a free lunch; it works for Li, and the paper should say so.

The circularity of optimizing against atomic CISD and then re-evaluating the same atoms at FCI is not a real flaw—it is a legitimate design objective, and the molecular tests are independent. The resource estimates are order-of-magnitude, clearly labeled, and adequate for comparing basis sets.

Who is this for? People doing near-term quantum chemistry resource estimation and basis set design. It deserves serious peer review because the method is sound and the code is real, but the authors need to correct the Dunning tables, revise the abstract to match their own tables, and complete the basis parameter listings. The fixable errors are concentrated in presentation and honesty of the headline claims, not in the underlying approach.

Referee Report

5 major / 5 minor

Summary. The paper proposes re-optimizing minimal STO-kG basis sets (k=2–11) for atoms H through F (excluding He) using a memetic algorithm, with the goal of improving quantum-chemistry energies on quantum computers while keeping the number of spin orbitals (and hence qubits) fixed. The authors report atomic FCI energies for MSTO-kG bases, compare them with STO-kG, 6-31G, and Dunning basis sets, present molecular potential energy curves for H2, Li2, C2, LiH, BeH, and BeH2, and estimate quantum resources for VQE-UCCSD, QPE-CASCI, and HHL-LCCSD using Li as a representative example. The central claim is that MSTO bases achieve better or comparable energies than larger standard bases with fewer qubits and gates.

Significance. The idea of one-time classical preprocessing to design qubit-efficient basis sets is genuinely useful for near-term quantum chemistry, and the open-source implementation (https://github.com/subimal/MSTO-kG) is a commendable contribution. The resource-scaling analysis for VQE, QPE, and HHL is transparent and includes explicit gate-count formulas. However, as presented, the headline numerical comparisons are not reliable: several table entries for the Dunning basis sets are physically implausible, and the abstract's blanket statement that MSTO FCI energies are 'comparable or sometimes even lower' than 6-31G is contradicted by the paper's own tables for B, C, N, O, and F. The underlying methodology is defensible, but the manuscript needs substantial corrections and clarifications before its central claims can be considered sound.

major comments (5)

[Appendix B, Tables II–IX; Section IV.A] The cc-pVTZ and cc-pVQZ entries in Tables II–IX are numerically identical to the 6-31G entries for every atom (e.g., Li: -7.431235/-7.431554; F: -99.360218/-99.447423). A genuine full-basis FCI calculation with cc-pVQZ cannot produce exactly the same energy as 6-31G; for Li, the tabulated cc-pVQZ FCI value of -7.431554 Ha is 46.5 mHa above the Hylleraas-infinity value of -7.478060 Ha that the paper itself quotes in Table III. Therefore the statement in Section IV.A and in the abstract that MSTO-11G (-7.452345 Ha) 'surpasses the performance of cc-pVQZ' is not supported by the data as printed. The authors must recompute the Dunning-basis values, or explicitly state and justify if these are truncated-active-space results, and revise all claims based on them.
[Abstract and Section IV.A, Tables V–IX] The abstract states: 'The ground state energies of H through F using our MSTO bases at FCI level of theory yield ground state energies that are comparable or sometimes even lower than those obtained using 6-31G basis sets.' This is contradicted by the paper's own data: MSTO-11G is higher than the 6-31G FCI energy by 6.8 mHa for B, 16.3 mHa for C, 30.4 mHa for N, 49.9 mHa for O, and 56.0 mHa for F. The Conclusion (Section VII) already concedes the limitation for N, O, and F. The abstract and the corresponding sentences in the Introduction should be corrected to reflect the actual, element-dependent behavior.
[Section IV.A and Table I] The comparison between MSTO bases (10 spin orbitals) and the reference bases 6-31G, cc-pVDZ, cc-pVTZ, and cc-pVQZ is ambiguous: the text discusses a 10-spin-orbital active space for the reference bases in Table I, but the tables in Appendix B do not state whether the reported 6-31G and Dunning energies are full-basis FCI or truncated-active-space FCI. Because the central claim of 'better accuracy with fewer qubits' depends on the reference calculations being the standard full-basis results, the authors must specify the level of calculation for every table entry and ensure that the comparison is consistent.
[Section V, resource estimation] The resource analysis uses FCI energies in each basis as proxies for the energies that VQE-UCCSD, QPE-CASCI, and HHL-LCCSD would produce. The authors disclose this approximation, but the resulting claim that MSTO bases 'yield better energies than the competing basis sets while incurring fewer qubits' rests on the energy values that are in question due to the Dunning-table errors and on the assumption that the quantum algorithms recover the full FCI correlation energy. The authors should re-evaluate the resource comparison using corrected energies and should discuss the validity of the FCI proxy for each algorithm, particularly for UCCSD and LCCSD, which are approximate methods.
[Section III and Section IV.A] The basis parameters are optimized by minimizing CISD energies of the same atoms that are subsequently evaluated at the FCI level. This creates a circularity in the interpretation of the atomic energy improvements over the unoptimized STO bases: the improvement partly reflects the optimization target rather than an independent predictive gain. The authors should clarify how much of the reported atomic improvement is independent, for example by reporting results for molecules or for test atoms not used in the optimization. This does not invalidate the approach, but it is load-bearing for the atomic comparisons as currently presented.

minor comments (5)

[Table III header] The header contains a typo: 'Hyleraas' should be written as 'Hylleraas'.
[Section II, Eq. (2)] Equation (2) is presented without clear definitions of all symbols beyond the text; please add a sentence explaining that s_ij = alpha_i + alpha_j and that the normalization condition was used to determine d_i.
[Throughout] The notation is inconsistent: 'STO-KG', 'STO-kG', and 'MSTO-kG' are all used. Please standardize to 'STO-kG' and 'MSTO-kG'.
[Section V, Table XI and XII] The Pauli-term counts for STO-6G and MSTO-11G are reported as identical (156) because both have 10 spin orbitals; please mention that this is expected due to the same number of spatial orbitals, not because the integrals are identical.
[References] Some reference entries are incomplete or inconsistent (e.g., Ref. [34] lacks full page range, Ref. [7] is an arXiv identifier without a title). Please harmonize the bibliography style.

Circularity Check

2 steps flagged · score 2.0 of 10

Mild circularity: the atomic energies are the optimization objective and the cc-pVQZ tables duplicate 6-31G values, but the molecular and resource calculations provide independent checks.

fitted input called prediction [Section III (Algorithms 1–4) and Section IV.A / Tables II–IX]
"The minimization is performed at the configuration interaction singles and doubles level of theory. ... The ground state energies of H through F using our MSTO bases at full configuration interaction (FCI) level of theory yield ground state energies that are comparable or sometimes even better (lower) than those obtained using 6-31G basis sets."

The MSTO exponents and contraction coefficients are selected by minimizing the CISD ground-state energy of each atom, and the headline atomic results are FCI energies of those same atoms in those same optimized bases. The atomic improvement over STO/6-31G is therefore the optimization objective restated at a closely related correlation level, not an out-of-sample prediction. This is partial rather than complete circularity because FCI is a different level of theory than the CISD objective, and the molecular PECs and the VQE/QPE/HHL resource estimates are independent checks.
other [Appendix B, Tables II–IX (e.g., Table III for Li)]
"6-31G -7.431235 -7.431554 -0.000319 cc-pVDZ -7.432420 -7.432638 -0.000218 cc-pVTZ -7.431235 -7.431554 -0.000319 cc-pVQZ -7.431235 -7.431554 -0.000319"

For every atom, the cc-pVTZ and cc-pVQZ HF/FCI entries are numerically identical to the 6-31G row (e.g., Li: all three are -7.431235/-7.431554). A genuine cc-pVQZ FCI calculation for Li should be far closer to the Hylleraas-infinity value (-7.478060 Ha) quoted in the same table. The abstract's claim that MSTO bases 'surpass the performance of cc-pVQZ' for Li therefore compares MSTO-11G (-7.452345 Ha) against a duplicated 6-31G baseline, not an independent Dunning-basis result; the external benchmark is internally generated and cannot support the headline comparison.

full rationale

The core basis-set construction is self-contained and disclosed: MSTO-kG parameters are produced by a memetic algorithm whose objective is the atomic CISD energy, so reporting lower atomic FCI energies in those bases is partly a restatement of the fitting target rather than a discovery. However, the paper's contribution is basis-set engineering, where using the target energy as the objective is standard practice, and the authors do not hide this. The molecular calculations (H2, Li2, C2, LiH, BeH, BeH2) against STO-6G and 6-31G, the comparisons with Andrade, Hehre, Tavouktsoglou–Huzinaga and Kapusta, and the VQE, QPE-CASCI and HHL-LCCSD resource estimates provide independent checks outside the atomic fitting loop. No load-bearing mathematical claim rests on a self-citation: the cited works by the present authors are background references or resource-estimation inputs, not uniqueness theorems or suppressed alternatives. The genuinely serious problem is the data artifact in Tables II–IX, where the cc-pVTZ and cc-pVQZ columns repeat the 6-31G numbers exactly; this is not an equation-level circularity of the derivation but it does invalidate the specific 'Li surpasses cc-pVQZ' headline. Overall, the paper is not circular in its derivation chain; there is one mild fitted-input aspect inherent to basis optimization and one benchmark-identity artifact, so the circularity score is low.

Assumptions & free parameters 1 free parameters · 5 assumptions · 0 invented entities

The paper introduces no new particles, forces or physical entities. Its central ingredients are fitted basis set parameters, which are a standard form of free parameter in quantum chemistry. The optimizations rely on domain assumptions about finite-basis electronic structure and on several ad-hoc choices in the memetic algorithm and the resource comparison methodology.

free parameters (1)

MSTO-kG exponents and contraction coefficients {alpha_i, d_i} for H through F, k=2..11 = Listed in Appendix A (tables per element, k=2..11)
These 1040 parameters were optimized by the memetic algorithm to minimize CISD atomic ground state energies. The paper's reported atomic FCI energies are direct evaluations using these fitted parameters, so the atomic energy improvements are the quality of the fit, not an independent prediction.

assumptions (5)

domain assumption The electronic structure is computed at fixed finite-basis HF, CISD or FCI level without complete-basis-set extrapolation.
All comparisons are finite-basis energies. For N, O and F the minimal basis has no virtuals, so FCI equals HF and captures zero correlation, as shown in Tables VII-IX.
ad hoc to paper CISD energy is a suitable objective for optimizing basis parameters intended to improve FCI energies.
Section III: the memetic algorithm minimizes CISD energy for each atom, then the paper reports FCI energies. There is no proof that CISD-optimal parameters are FCI-optimal, and the two can differ.
ad hoc to paper The genetic algorithm with population size N=10 and the chosen refinement strategy converges close enough to the global optimum that the reported energies are representative of the basis shape.
Section III admits the metaheuristic may not reach the analytical minimum; the 1e-10 Ha tolerance is only within the candidate population.
ad hoc to paper For resource estimates, FCI energies in each basis can proxy for VQE-UCCSD, QPE-CASCI and HHL-LCCSD energies.
Section V explicitly states this approximation, arguing that the HF contribution dominates the total energy and the correlation contribution is a small fraction.
domain assumption The comparison against 6-31G and cc-pVXZ is made at equal active space size (10 spin orbitals) rather than full-basis FCI.
Table I and Tables III-IX show 6-31G and cc-pVXZ FCI values computed in a 10-spin-orbital active space, not full FCI. The claim that MSTO bases beat larger bases relies on this equal-active-space benchmark being the relevant one for quantum computing.

how reviews work

0 comments

Cite this review

Pith. "Pith review of Better accuracy with fewer qubits: Single-particle basis set optimization for quantum chemistry on quantum computers." pith.science (2026). https://pith.science/paper/AP6DUHGO

@misc{pith2026260802119,
  author       = {Pith},
  title        = {Pith review of: Better accuracy with fewer qubits: Single-particle basis set optimization for quantum chemistry on quantum computers},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/AP6DUHGO}},
  note         = {Machine review of arXiv:2608.02119}
}

read the original abstract

In spite of recent advances, quantum computers are expected to be sufficiently noisy in the coming few years to the extent of limiting quantum chemical calculations to relatively small number of orbitals. However, even with reasonable quality single particle basis sets, small active spaces with limited orbitals can result in a significant fraction of correlation energy being lost, motivating the design of moderate quality qubit-efficient basis sets for quantum algorithms. We begin by reoptimizing the existing minimal basis sets using a genetic algorithm-inspired approach in conjunction with aggressive refinement strategies, and generate modified minimal basis sets (MSTO-kG basis; k = 2-11) for atoms from H through F. The ground state energies of H through F using our MSTO bases at FCI level of theory yield ground state energies that are comparable or sometimes even lower than those obtained using 6-31G basis sets. In the case of Li, the MSTO bases surpass the performance of cc-pVQZ bases. Thus, we obtain better atomic energies with same number of qubits relative to STO bases, and better/comparable energies with fewer qubits relative to higher quality bases. In the case of molecules, H2 performs poorly; a finding that is consistent with an earlier work in literature. For other molecules, Li2, C2, LiH, BeH and BeH2, the FCI results (except C2 for which we employ CISD) from our bases are comparable to/outperform those from 6-31G basis. Finally, we compare the resources required between different bases and find that MSTO bases yield better energies than the competing basis sets while incurring fewer qubits and two-qubit gates with VQE, QPE, and HHL. The logical T-gate counts are also found to be considerably lower for QPE and HHL respectively. Overall, our work paves way for more accurate yet less qubit-hungry quantum chemical calculations using near-term quantum computers.

Figures

Figures reproduced from arXiv: 2608.02119 by the authors.

**Figure 1.** FIG. 1. Schematic of our workflow. A typical quantum chemical calculation in the quantum computing framework involves [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗

**Figure 2.** FIG. 2. HF and FCI ground state energies of the hydrogen [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗

**Figure 3.** FIG. 3. HF and FCI ground state energies of (a) Li and (c) Be with our MSTO- [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗

Figures from the paper (7 more)

**Figure 4.** Figure 4: FIG. 4. HF and FCI ground state energies of (a) B and (c) C with our MSTO- [PITH_FULL_IMAGE:figures/full_fig_p008_4.png]

**Figure 5.** Figure 5: FIG. 5. HF and FCI ground state energies of (a) Nitrogen, [PITH_FULL_IMAGE:figures/full_fig_p009_5.png]

**Figure 6.** Figure 6: FIG. 6. The HF (left panels), FCI (right panels) PECs for (a) H [PITH_FULL_IMAGE:figures/full_fig_p010_6.png]

**Figure 7.** Figure 7: FIG. 7. The HF (left panels) and FCI (right panels) PECs for (a) LiH and (b) BeH. The PECs for the atom optimized [PITH_FULL_IMAGE:figures/full_fig_p011_7.png]

**Figure 8.** Figure 8: FIG. 8. The HF (left panel) and FCI (right panel) PECs for BeH [PITH_FULL_IMAGE:figures/full_fig_p012_8.png]

**Figure 9.** Figure 9: FIG. 9. Comparison of resource requirements across different basis sets, for the Li atom. The top row presents our results [PITH_FULL_IMAGE:figures/full_fig_p013_9.png]

**Figure 10.** Figure 10: FIG. 10. Change in ground state energies for Li through F [PITH_FULL_IMAGE:figures/full_fig_p015_10.png]

Review history (2 revisions) →

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

59 extracted references · 47 canonical work pages

[1]

the minimal basis sets ( k of 2 through 6),

work page
[2]

and crossovers (Algorithm 3) of candidate basis sets for a given atom in a minimal basis set, and selection of the best candidates (where the objective function is the ground state electronic energy, computed using the Configuration Interaction Singles and Doubles (CISD) method) heuristically optimizes the basis set parameters, often reducing the ground s...

work page
[3]

our MSTO-kG (k of 2 through 11),

work page
[4]

the split-valence 6-31G, and FIG. 2. HF and FCI ground state energies of the hydrogen atom from MSTO- kG basis, compared with minimal basis sets and split valence basis sets (6-31G)

work page
[5]

3), with the accompanying data in Tables II through IX of Appendix B

cc-pVXZ (X=D, T, Q in Fig. 3), with the accompanying data in Tables II through IX of Appendix B. The tables in the Appendix also provides energies from the optimized STO-kG (k = 3, 6) basis sets optimized by generalized simulated annealing [34], STO- kG (3≤k≤ 6) basis sets by Hehere et al and the exact values for STOs (the last two are taken from [27]). F...

work page
[6]

For our analysis, we only consider the quantum al- gorithms in their vanilla form. This is for simplic- ity, as often, reduction in quantum resources that occur in different variants of an algorithm either incurs classical computing overheads that compli- cate estimating costs (for example, a recently in- troduced quantum-information inspired ansatz for V...

work page
[7]

Using other choices would change the gate counts but not the overall observed trends

For the Li atom example, we use the {RZ,X,SX,CX } basis as the native gate set. Using other choices would change the gate counts but not the overall observed trends

work page
[8]

This approximation is reasonable, since the HF contribution for a system, which constitutes al- most all of the total energy, varies substantially across the basis sets considered

In view of the cost, we do not compute energies us- ing the quantum algorithms themselves, but rather just use the FCI energies in each basis as prox- ies for the energies that those algorithms would yield. This approximation is reasonable, since the HF contribution for a system, which constitutes al- most all of the total energy, varies substantially acr...

work page

Show all 59 references

[9]

Verma, A

S. Verma, A. Mitra, Q. Wang, R. D’Cunha, B. Jangid, M. R. Hennefarth, V. Agarawal, L. Otis, S. Haldar, M. R. Hermes, et al., Chemical reviews 126, 184 (2026)

2026
[10]

A. Y. Kitaev, arXiv preprint quant-ph/9511026 (1995)

1995 arXiv
[11]

Aspuru-Guzik, A

A. Aspuru-Guzik, A. D. Dutoi, P. J. Love, and M. Head- Gordon, Science 309, 1704 (2005)

2005
[12]

D. S. Abrams and S. Lloyd, Physical Review Letters 83, 5162 (1999)

1999
[13]

A. W. Harrow, A. Hassidim, and S. Lloyd, Physical Re- view Letters 103, 150502 (2009)

2009
[14]

Baskaran, A

N. Baskaran, A. S. Rawat, A. Jayashankar, D. Chakravarti, K. Sugisaki, S. Roy, S. B. Mandal, D. Mukherjee, and V. S. Prasannaa, Physical Review Research 5, 043113 (2023)

2023
[15]

P. B. Tsemo, A. Jayashankar, K. Sugisaki, N. Baskaran, S. Chakraborty, and V. S. Prasannaa, Physical Review Research 7, 023270 (2025)

2025
[16]

P. B. Tsemo, K. sugisaki, I. Bhattacharjee, and V. S. Prasannaa, arXiv2607.08220 (2026)

2026 arXiv
[17]

Motlagh, R

D. Motlagh, R. A. Lang, P. Jain, J. A. Campos-Gonzalez- Angulo, W. Maxwell, T. Zeng, A. Aspuru-Guzik, and J. Miguel Arrazola, Quantum Science and Technology 10, 045048 (2025)

2025
[18]

S. Guo, J. Sun, H. Qian, M. Gong, Y. Zhang, F. Chen, Y. Ye, Y. Wu, S. Cao, K. Liu, et al., Nature Physics 20, 1240 (2024)

2024
[19]

Y. Zhou, J. Chen, J. Cheng, X. Cao, Y. Zhang, G. Kare- more, M. Zitnik, F. T. Chong, J. Liu, T. Fu, et al., npj Drug Discovery 3, 1 (2026)

2026
[20]

Santagati, A

R. Santagati, A. Aspuru-Guzik, R. Babbush, M. Deg- roote, L. Gonz´ alez, E. Kyoseva, N. Moll, M. Oppel, R. M. 17 Parrish, N. C. Rubin, et al. , Nature Physics 20, 549 (2024)

2024
[21]

Peruzzo, J

A. Peruzzo, J. McClean, P. Shadbolt, M.-H. Yung, X.-Q. Zhou, P. J. Love, A. Aspuru-Guzik, and J. L. O’brien, Nature Communications 5, 4213 (2014)

2014
[22]

Kandala, A

A. Kandala, A. Mezzacapo, K. Temme, M. Takita, M. Brink, J. M. Chow, and J. M. Gambetta, Nature 549, 242 (2017)

2017
[23]

H. R. Grimsley, S. E. Economou, E. Barnes, and N. J. Mayhall, Nature Communications 10, 3007 (2019)

2019
[24]

I. A. Mohammad, Y. Chernyak, and M. Plesch, arXiv preprint arXiv:2508.13651 (2025)

2025 arXiv
[25]

Chawla, Shweta, K

P. Chawla, Shweta, K. Swain, T. Patel, R. Bala, D. Shetty, K. Sugisaki, S. B. Mandal, J. Riu, J. Nogue, et al., Physical Review A 111, 022817 (2025)

2025
[26]

Chawla, D

P. Chawla, D. Shetty, P. B. Tsemo, K. Sugisaki, J. Riu, J. Nogu´ e, D. Mukherjee, and V. Prasannaa, The Euro- pean Physical Journal Plus 140, 924 (2025)

2025
[27]

and [34], as a visual indicator of the performance of our basis sets relative to these two works. In Ref. [26], the author uses both least squares fit and energy minimization approaches for the H atom for k of 2, 3, and 5, and finds that the latter approach yields lower energi...

2023
[28]

Yamamoto, Y

K. Yamamoto, Y. Kikuchi, D. Amaro, B. Criger, S. Dilkes, C. Ryan-Anderson, A. Tranter, J. M. Dreil- ing, D. Gresh, C. Foltz, M. Mills, S. A. Moses, P. E. Siegfried, M. D. Urmey, J. J. Burau, A. Hankin, D. Luc- chetti, J. P. Gaebler, N. C. Brown, B. Neyenhuis, and D. M. n. Ramo...

2026
[29]

Li, Physical Review A 109, 032606 (2024)

J. Li, Physical Review A 109, 032606 (2024)

2024
[30]

B. F. Schiffer, D. S. Wild, N. Maskara, M. D. Lukin, and J. I. Cirac, PRX Quantum 6, 040348 (2025)

2025
[31]

Wang, Quantum Science and Technology 10, 035036 (2025)

Y. Wang, Quantum Science and Technology 10, 035036 (2025)

2025
[32]

Verma, L

P. Verma, L. Huntington, M. P. Coons, Y. Kawashima, T. Yamazaki, and A. Zaribafiyan, The Journal of Chem- ical Physics 155 (2021)

2021
[33]

P. E. Hoggan, M. B. Ruiz, and T. ¨Ozdogan, Quantum frontiers of atoms and molecules (Nova Science Publish- ers, Inc., 2010) Chap. 4, pp. 63–90

2010
[34]

Nagy and F

B. Nagy and F. Jensen, Reviews in Computational Chem- istry 30, 93 (2017)

2017
[35]

A. L. Magalhaes, Journal of Chemical Education 91, 2124 (2014)

2014
[36]

W. J. Hehre, R. F. Stewart, and J. A. Pople, The Journal of Chemical Physics 51, 2657 (1969)

1969
[37]

Shavitt, in Methods in Computational Physics: Ad- vances in Research and Applications, edited by B

I. Shavitt, in Methods in Computational Physics: Ad- vances in Research and Applications, edited by B. Alder, S. Fernbach, and M. Rotenberg (Academic Press, New York and London, 1963) pp. 1–45

1963
[38]

J. H. Holland, Scientific american 267, 66 (1992)

1992
[39]

Forrest, ACM computing surveys (CSUR) 28, 77 (1996)

S. Forrest, ACM computing surveys (CSUR) 28, 77 (1996)

1996
[40]

Walton, O

S. Walton, O. Hassan, K. Morgan, and M. Brown, Chaos, Solitons & Fractals 44, 710 (2011)

2011
[41]

Chinnasamy, M

S. Chinnasamy, M. Ramachandran, M. Amudha, and K. Ramu, Recent trends in management and commerce 3, 1 (2022)

2022
[42]

Gupta, Y.-S

A. Gupta, Y.-S. Ong, and L. Feng, IEEE Transactions on Emerging Topics in Computational Intelligence 2, 51 (2017)

2017
[43]

De Andrade, M

M. De Andrade, M. Nascimento, K. Mundim, A. So- brinho, and L. Malbouisson, International Journal of Quantum Chemistry 108, 2486 (2008)

2008
[44]

Q. Sun, T. C. Berkelbach, N. S. Blunt, G. H. Booth, S. Guo, Z. Li, J. Liu, J. D. McClain, E. R. Sayfutyarova, S. Sharma, et al., Wiley Interdisciplinary Reviews: Com- putational Molecular Science 8, e1340 (2018)

2018
[45]

Q. Sun, X. Zhang, S. Banerjee, P. Bao, M. Barbry, N. S. Blunt, N. A. Bogdanov, G. H. Booth, J. Chen, Z.-H. Cui, et al., The Journal of Chemical Physics 153 (2020)

2020
[46]

Puchalski, D

M. Puchalski, D. Kedziera, and K. Pachucki, Physical Review A—Atomic, Molecular, and Optical Physics 80, 032521 (2009)

2009
[47]

Kalam, P

A. Kalam, P. Deb, A. Sakurai, B. K. Sahoo, V. S. Prasan- naa, and B. P. Das, Phys. Rev. Res. 8, 023272 (2026)

2026
[48]

A. M. Childs, R. Kothari, and R. D. Somma, SIAM Journal on Computing 46, 1920 (2017), https://doi.org/10.1137/16M1087072

2017 doi
[49]

J. D. Whitfield, J. Biamonte, and A. Aspuru-Guzik, Molecular Physics 109, 735 (2011)

2011
[50]

N. S. Blunt, G. P. Geh´ er, and A. E. Moylett, Physical Review Research 6, 013325 (2024)

2024
[51]

A. G. Fowler, M. Mariantoni, J. M. Martinis, and A. N. Cleland, Physical Review A—Atomic, Molecular, and Optical Physics 86, 032324 (2012)

2012
[52]

A. M. Steane, Physical Review Letters 77, 793 (1996)

1996
[53]

Mottonen, J

M. Mottonen, J. J. Vartiainen, V. Bergholm, and M. M. Salomaa, arXiv preprint quant-ph/0407010 (2004)

2004 arXiv
[54]

A. A. Zade, K. Sugisaki, M. Werner, A. Palacios, J. Riu, J. Nogu´ e, A. Garcia-Saez, A. Riera, and V. Prasannaa, The European Physical Journal Plus 140, 930 (2025)

2025
[55]

A. N. Tavouktsoglou and S. Huzinaga, The Journal of Chemical Physics 72, 1385 (1980)

1980
[56]

Kapusta, E

K. Kapusta, E. O. Voronkov, S. I. Okovytyy, V. I. Ko- robov, and J. Leszczynski, Russian Journal of Physical Chemistry A 92, 2827 (2018)

2018
[57]

H.-Y. Kwon, G. M. Curtin, Z. Morrow, C. Kelley, and E. Jakubikova, International Journal of Quantum Chem- istry 123, e27123 (2023)

2023
[58]

R. T. Ireland, S. J. Pitman, and L. K. McKemmish, Journal of Chemical Theory and Computation 21, 11481 (2025)

2025
[59]

C. S. Cox, J. C. Zapata, and L. K. McKemmish, Aus- tralian Journal of Chemistry 73, 911 (2020). 18 Appendix A: Computed MSTO- kG basis sets Element l k Exponent Coefficient H 0 2 1.332500 0.335072 0.201530 1.002799 H 0 3 4.492911 0.062664 0.680729 0.362123 0.151340 0.574683 H ...

2020

Pith tools

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

[1] [1]

the minimal basis sets ( k of 2 through 6),

work page

[2] [2]

and crossovers (Algorithm 3) of candidate basis sets for a given atom in a minimal basis set, and selection of the best candidates (where the objective function is the ground state electronic energy, computed using the Configuration Interaction Singles and Doubles (CISD) method) heuristically optimizes the basis set parameters, often reducing the ground s...

work page

[3] [3]

our MSTO-kG (k of 2 through 11),

work page

[4] [4]

the split-valence 6-31G, and FIG. 2. HF and FCI ground state energies of the hydrogen atom from MSTO- kG basis, compared with minimal basis sets and split valence basis sets (6-31G)

work page

[5] [5]

3), with the accompanying data in Tables II through IX of Appendix B

cc-pVXZ (X=D, T, Q in Fig. 3), with the accompanying data in Tables II through IX of Appendix B. The tables in the Appendix also provides energies from the optimized STO-kG (k = 3, 6) basis sets optimized by generalized simulated annealing [34], STO- kG (3≤k≤ 6) basis sets by Hehere et al and the exact values for STOs (the last two are taken from [27]). F...

work page

[6] [6]

For our analysis, we only consider the quantum al- gorithms in their vanilla form. This is for simplic- ity, as often, reduction in quantum resources that occur in different variants of an algorithm either incurs classical computing overheads that compli- cate estimating costs (for example, a recently in- troduced quantum-information inspired ansatz for V...

work page

[7] [7]

Using other choices would change the gate counts but not the overall observed trends

For the Li atom example, we use the {RZ,X,SX,CX } basis as the native gate set. Using other choices would change the gate counts but not the overall observed trends

work page

[8] [8]

This approximation is reasonable, since the HF contribution for a system, which constitutes al- most all of the total energy, varies substantially across the basis sets considered

In view of the cost, we do not compute energies us- ing the quantum algorithms themselves, but rather just use the FCI energies in each basis as prox- ies for the energies that those algorithms would yield. This approximation is reasonable, since the HF contribution for a system, which constitutes al- most all of the total energy, varies substantially acr...

work page