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REVIEW 4 major objections 6 minor 1 cited by

Shot-Efficient ADAPT-VQE via Reused Pauli Measurements and Variance-Based Shot Allocation

T0 review · 4 major / 6 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read ADAPT-VQE's shot count drops to 32.29% of naive usage by reusing Pauli measurements, and variance-based allocation adds 43–51% savings at chemical accuracy.

desk verdict Sound reuse idea, unsupported headline numbers, and an appendix that copies text and figures from Ref. [47] without marking—worth reviewing after a serious revision. read the letter →

arxiv 2507.16879 v1 pith:AYM4G5PV submitted 2025-07-22 quant-ph physics.chem-phphysics.comp-ph

Azhar Ikhtiarudin , Gagus Ketut Sunnardianto , Fadjar Fathurrahman , Mohammad Kemal Agusta , Hermawan Kresno Dipojono This is my paper
classification quant-phphysics.chem-phphysics.comp-ph
keywords ADAPT-VQEmeasurementreuseshotallocationvariance-basedqubit-wisecommutativityPaulistringgroupingvariationalquantumeigensolverNISQchemistry
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 tries to show that the main practical cost of ADAPT-VQE—the flood of quantum measurements needed both to optimize circuit angles and to pick the next operator to add—can be sharply reduced without sacrificing accuracy. Its first idea is to recycle: the Pauli-string measurement outcomes already collected during VQE parameter optimization at iteration n are reused for the gradient evaluation at iteration n+1, because the quantum state is the same and some of the Hamiltonian's Pauli strings also appear in the commutator [H,A_k] used to compute gradients. Its second idea is to stop spending shots uniformly: variance-based shot allocation is applied not only to the Hamiltonian but also to the gradient measurements, so noisy cliques get more shots and quiet cliques get fewer. On six molecules and four operator pools, grouping plus reuse lowers average shot usage to 32.29% of the naive scheme, and on H2 and LiH the variance-threshold method VPSR cuts shots by 43.21% and 51.23% relative to uniform allocation while remaining within chemical accuracy. If these savings carry over to real shot accounting, they make the resource-starved adaptive variational algorithms substantially cheaper to run on near-term hardware.

What carries the argument

The carrying object is the joint set of qubit-wise-commuting cliques built from the Hamiltonian $\hat{H}$ and from the commutators $[\hat{H},\hat{A}_k]$ of the operator pool, because those cliques determine which measurement outcomes can be shared. The reuse rests on the identity $g_k = \langle\psi^{(n)}|[\hat{H},\hat{A}_k]|\psi^{(n)}\rangle = \sum_j h_j \langle\psi^{(n)}|[\hat{H}_j,\hat{A}_k]|\psi^{(n)}\rangle$, combined with the observation that the state used for the Hamiltonian measurement at iteration n is exactly the state $\psi^{(n)}$ used for the gradient measurement at iteration n+1. Variance-based allocation (VMSA and VPSR) then assigns shots to each clique according to its empirically measured variance instead of uniformly, with VPSR reducing total shots until a target variance threshold is met. Qubit-wise commutativity, the condition that each single-qubit Pauli factor commutes with its counterpart, is the grouping criterion used, with single-qubit basis rotations mapping each Pauli string to the computational basis.

What would settle it

Run the paper's H2 and LiH experiments while logging the total number of shots actually consumed by the sampler under the proposed grouping-plus-reuse and VPSR protocols, and compare that total with the naive uniform baseline; if the real shot totals do not reproduce the reported 32.29%, 43.21%, and 51.23% reductions at chemical accuracy, or if VPSR requires a variance threshold $\delta$ for which no reduction is achieved, then the central claim is not supported.

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Extended reading notes

Core claim

The central claim is that the two measurement-hungry halves of ADAPT-VQE—the energy measurement that drives parameter optimization and the gradient measurement that drives operator selection—can share most of their shots instead of being counted separately. The paper rewrites the gradient observable as $g_k = \langle\psi|[\hat{H},\hat{A}_k]|\psi\rangle$ and expands the commutator into Pauli strings; when a string in the gradient expansion coincides with a string already measured for the Hamiltonian, or can be measured in the same basis under qubit-wise commutativity grouping, the stored outcomes from the final VQE iteration at step n are reused at step n+1 at no extra shot cost. On top of the reuse, the paper groups all Hamiltonian and gradient Pauli strings into commuting cliques and applies variance-based shot allocation, extending the variance-minimized (VMSA) and variance-preserved shot reduction (VPSR) methods to gradient measurements. The numerical evidence, from H2 through BeH2 and N2H4, reports that grouping with reuse uses on average 32.29% of the naive Pauli-string budget, and that VPSR reduces shots by 43.21% for H2 and 51.23% for LiH relative to uniform allocation while the energy error stays below chemical accuracy.

Load-bearing premise

The reported savings treat the number of Pauli strings or grouped measurement settings as the shot count, assuming each term or clique consumes the same fixed shot budget; if per-clique budgets are instead set by variance, reducing the string count does not directly translate into the reported shot reduction.

Editorial extensions

If this is right

  • Every Pauli string shared between the Hamiltonian and the gradient commutator is measured once and used twice, so the per-gradient measurement cost drops roughly in proportion to that overlap.
  • The shot savings accumulate over ADAPT iterations and grow with system size, since larger molecules run more iterations and have more overlap between Hamiltonian and commutator strings.
  • Because the reuse and variance-based allocation are modular, they can be layered on top of any operator pool and any commuting-grouping method, including more efficient non-QWC grouping schemes.
  • At low noise (error probability p=0.0001) the algorithm still reaches chemical accuracy, and even when strong noise p=0.001 prevents convergence, the variance-based methods consume fewer cumulative shots for the same accuracy.
  • The same combined strategy transfers to other adaptive variational algorithms, such as ADAPT-QAOA, as the paper explicitly notes.

Reading between the lines

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

  • Editorial: The paper's headline reductions count Pauli strings or grouped settings rather than the actual number of shots emitted after variance-based allocation; a direct shot-counting benchmark could report different savings.
  • Editorial: The VPSR savings are defined relative to an unstated variance threshold $\delta$; without a principled choice of $\delta$ tied to chemical accuracy, the 43% and 51% figures are not uniquely determined by the algorithm.
  • Editorial: The reuse identity depends on the state at iteration n being exactly the state at the start of iteration n+1; any algorithmic change that perturbs the state between steps, such as noisy mid-circuit updates, would shrink the reusable overlap.
  • Editorial: The same commutator-reuse logic extends naturally to the Hessian or to higher-order derivatives in adaptive variational algorithms, where even more Pauli strings overlap and the savings could be larger.
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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

4 major / 6 minor

Summary. The paper proposes two mechanisms to reduce the quantum-measurement cost of ADAPT-VQE: (i) reusing Pauli-string measurement outcomes from the final VQE parameter-optimization step at ADAPT iteration n in the gradient evaluation of iteration n+1, exploiting that both are measured on the same state, and (ii) applying variance-based shot allocation (VMSA and VPSR, adapted from Ref. [33]) to both Hamiltonian and gradient cliques. The authors report average Pauli-measurement reductions of 32.29% with grouping and reuse versus 38.59% with grouping only across six molecules and four operator pools, and VPSR shot reductions of 43.21% for H2 and 51.23% for LiH relative to uniform allocation. The reuse logic is sound in the noiseless limit, and the paper includes source code and 1000-run shot-noise simulations.

Significance. The reuse idea is simple and credible: because the state after VQE optimization is identical to the state used for the next gradient, identical Pauli strings with the same eigenbasis can share measurement outcomes. The paper is also useful in that it tests this across multiple operator pools and releases code. If the quantitative claims were properly anchored—with a specified variance threshold, a consistent shot-counting convention, and corrected tables—the work would be a worthwhile incremental contribution to measurement-frugal ADAPT-VQE. However, the headline percentages are not currently supported for the reasons detailed in the major comments.

major comments (4)
  1. [Section II C, Eqs. (11)-(13)] The VPSR savings are underdetermined by an unstated threshold δ. The solution of Eq. (11) is N_total = (Σ_i σ_i)^2/δ, so the reported savings relative to uniform allocation depend entirely on δ, which is never specified in the text or tied to chemical accuracy. If δ is set equal to the variance of the uniform allocation at the fixed budget N, the total is ηN with η from Eq. (13), and the reported 43.21% and 51.23% are just 1−η for the realized variance spread; with any other δ the savings can range from 0 to nearly 100%. The value of N0 in Eqs. (10) and (12) is likewise not reported (Algorithm 1 lists it as an input but gives no default), and the results may depend on it. The paper should report δ (or an externally motivated rule for setting it), the per-clique variance estimates, and N0, or the headline savings should be withdrawn.
  2. [Section III A, Table I and Figure 2] Section III A and Table I count Pauli strings or grouped measurement settings, but the text and Figure 2 present these counts as "shot usage." Under the paper's own variance-based allocation (Section II C), different cliques receive different numbers of shots, and a measurement setting shared between a Hamiltonian clique and a gradient clique may still need to be run for the clique's other terms; the number of distinct Pauli strings is therefore not equal to the number of shots. The average reduction to 32.29% should be re-expressed either as a reduction in distinct measurement settings or as a true shot-count comparison with an explicit allocation of reused samples.
  3. [Table I, H5/Fermionic row] Table I lists Full=36,106 and Reused=101,142 for the H5 molecule with the Fermionic pool. Reuse cannot increase the number of required measurements, so this entry is internally inconsistent and indicates an error in the accounting that feeds the average savings figures and Figure 2. The row must be corrected or explained before the reuse claim can be assessed.
  4. [Appendix A, after Eq. (A10)] Appendix A contains a long passage beginning with "B. Multiple Variational Parameters (MVP)-CEOs" that appears to be taken from another paper: it discusses circuit implementations, refers to Figures 1–4 that do not exist in this manuscript, and cites numbered equations from a different context. This passage is not integrated with the present work and must be removed or rewritten. This is a manuscript-integrity issue independent of the technical content.
minor comments (6)
  1. [Section II A, Eq. (1)] The notation is inconsistent between Ĥ_f and Ĥ_q and the definitions of the symbols (h_pq, h_pqrs) are not fully specified; the authors should define all symbols consistently.
  2. [Throughout] The grammar should be corrected, including "one categories of ansatz," "similiar," and other typographical errors.
  3. [Section III B, Figure 4] The stacked bar chart is hard to read; the description of the three sections and the "uppermost section" in light gray does not clearly match the figure, so the shot-budget composition should be clarified.
  4. [Section III B] The LiH Hamiltonian approximation to four qubits is cited to Refs. [13,33,65–69], but the specific approximation is not described; a one-sentence description would improve reproducibility.
  5. [Section III B, Figure 5] The noise model is not fully specified: the text does not explain how the error probability p is applied to each gate type, error locations, or circuit depth, so the noise simulations cannot be reproduced from the manuscript alone.
  6. [Algorithm 1, Steps 8 and 15] The accounting for reused samples is ambiguous: the paper should state explicitly how saved measurement results from Step 15 are combined with the variance-based allocation in Step 8, since this affects the stacked-bar shot budget in Figure 4.

Circularity Check

1 steps flagged · score 6.0 of 10

The VPSR shot-savings claim reduces by construction: Eq. (12)-(13) fix the VPSR total at η times the uniform budget with η ≤ 1 by Cauchy, and the variance threshold δ in Eq. (11) is never stated, making the 43.21%/51.23% reductions a restatement of the variance spread plus an unstated knob; the Pauli-reuse protocol and the accuracy checks retain independent content.

  1. fitted input called prediction [Section II.C (Eqs. 11-13); Section III.B (VPSR results, Fig. 4)]
    "The second strategy, first introduced in [33], aims to optimize shot allocation by decreasing the number of shots if the variance falls below a target threshold δ... Since η ≤ 1, this ensures that the total number of shots required to meet the target variance threshold will always be less than or equal to the number of shots allocated by the VMSA strategy... From this simulation, we obtain that the variance-based shot allocation method reduces the required shots to reach chemical accuracy by up to 6.71% for VMSA and 43.21% for VPSR in H2, as well as 5.77% for VMSA and 51.23% for VPSR in LiH."

    By Eq. (12), the VPSR total budget is mN0 + η(N − mN0), i.e., η times the uniform/VMSA budget N up to the N0 term, with Eq. (13)'s η ≤ 1 a Cauchy–Schwarz identity over the same variance estimates σ_i that are the method's entire input. The reported savings (43.21% H2, 51.23% LiH) are thus the Cauchy gap 1−η restated as a simulated discovery rather than a definitional property. The threshold δ in Eq. (11) is never assigned a value or external criterion (e.g., the variance needed for chemical accuracy), so the savings anchor only to an unreported knob: setting δ to the uniform-allocation variance makes the reduction exactly 1−η; any other δ gives any other percentage in (0, 1).

full rationale

The two central claims differ in circularity status. (1) The reused-Pauli-measurement protocol is an honest counting comparison: Table I and Fig. 2 count Pauli strings (or grouped cliques) under full versus grouped+reused protocols, and the savings depend on the concrete overlap between Hamiltonian terms and commutator strings [H, A_k] of Eq. (14). That comparison is self-contained, externally benchmarked against FCI energies from PySCF, and not circular. It is only as reliable as its accounting, however: the H5/Fermionic row of Table I lists Reused=101,142 > Full=36,106, which is impossible for a reuse protocol and signals a swap or counting error, and the text equates Pauli-string counts with shot counts even though the methods' own variance allocation gives each clique a different shot budget. These are correctness/rigor concerns, not circularity. (2) The variance-based claims are where partial circularity enters. VMSA and VPSR are transparently adapted from external Ref. [33]; the bibliography contains no self-citations by the present authors, so self-citation patterns 3-5 do not apply. But the VPSR savings reported in Section III.B are forced by the method's closed form: Eq. (12) fixes the total VPSR budget at mN0 + η(N − mN0) with η ≤ 1 a Cauchy identity of the input variances, and the target δ of Eq. (11) is never given a value or tied to an external accuracy criterion. The headline reductions are therefore the Cauchy gap 1−η (up to the N0 correction) relabeled as empirical gains; if δ was chosen after observing results, they are fitted rather than measured. The genuinely empirical content — that VPSR still reaches chemical accuracy (Fig. 4, 1000 runs per setting) — is real and stops the score from rising higher. On balance: one central prediction (the VPSR savings) reduces by construction, while the reuse protocol and the accuracy-maintenance checks keep independent content; no self-citation chain is load-bearing. Score 6 reflects this partial circularity: the savings number is an identity plus an unstated parameter, not an independent measurement.

Assumptions & free parameters 2 free parameters · 5 assumptions · 0 invented entities

The central claim rests on prior ADAPT-VQE gradient formulas, QWC grouping, and the variance allocation scheme of Ref [33]; no new physical entities are introduced. The main unstated choices are the VPSR target variance δ and the initial estimation budget N0, whose values are not given in the paper.

free parameters (2)
  • VPSR variance target threshold δ = not reported
    Controls the total shot budget in VPSR (Eq. 11); no value or selection rule is given in the paper, so the reported savings could depend on a post hoc choice.
  • Initial variance-estimation shot budget N0 = not reported
    Used in Eqs. 10 and 12 to estimate clique variances before allocating the remaining shots; the paper states only that N0 < N/m, not the actual value.
assumptions (5)
  • domain assumption The energy gradient for operator selection is ⟨ψ|[H,A_k]|ψ⟩ at θ_k=0 (Eq. 4), and the commutator expands into a sum of Pauli strings (Eq. 14).
    Adopted from Ref [22] and Ref [38] without re-derivation.
  • domain assumption The quantum state at the end of VQE optimization in iteration n is identical to the state used for gradient evaluation in iteration n+1, so Hamiltonian Pauli samples can be reused for gradient terms.
    This is the reuse premise; it holds exactly only if the VQE routine returns the same parameterized circuit and no additional operations are inserted.
  • standard math Qubit-wise commutativity is a sufficient condition for simultaneous measurement of Pauli observables.
    Standard result cited to Refs [54,55]; used throughout for clique construction.
  • domain assumption VMSA/VPSR shot allocation formulas (Eqs. 10, 12, 13) from Ref [33] remain valid when applied to gradient observables.
    The paper extends these formulas beyond Hamiltonian estimation without re-deriving the optimality conditions for gradient measurements.
  • domain assumption The empirical variance σ_i(θ) estimated from N0 shots is a reliable proxy for optimal shot allocation.
    A standard heuristic in shot allocation; the paper does not analyze the error introduced by finite-N0 variance estimation.

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Cite this review

Pith. "Pith review of Shot-Efficient ADAPT-VQE via Reused Pauli Measurements and Variance-Based Shot Allocation." pith.science (2026). https://pith.science/paper/AYM4G5PV

@misc{pith2026250716879,
  author       = {Pith},
  title        = {Pith review of: Shot-Efficient ADAPT-VQE via Reused Pauli Measurements and Variance-Based Shot Allocation},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/AYM4G5PV}},
  note         = {Machine review of arXiv:2507.16879}
}
read the original abstract

The Adaptive Variational Quantum Eigensolver (ADAPT-VQE) is a promising approach for quantum algorithms in the Noisy Intermediate-Scale Quantum (NISQ) era, offering advantages over traditional VQE methods by reducing circuit depth and mitigating challenges in classical optimization. However, a major challenge in ADAPT-VQE is the high quantum measurement (shot) overhead required for circuit parameter optimization and operator selection. In this work, we propose two integrated strategies to reduce the shot requirements in ADAPT-VQE. First, we reuse Pauli measurement outcomes obtained during VQE parameter optimization in the subsequent operator selection step of the next ADAPT-VQE iteration, which involves operator gradient measurements. Second, we apply variance-based shot allocation to both Hamiltonian and operator gradient measurements. Our numerical results demonstrate that each method, individually and in combination, significantly reduces the number of shots needed to achieve chemical accuracy while maintaining result fidelity across the studied molecular systems.

Figures

Figures reproduced from arXiv: 2507.16879 by the authors.

Figure 1
Figure 1. FIG. 1: Schematic of measurement optimization in ADAPT-VQE proposed in this research. (a) Modified [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2: The figure compares total shot usage in single gradient calculation between measurement grouping only [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3: Comparison of energy error versus the number of measurements required to reach convergence using the [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figures from the paper (3 more)
Figure 4
Figure 4. Figure 4: FIG. 4: Shot-Optimized ADAPT-VQE simulation results for the H [PITH_FULL_IMAGE:figures/full_fig_p009_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5: The performance of Shot-Optimized ADAPT-VQE was compared under different noise levels for the H [PITH_FULL_IMAGE:figures/full_fig_p010_5.png]
Figure 3
Figure 3. Figure 3: FIG. 3. Explicit implementation of the qubit excitation evolution Uα1β1→α2β2. FIG. 6: Explicit circuit implementation using only single-qubit and CNOT gate of qubit excitation operator in [PITH_FULL_IMAGE:figures/full_fig_p013_3.png]

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Cited by 1 Pith paper

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Reference graph

Works this paper leans on

80 extracted references · 40 canonical work pages · cited by 1 Pith paper

  1. [47]

    Ramˆ oa, P

    M. Ramˆ oa, P. G. Anastasiou, L. P. Santos, N. J. May- hall, E. Barnes, and S. E. Economou, Reducing the re- sources required by adapt-vqe using coupled exchange operators and improved subroutines, arXiv preprint arXiv:2407.08696 (2024)

    arXiv 2024

  2. [33]

    L. Zhu, S. Liang, C. Yang, and X. Li, Optimizing shot assignment in variational quantum eigensolver measure- ment, Journal of Chemical Theory and Computation 20, 2390 (2024)

    work page 2024

  3. [1]

    R. P. Feynman, Simulating physics with computers (1982)

    work page 1982

  4. [2]

    P. W. Shor, Polynomial-time algorithms for prime factor- ization and discrete logarithms on a quantum computer *

    work page

  5. [3]

    Y. Cao, J. Romero, J. P. Olson, M. Degroote, P. D. John- son, M. Kieferov´ a, I. D. Kivlichan, T. Menke, B. Per- opadre, N. P. D. Sawaya, S. Sim, L. Veis, and A. Aspuru- Guzik, Quantum chemistry in the age of quantum com- puting 10.1021/acs.chemrev.8b00803 (2018)

    doi:10.1021/acs.chemrev.8b00803 2018

  6. [4]

    A. J. Daley, I. Bloch, C. Kokail, S. Flannigan, N. Pearson, M. Troyer, and P. Zoller, Practical quantum advantage in quantum simulation, Nature 607, 667 (2022)

    2022

  7. [5]

    Arute, K

    F. Arute, K. Arya, R. Babbush, D. Bacon, J. C. Bardin, R. Barends, R. Biswas, S. Boixo, F. G. Brandao, D. A. Buell, et al., Quantum supremacy using a programmable superconducting processor, Nature 574, 505 (2019)

    2019

  8. [6]

    McArdle, S

    S. McArdle, S. Endo, A. Aspuru-Guzik, S. Ben- jamin, and X. Yuan, Quantum computational chemistry 10.1103/RevModPhys.92.015003 (2018)

    doi:10.1103/revmodphys.92.015003 2018

Show all 80 references
  1. [7]

    R. H. Lavroff, D. L. Pennington, A. S. Hua, B. Y. Li, J. A. Williams, and A. N. Alexandrova, Recent innovations in solid-state and molecular qubits for quantum information applications, The Journal of Physical Chemistry C 125, 24285 (2021), https://doi.org/10.1021/acs.jpcc.1c08530

    2021 doi

  2. [8]

    Preskill, Quantum computing in the nisq era and be- yond 10.22331/q-2018-08-06-79 (2018)

    J. Preskill, Quantum computing in the nisq era and be- yond 10.22331/q-2018-08-06-79 (2018)

    2018 doi

  3. [9]

    Cerezo, A

    M. Cerezo, A. Arrasmith, R. Babbush, S. C. Benjamin, S. Endo, K. Fujii, J. R. McClean, K. Mitarai, X. Yuan, L. Cincio, et al., Variational quantum algorithms, Nature Reviews Physics 3, 625 (2021)

    2021

  4. [10]

    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, A variational eigenvalue solver on a photonic quantum processor, Nature communications 5, 4213 (2014)

    2014

  5. [11]

    D. A. Fedorov, B. Peng, N. Govind, and Y. Alexeev, Vqe method: A short survey and recent developments, (2021)

    2021

  6. [12]

    Tilly, H

    J. Tilly, H. Chen, S. Cao, D. Picozzi, K. Setia, Y. Li, E. Grant, L. Wossnig, I. Rungger, G. H. Booth, et al., The variational quantum eigensolver: a review of meth- ods and best practices, Physics Reports 986, 1 (2022)

    2022

  7. [13]

    Kandala, A

    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, nature549, 242 (2017)

    2017

  8. [14]

    Bittel and M

    L. Bittel and M. Kliesch, Training variational quan- tum algorithms is np-hard, Physical review letters 127, 120502 (2021)

    2021

  9. [15]

    Haidar, M

    M. Haidar, M. J. Ranˇ ci´ c, Y. Maday, and J.-P. Pique- mal, Extension of the trotterized unitary coupled cluster to triple excitations, The Journal of Physi- cal Chemistry A 127, 3543 (2023), pMID: 37039518, https://doi.org/10.1021/acs.jpca.3c01753

    2023 doi

  10. [16]

    S. E. Ghasempouri, G. W. Dueck, and S. De Baerdemacker, Modular cluster circuits for the variational quantum eigensolver, The Journal of Physical Chemistry A 127, 8168 (2023), pMID: 37729640, https://doi.org/10.1021/acs.jpca.3c03015

    2023 doi

  11. [17]

    S. Sun, C. Kumar, K. Shen, E. Shishenina, and C. B. Mendl, Evaluating ground state energies of chemical systems with low-depth quantum cir- cuits and high accuracy, The Journal of Physical Chemistry A 129, 2379 (2025), pMID: 40029977, https://doi.org/10.1021/acs.jpca.4c07045

    2025 doi

  12. [18]

    S. G. Mehendale, B. Peng, N. Govind, and Y. Alex- eev, Exploring parameter redundancy in the uni- tary coupled-cluster ans¨ atze for hybrid variational quantum computing, The Journal of Physical Chemistry A 127, 4526 (2023), pMID: 37193645, https://doi.org/10.1021/acs.jpca.3c00550

    2023 doi

  13. [19]

    J. R. McClean, S. Boixo, V. N. Smelyanskiy, R. Bab- bush, and H. Neven, Barren plateaus in quantum neural network training landscapes, Nature communications 9, 4812 (2018)

    2018

  14. [20]

    Holmes, K

    Z. Holmes, K. Sharma, M. Cerezo, and P. J. Coles, Con- necting ansatz expressibility to gradient magnitudes and barren plateaus, PRX Quantum 3, 010313 (2022)

    2022

  15. [21]

    D’Cunha, T

    R. D’Cunha, T. D. Crawford, M. Motta, and J. E. Rice, Challenges in the use of quantum computing hardware- efficient ans¨ atze in electronic structure theory, The Jour- nal of Physical Chemistry A 127, 3437 (2023), pMID: 14 37040444, https://doi.org/10.1021/acs.jpca.2c08430

    2023 doi

  16. [22]

    H. R. Grimsley, S. E. Economou, E. Barnes, and N. J. Mayhall, An adaptive variational algorithm for exact molecular simulations on a quantum computer, Na- ture Communications 10, 10.1038/s41467-019-10988-2 (2019)

    2019 doi

  17. [23]

    H. R. Grimsley, G. S. Barron, E. Barnes, S. E. Economou, and N. J. Mayhall, Adapt-vqe is insensitive to rough parameter landscapes and barren plateaus, 2022, URL: https://arxiv. org/abs/2204.07179. doi 10

    2022 arXiv

  18. [24]

    Patel, P

    S. Patel, P. Jayakumar, T.-C. Yen, and A. F. Izmaylov, Quantum measurement for quantum chemistry on a quantum computer, arXiv preprint arXiv:2501.14968 (2025)

    2025 arXiv

  19. [25]

    J. M. K¨ ubler, A. Arrasmith, L. Cincio, and P. J. Coles, An adaptive optimizer for measurement-frugal varia- tional algorithms, Quantum 4, 263 (2020)

    2020

  20. [26]

    Arrasmith, L

    A. Arrasmith, L. Cincio, R. D. Somma, and P. J. Coles, Operator sampling for shot-frugal optimization in variational algorithms, arXiv preprint arXiv:2004.06252 (2020)

    2020 arXiv

  21. [27]

    A. Gu, A. Lowe, P. A. Dub, P. J. Coles, and A. Arrasmith, Adaptive shot allocation for fast conver- gence in variational quantum algorithms, arXiv preprint arXiv:2108.10434 (2021)

    2021 arXiv

  22. [28]

    S. S. Kahani and A. Nobakhti, A novel framework for shot number minimization in quantum variational algo- rithms, arXiv preprint arXiv:2307.04035 (2023)

    2023 arXiv

  23. [29]

    Y. Kim, E. Jang, H. Kim, S. Choi, C. Lee, D. Kim, W. Kyoung, K. Shin, and W. W. Ro, Distribution- adaptive dynamic shot optimization for variational quan- tum algorithms, arXiv preprint arXiv:2412.17485 (2024)

    2024 arXiv

  24. [30]

    S. Choi, I. Loaiza, and A. F. Izmaylov, Fluid fermionic fragments for optimizing quantum measurements of elec- tronic hamiltonians in the variational quantum eigen- solver, Quantum 7, 889 (2023)

    2023

  25. [31]

    T.-C. Yen, A. Ganeshram, and A. F. Izmaylov, Deter- ministic improvements of quantum measurements with grouping of compatible operators, non-local transforma- tions, and covariance estimates, npj Quantum Informa- tion 9, 14 (2023)

    2023

  26. [32]

    Choi, T.-C

    S. Choi, T.-C. Yen, and A. F. Izmaylov, Improving quan- tum measurements by introducing “ghost” pauli prod- ucts, Journal of Chemical Theory and Computation 18, 7394 (2022)

    2022

  27. [34]

    Liang, L

    S. Liang, L. Zhu, X. Liu, C. Yang, and X. Li, Artificial- intelligence-driven shot reduction in quantum measure- ment, arXiv preprint arXiv:2405.02493 (2024)

    2024 arXiv

  28. [35]

    J. Liu, Z. Li, and J. Yang, An efficient adap- tive variational quantum solver of the schr¨ odinger equation based on reduced density matrices, The Journal of Chemical Physics 154, 244112 (2021), https://pubs.aip.org/aip/jcp/article- pdf/doi/10.1063/5.0054822/15965352/244112 1...

    2021 doi

  29. [36]

    Nyk¨ anen, M

    A. Nyk¨ anen, M. A. Rossi, E.-M. Borrelli, S. Manis- calco, and G. Garc ´ ıa-P´ erez, Mitigating the measure- ment overhead of adapt-vqe with optimised information- ally complete generalised measurements, arXiv preprint arXiv:2212.09719 (2022)

    2022

  30. [37]

    Majland, P

    M. Majland, P. Ettenhuber, and N. T. Zinner, Fermionic adaptive sampling theory for variational quantum eigensolvers, Physical Review A 108, 10.1103/phys- reva.108.052422 (2023)

    2023 doi

  31. [38]

    P. G. Anastasiou, N. J. Mayhall, E. Barnes, and S. E. Economou, How to really measure operator gradients in adapt-vqe, arXiv preprint arXiv:2306.03227 (2023)

    2023 arXiv

  32. [39]

    Fradkin, Jordan-wigner transformation for quantum- spin systems in two dimensions and fractional statistics, Physical review letters 63, 322 (1989)

    E. Fradkin, Jordan-wigner transformation for quantum- spin systems in two dimensions and fractional statistics, Physical review letters 63, 322 (1989)

    1989

  33. [40]

    Bravyi, J

    S. Bravyi, J. M. Gambetta, A. Mezzacapo, and K. Temme, Tapering off qubits to simulate fermionic hamiltonians (2017), arXiv:1701.08213 [quant-ph]

    2017 arXiv

  34. [41]

    S. B. Bravyi and A. Y. Kitaev, Fermionic quantum com- putation, Annals of Physics 298, 210 (2002)

    2002

  35. [42]

    Ruder, An overview of gradient descent optimization algorithms (2017), arXiv:1609.04747 [cs.LG]

    S. Ruder, An overview of gradient descent optimization algorithms (2017), arXiv:1609.04747 [cs.LG]

    2017 arXiv

  36. [43]

    M. J. D. Powell, A direct search optimization method that models the objective and constraint functions by lin- ear interpolation, in Advances in Optimization and Nu- merical Analysis, edited by S. Gomez and J.-P. Hennart (Springer Netherlands, Dordrecht, 1994) pp. 51–67

    1994

  37. [44]

    J. A. Nelder and R. Mead, A simplex method for function minimization, The Computer Journal 7, 308 (1965), https://academic.oup.com/comjnl/article- pdf/7/4/308/1013182/7-4-308.pdf

    1965

  38. [45]

    H. L. Tang, V. O. Shkolnikov, G. S. Barron, H. R. Grim- sley, N. J. Mayhall, E. Barnes, and S. E. Economou, qubit-adapt-vqe: An adaptive algorithm for construct- ing hardware-efficient ansatze on a quantum processor 10.1103/PRXQuantum.2.020310 (2019)

    2019 doi

  39. [46]

    Y. S. Yordanov, V. Armaos, C. H. Barnes, and D. R. Arvidsson-Shukur, Qubit-excitation-based adaptive vari- ational quantum eigensolver, Communications Physics4, 10.1038/s42005-021-00730-0 (2021)

    2021 doi

  40. [48]

    P. G. Anastasiou, Y. Chen, N. J. Mayhall, E. Barnes, and S. E. Economou, Tetris-adapt-vqe: An adaptive algorithm that yields shallower, denser circuit ans¨ atze 10.1103/PhysRevResearch.6.013254 (2022)

    2022 doi

  41. [49]

    Feniou, M

    C. Feniou, M. Hassan, D. Traor´ e, E. Giner, Y. Ma- day, and J. P. Piquemal, Overlap-adapt-vqe: practical quantum chemistry on quantum computers via overlap- guided compact ans¨ atze, Communications Physics 6, 10.1038/s42005-023-01312-y (2023)

    2023 doi

  42. [50]

    V. O. Shkolnikov, N. J. Mayhall, S. E. Economou, and E. Barnes, Avoiding symmetry roadblocks and minimiz- ing the measurement overhead of adaptive variational quantum eigensolvers, Quantum 7, 1040 (2023)

    2023

  43. [51]

    L. W. Bertels, H. R. Grimsley, S. E. Economou, E. Barnes, and N. J. Mayhall, Symmetry breaking slows convergence of the adapt variational quantum eigen- solver, Journal of Chemical Theory and Computation18, 6656 (2022)

    2022

  44. [52]

    Ramˆ oa, L

    M. Ramˆ oa, L. P. Santos, N. J. Mayhall, E. Barnes, and S. E. Economou, Reducing measurement costs by recy- cling the hessian in adaptive variational quantum algo- rithms, arXiv preprint arXiv:2401.05172 (2024)

    2024 arXiv

  45. [53]

    Fitzpatrick, A

    A. Fitzpatrick, A. Nyk¨ anen, N. W. Talarico, A. Lunghi, S. Maniscalco, G. Garc ´ ıa-P´ erez, and S. Knecht, Self-consistent field approach for the 15 variational quantum eigensolver: Orbital opti- mization goes adaptive, The Journal of Physical Chemistry A 128, 2843 (2024), p...

    2024 doi

  46. [54]

    Shankar, Principles of quantum mechanics(Springer Science & Business Media, 2012)

    R. Shankar, Principles of quantum mechanics(Springer Science & Business Media, 2012)

    2012

  47. [55]

    T.-C. Yen, V. Verteletskyi, and A. F. Izmaylov, Measur- ing all compatible operators in one series of single-qubit measurements using unitary transformations, Journal of chemical theory and computation 16, 2400 (2020)

    2020

  48. [56]

    Gokhale, O

    P. Gokhale, O. Angiuli, Y. Ding, K. Gui, T. Tomesh, M. Suchara, M. Martonosi, and F. T. Chong, Mini- mizing state preparations in variational quantum eigen- solver by partitioning into commuting families (2019), arXiv:1907.13623 [quant-ph]

    2019 arXiv

  49. [57]

    B. Wu, J. Sun, Q. Huang, and X. Yuan, Overlapped grouping measurement: A unified framework for mea- suring quantum states, Quantum 7, 896 (2023)

    2023

  50. [58]

    Crawford, B

    O. Crawford, B. v. Straaten, D. Wang, T. Parks, E. Campbell, and S. Brierley, Efficient quantum measure- ment of Pauli operators in the presence of finite sampling error, Quantum 5, 385 (2021)

    2021

  51. [59]

    Zhang, K

    Z.-J. Zhang, K. Nakaji, M. Choi, and A. Aspuru-Guzik, A composite measurement scheme for efficient quantum observable estimation, arXiv preprint arXiv:2305.02439 (2023)

    2023 arXiv

  52. [60]

    Verteletskyi, T.-C

    V. Verteletskyi, T.-C. Yen, and A. F. Izmaylov, Measure- ment optimization in the variational quantum eigensolver using a minimum clique cover, The Journal of Chemical Physics 152, 10.1063/1.5141458 (2020)

    2020 doi

  53. [61]

    opposite-spin excita- tions

    and PySCF [62] packages. The quantum simulators utilized in this research include both the statevector sim- ulator, which performs exact simulations using matrix algebra following previous works [22, 45, 47], and the shots-based simulator developed using the Qiskit Aer- Simula...

  54. [62]

    J. R. McClean, N. C. Rubin, K. J. Sung, I. D. Kivlichan, X. Bonet-Monroig, Y. Cao, C. Dai, E. S. Fried, C. Gid- ney, B. Gimby, et al., Openfermion: the electronic struc- ture package for quantum computers, Quantum Science and Technology 5, 034014 (2020)

    2020

  55. [63]

    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., Pyscf: the python-based simulations of chemistry framework, Wiley Interdisciplinary Reviews: Computational Molecular Science 8, e1340 (2018)

    2018

  56. [64]

    Javadi-Abhari, M

    A. Javadi-Abhari, M. Treinish, K. Krsulich, C. J. Wood, J. Lishman, J. Gacon, S. Martiel, P. D. Nation, L. S. Bishop, A. W. Cross, B. R. Johnson, and J. M. Gambetta, Quantum computing with Qiskit (2024), arXiv:2405.08810 [quant-ph]

    2024 arXiv

  57. [65]

    Virtanen, R

    P. Virtanen, R. Gommers, T. E. Oliphant, M. Haber- land, T. Reddy, D. Cournapeau, E. Burovski, P. Pe- terson, W. Weckesser, J. Bright, S. J. van der Walt, M. Brett, J. Wilson, K. J. Millman, N. Mayorov, A. R. J. Nelson, E. Jones, R. Kern, E. Larson, C. J. Carey, ˙I. Po- lat, Y...

    2020

  58. [66]

    A. G. Rattew, S. Hu, M. Pistoia, R. Chen, and S. Wood, A domain-agnostic, noise-resistant, hardware- efficient evolutionary variational quantum eigensolver, arXiv preprint arXiv:1910.09694 (2019)

    2019 arXiv

  59. [67]

    Lolur, M

    P. Lolur, M. Skogh, W. Dobrautz, C. Warren, J. Bizn´ arov´ a, A. Osman, G. Tancredi, G. Wendin, J. By- lander, and M. Rahm, Reference-state error mitigation: A strategy for high accuracy quantum computation of chemistry, Journal of Chemical Theory and Computation 19, 783 (2023)

    2023

  60. [68]

    Choy and D

    B. Choy and D. J. Wales, Molecular energy landscapes of hardware-efficient ansatze in quantum computing, Jour- nal of chemical theory and computation 19, 1197 (2023)

    2023

  61. [69]

    A. F. Izmaylov, T.-C. Yen, and I. G. Ryabinkin, Revis- ing the measurement process in the variational quantum eigensolver: is it possible to reduce the number of sep- arately measured operators?, Chemical science 10, 3746 (2019)

    2019

  62. [70]

    Handy, R

    N. Handy, R. Harrison, P. Knowles, and H. Schae- fer III, An accurate variational wave function for lithium hydride, The Journal of Physical Chemistry 88, 4852 (1984)

    1984

  63. [71]

    Yanakiev, N

    N. Yanakiev, N. Mertig, C. K. Long, and D. R. M. Arvidsson-Shukur, Dynamic-adapt-qaoa: An algo- rithm with shallow and noise-resilient circuits (2023), arXiv:2309.00047 [quant-ph]

    2023

  64. [72]

    Y. S. Yordanov, D. R. M. Arvidsson-Shukur, and C. H. W. Barnes, Efficient quantum circuits for quan- tum computational chemistry, Physical Review A 102, 10.1103/physreva.102.062612 (2020)

    2020 doi

  65. [73]

    Nam, J.-S

    Y. Nam, J.-S. Chen, N. C. Pisenti, K. Wright, C. Delaney, D. Maslov, K. R. Brown, S. Allen, J. M. Amini, J. Apis- dorf, K. M. Beck, A. Blinov, V. Chaplin, M. Chmielewski, C. Collins, S. Debnath, A. M. Ducore, K. M. Hudek, M. Keesan, S. M. Kreikemeier, J. Mizrahi, P. Solomon, M...

    2019 arXiv

  66. [74]

    Q. Wang, M. Li, C. Monroe, and Y. Nam, Resource- optimized fermionic local-hamiltonian simulation on a quantum computer for quantum chemistry, Quantum 5, 509 (2021)

    2021

  67. [75]

    C. D. Bruzewicz, J. Chiaverini, R. McConnell, and J. M. Sage, Trapped-ion quantum computing: Progress and challenges 10.1063/1.5088164 (2019)

    2019 doi

  68. [76]

    H. L. Huang, D. Wu, D. Fan, and X. Zhu, Superconduct- ing quantum computing: a review (2020)

    2020

  69. [77]

    Aspuru-Guzik, A

    A. Aspuru-Guzik, A. D. Dutoi, P. J. Love, and M. Head- Gordon, Chemistry: Simulated quantum computation of molecular energies, Science 309, 1704 (2005)

    2005

  70. [78]

    J. R. McClean, J. Romero, R. Babbush, and A. Aspuru- Guzik, The theory of variational hybrid quantum- classical algorithms, New Journal of Physics 18, 023023 (2016)

    2016

  71. [79]

    Lan and W

    Z. Lan and W. Liang, Amplitude reordering accelerates the adaptive variational quantum eigensolver algorithms, Journal of Chemical Theory and Computation 18, 5267 (2022)

    2022

  72. [80]

    DalFavero, R

    B. DalFavero, R. Sarkar, D. Camps, N. Sawaya, and R. LaRose, k-commutativity and measurement reduction for expectation values, arXiv preprint arXiv:2312.11840 (2023)

    2023

Pith tools

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