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arxiv: 2606.07084 · v1 · pith:KCYJLH27new · submitted 2026-06-05 · 🪐 quant-ph

Projector Quantum Variational Ansatz

Thomas Dumontier , Robin Ollive , Stephane Louise This is my paper

Pith reviewed 2026-06-27 21:43 UTC · model grok-4.3

classification 🪐 quant-ph
keywords variational quantum eigensolverprojector ansatzADAPT-VQEground stateNISQ algorithmsquantum signal processingvariational circuit
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The pith

A projector-based variational ansatz converges to ground states using shallower circuits than standard ADAPT-VQE.

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

The paper introduces the Projector Variational Ansatz as a VQE structure that builds a parametrized projector rather than a direct state transition. This design draws from fault-tolerant algorithms that use ancillary flags and post-selection to identify the ground state. The ansatz can be parametrized to match either an intermediate-scale quantum signal processing circuit or an ADAPT-VQE structure. Experiments show that this projector form reaches the target energy with fewer layers than the usual adaptive derivative-assembled pseudo-Trotter method. A reader would care because reduced circuit depth directly lowers error accumulation on present-day noisy hardware.

Core claim

The Projector Variational Ansatz constructs a variational circuit that applies a parametrized projector to identify the ground state of a Hamiltonian, and experimental results demonstrate that this structure converges with a shallower ansatz than the usual ADAPT-VQE.

What carries the argument

The Projector Variational Ansatz (PVA), a parametrized circuit that applies a projector-like operation to flag the ground state, which can be tuned to reproduce either ISQ-QSP or ADAPT-VQE circuit structures.

If this is right

  • PVA achieves ground-state convergence with reduced circuit depth relative to ADAPT-VQE on the tested Hamiltonians.
  • The same ansatz structure can be reparametrized to match the circuit layout of intermediate-scale quantum signal processing.
  • Iterative ansatz growth guided by projector operators yields shallower final circuits than derivative-assembled pseudo-Trotter growth.
  • The projector form allows direct comparison between variational and fault-tolerant projector techniques within a single VQE framework.

Where Pith is reading between the lines

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

  • If the depth advantage persists across broader Hamiltonians, PVA could extend practical VQE calculations to modestly larger molecular systems on current hardware.
  • The structural similarity to fault-tolerant projectors suggests a route for gradually incorporating non-variational elements into VQE workflows.
  • Measuring the total resource cost including ancillary qubit overhead would clarify whether the depth saving translates into an overall resource gain.

Load-bearing premise

The projector parametrization delivers the observed depth reduction without hidden increases in measurement overhead or optimization difficulty that would cancel the benefit.

What would settle it

A benchmark on a system where the PVA requires equal or greater circuit depth than ADAPT-VQE to reach the same energy accuracy within a fixed measurement budget.

Figures

Figures reproduced from arXiv: 2606.07084 by Robin Ollive, Stephane Louise, Thomas Dumontier.

Figure 1
Figure 1. Figure 1: Quantum circuit of the ISQ-QSP algorithm that measures the expectation value of the summand [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Quantum circuit of the ADAPT-VQE ansatz at the [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Quantum circuit of the Projector-ADAPT-VQE ansatz at the [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Quantum circuit used to measure an expectation value of the [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Performance comparison of the PVA versus standard Qubit-ADAPT-VQE and Fermionic-ADAPT-VQE [PITH_FULL_IMAGE:figures/full_fig_p005_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Quantum circuit that represents the part (dotted boxes) of the exponentialized operator from which the CNOT count differs ( dd [PITH_FULL_IMAGE:figures/full_fig_p006_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Finite shots simulation of our PVA method for [PITH_FULL_IMAGE:figures/full_fig_p006_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Basic Ansatz Classification Diagram. • Linear System (VQLS): Hcp |ψx⟩ ∝ |ψb⟩ ⇒ |ψx⟩ ∝ Hcp −1 |ψb⟩ Ib= Hcp −1 Hcp ⇒ 0 = ⟨ψb| Ib− HcpAb(θ)|ψb⟩ C(θ) = min[1 − | ⟨ψb| HcpAb(θ)|ψb⟩ |] (17) It is equivalent to searching a ground-state of HdG using VQE: HdG = Ib− HdP |ψb⟩ ⟨ψb| HdP † (18) Without explicitly constructing this matrix.. • State Initialization: C(θ) = min[⟨ψf |ψ(θ)⟩] = min[⟨0| UcψA[(θ)|ψi⟩] (19) • Exc… view at source ↗
read the original abstract

Quantum computing offers several algorithms to compute the ground state of a problem Hamiltonian. The most desirable algorithms belong to the Fault Tolerant QuantumComputing (FTQC) regime, such as quantum algorithms with repetitive structure like Quantum Phase Estimation (QPE) and Quantum Signal Processing (QSP). However, in the Noisy In-termediate Scale Quantum (NISQ) regime, the most realistic approaches involve Variational Quantum Eigensolver (VQE) algorithms and their variants. VQE is an algorithm that searches for a parametrized unitary matrix called an ansatz whose purposeis to transform an easily prepared initial state into the groundstate of a given Hamiltonian. Adaptive Derivative-AssembledPseudo-Trotter (ADAPT)-VQE is a variant of VQE that im-proves this approach by constructing the ansatz iteratively so that the associated quantum circuit is as shallow as possible. A major difference between FTQC (i.e. not variational) algorithms and VQE is that FTQC algorithms do not construct a state transitiondirectly. Instead, they construct a projector that identifies the ground state using ancillary qubits that flag the good solution. The desired state is then obtained via amplitude amplification orpost-selection. In this work, we propose a VQE ansatz whose structure is more similar to that of an FTQC algorithm. Depending on its parametrization, this ansatz can be equivalent to either an Intermediate Scale Quantum (ISQ)-QSP or to an ADAPT-VQE quantum circuit structure. Our experimental results show that this first proposal of Projector Variational Ansatz (PVA) converges with a shallower ansatz than the usual ADAPT-VQE.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript introduces the Projector Variational Ansatz (PVA), a VQE-style ansatz whose structure mimics FTQC projector methods by using ancillary qubits to flag the ground state, with post-selection or amplitude amplification to extract it. Depending on parametrization, PVA reduces to either ISQ-QSP or ADAPT-VQE circuit structure. The central experimental claim is that PVA reaches convergence using a shallower ansatz than standard ADAPT-VQE.

Significance. If the reported depth reduction is shown to yield a genuine net resource saving after all costs are tallied, the work would provide a concrete bridge between variational NISQ methods and projector-based FTQC primitives, with the parametrization equivalence offering a useful unification. The manuscript would then merit attention for opening a new ansatz family whose performance can be directly compared to both VQE and QSP lineages.

major comments (2)
  1. [Abstract] The abstract states that PVA 'converges with a shallower ansatz than the usual ADAPT-VQE,' yet the comparison metrics are not specified. If the experiments track only gate depth or iteration count while omitting ancillary-qubit count, post-selection success probability, or the number of shots required to evaluate the projector, the headline claim of improved performance does not follow.
  2. [Experimental Results] The skeptic note correctly identifies that the projector construction necessarily introduces ancillary qubits and post-selection. Without an explicit resource table (circuit depth + measurement overhead + success probability) comparing PVA to ADAPT-VQE on the same Hamiltonians, the central experimental result cannot be assessed as a net improvement.
minor comments (2)
  1. Define the precise parametrization choices that recover ADAPT-VQE versus ISQ-QSP, ideally with a short table or diagram showing the operator pool and measurement protocol in each limit.
  2. Clarify whether the PVA projector is evaluated via direct measurement on the ancilla or via post-selection, and state the associated sampling overhead explicitly.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments on resource accounting and metric clarity. We agree that the headline claim requires explicit qualification and that a full resource comparison is needed to substantiate net improvement. We will revise the manuscript accordingly.

read point-by-point responses

  1. Referee: [Abstract] The abstract states that PVA 'converges with a shallower ansatz than the usual ADAPT-VQE,' yet the comparison metrics are not specified. If the experiments track only gate depth or iteration count while omitting ancillary-qubit count, post-selection success probability, or the number of shots required to evaluate the projector, the headline claim of improved performance does not follow.

    Authors: We agree the abstract should specify the metrics. The reported 'shallower ansatz' refers specifically to the reduced number of variational layers/gates in the primary register needed for convergence to a target accuracy, as measured in our experiments. Ancilla overhead and post-selection costs were not folded into that particular comparison. We will revise the abstract to state this explicitly and add a brief discussion of the ancillary and post-selection trade-offs. revision: yes

  2. Referee: [Experimental Results] The skeptic note correctly identifies that the projector construction necessarily introduces ancillary qubits and post-selection. Without an explicit resource table (circuit depth + measurement overhead + success probability) comparing PVA to ADAPT-VQE on the same Hamiltonians, the central experimental result cannot be assessed as a net improvement.

    Authors: We accept this assessment. The current experiments emphasize ansatz depth but omit a consolidated resource table. We will add an explicit comparison table for the same Hamiltonians that includes total circuit depth (with ancillas), estimated post-selection success probability, measurement overhead, and shot-count estimates. This will allow readers to judge net resource savings directly. revision: yes

Circularity Check

0 steps flagged

No circularity: PVA proposal is a novel construction with external experimental comparison

full rationale

The manuscript proposes PVA as a projector-based variational ansatz that, depending on parametrization, reduces to ISQ-QSP or ADAPT-VQE structures. The central result is an experimental demonstration of shallower circuit convergence versus ADAPT-VQE. No equations, fitted parameters, or predictions are shown that reduce to inputs by construction. No self-citations, uniqueness theorems, or ansatzes smuggled via prior author work appear in the text. The derivation chain is therefore self-contained and does not exhibit any of the enumerated circularity patterns.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

No free parameters, axioms, or invented entities are identifiable from the abstract alone.

pith-pipeline@v0.9.1-grok · 5826 in / 1036 out tokens · 21139 ms · 2026-06-27T21:43:21.211971+00:00 · methodology

discussion (0)

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Reference graph

Works this paper leans on

60 extracted references · 7 linked inside Pith

  1. [1]

    Variational quantum algorithms,

    M. Cerezo, A. Arrasmith, R. Babbush, S. C. Benjamin, S. Endo, K. Fujii, J. R. McClean, K. Mitarai, X. Yuan, L. Cincio, and P. J. Coles, “Variational quantum algorithms,”Nature Reviews Physics, vol. 3, pp. 625–644, Sept. 2021

    2021

  2. [2]

    Patterns for Hybrid Quantum Algorithms,

    M. Weigold, J. Barzen, F. Leymann, and D. Vietz, “Patterns for Hybrid Quantum Algorithms,” inService-Oriented Computing(J. Barzen, ed.), vol. 1429, pp. 34–51, Cham: Springer International Publishing, 2021. Series Title: Communications in Computer and Information Science

    2021

  3. [3]

    A variational eigenvalue solver on a (photonic) 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,”Nature Communications, vol. 5, p. 4213, July 2014. arXiv:1304.3061 [physics, physics:quant- ph]

    Pith/arXiv arXiv 2014

  4. [4]

    From transistor to trapped-ion com- puters for quantum chemistry,

    M.-H. Yung, J. Casanova, A. Mezzacapo, J. McClean, L. Lamata, A. Aspuru-Guzik, and E. Solano, “From transistor to trapped-ion com- puters for quantum chemistry,”Scientific Reports, vol. 4, p. 3589, Jan. 2014

    2014

  5. [5]

    The theory of variational hybrid quantum-classical algorithms,

    J. R. McClean, J. Romero, R. Babbush, and A. Aspuru-Guzik, “The theory of variational hybrid quantum-classical algorithms,”New Journal of Physics, vol. 18, p. 023023, Feb. 2016

    2016

  6. [6]

    VQE method: a short survey and recent developments,

    D. A. Fedorov, B. Peng, N. Govind, and Y . Alexeev, “VQE method: a short survey and recent developments,”Materials Theory, vol. 6, p. 2, Jan. 2022

    2022

  7. [7]

    Variational quantum eigensolvers by variance minimization,

    D.-B. Zhang, Z.-H. Yuan, and T. Yin, “Variational quantum eigensolvers by variance minimization,” June 2020. arXiv:2006.15781 [quant-ph]

    arXiv 2020

  8. [8]

    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,”Nature, vol. 549, pp. 242–246, Sept. 2017

    2017

  9. [9]

    Quantum implementation of the unitary coupled cluster for simulating molecular electronic structure,

    Y . Shen, X. Zhang, S. Zhang, J.-N. Zhang, M.-H. Yung, and K. Kim, “Quantum implementation of the unitary coupled cluster for simulating molecular electronic structure,”Physical Review A, vol. 95, p. 020501, Feb. 2017

    2017

  10. [10]

    Low-Depth Quantum Simulation of Materials,

    R. Babbush, N. Wiebe, J. McClean, J. McClain, H. Neven, and G. K.-L. Chan, “Low-Depth Quantum Simulation of Materials,”Physical Review X, vol. 8, p. 011044, Mar. 2018

    2018

  11. [11]

    Quantum algorithms for electronic structure calculations: Particle-hole Hamiltonian and optimized wave-function expansions,

    P. K. Barkoutsos, J. F. Gonthier, I. Sokolov, N. Moll, G. Salis, A. Fuhrer, M. Ganzhorn, D. J. Egger, M. Troyer, A. Mezzacapo, S. Filipp, and I. Tavernelli, “Quantum algorithms for electronic structure calculations: Particle-hole Hamiltonian and optimized wave-function expansions,” Physical Review A, vol. 98, p. 022322, Aug. 2018

    2018

  12. [12]

    Efficient symmetry-preserving state preparation circuits for the variational quantum eigensolver algorithm,

    B. T. Gard, L. Zhu, G. S. Barron, N. J. Mayhall, S. E. Economou, and E. Barnes, “Efficient symmetry-preserving state preparation circuits for the variational quantum eigensolver algorithm,”npj Quantum Informa- tion, vol. 6, p. 10, Jan. 2020

    2020

  13. [13]

    A diagrammatic approach to variational quantum ansatz construction,

    Y . Herasymenko and T. E. O’Brien, “A diagrammatic approach to variational quantum ansatz construction,”Quantum, vol. 5, p. 596, Dec

  14. [14]

    arXiv:1907.08157 [quant-ph]

    arXiv 1907

  15. [15]

    Quantum-optimal-control-inspired ansatz for variational quantum algorithms,

    A. Choquette, A. Di Paolo, P. K. Barkoutsos, D. S ´en´echal, I. Tavernelli, and A. Blais, “Quantum-optimal-control-inspired ansatz for variational quantum algorithms,”Physical Review Research, vol. 3, p. 023092, May

  16. [16]

    arXiv:2008.01098 [quant-ph]

    arXiv 2008

  17. [17]

    Quantum Compu- tation by Adiabatic Evolution,

    E. Farhi, J. Goldstone, S. Gutmann, and M. Sipser, “Quantum Compu- tation by Adiabatic Evolution,” Jan. 2000. arXiv:quant-ph/0001106

    Pith/arXiv arXiv 2000

  18. [18]

    Progress towards practical quantum variational algorithms,

    D. Wecker, M. B. Hastings, and M. Troyer, “Progress towards practical quantum variational algorithms,”Physical Review A, vol. 92, p. 042303, Oct. 2015

    2015

  19. [19]

    Strategies for solving the Fermi-Hubbard model on near-term quantum computers,

    C. Cade, L. Mineh, A. Montanaro, and S. Stanisic, “Strategies for solving the Fermi-Hubbard model on near-term quantum computers,” Physical Review B, vol. 102, p. 235122, Dec. 2020

    2020

  20. [20]

    Finding the ground state of the Hubbard model by variational methods on a quantum computer with gate errors,

    J.-M. Reiner, F. Wilhelm-Mauch, G. Sch ¨on, and M. Marthaler, “Finding the ground state of the Hubbard model by variational methods on a quantum computer with gate errors,”Quantum Science and Technology, vol. 4, p. 035005, July 2019

    2019

  21. [21]

    Hamiltonian variational ansatz without barren plateaus,

    C.-Y . Park and N. Killoran, “Hamiltonian variational ansatz without barren plateaus,”Quantum, vol. 8, p. 1239, Feb. 2024. arXiv:2302.08529 [quant-ph]

    arXiv 2024

  22. [22]

    Exploring entanglement and optimization within the Hamiltonian Variational Ansatz,

    R. Wiersema, C. Zhou, Y . d. Sereville, J. F. Carrasquilla, Y . B. Kim, and H. Yuen, “Exploring entanglement and optimization within the Hamiltonian Variational Ansatz,”PRX Quantum, vol. 1, p. 020319, Dec

  23. [23]

    arXiv:2008.02941 [quant-ph]

    arXiv 2008

  24. [24]

    Efficient variational simulation of non- trivial quantum states,

    W. W. Ho and T. H. Hsieh, “Efficient variational simulation of non- trivial quantum states,”SciPost Physics, vol. 6, p. 029, Mar. 2019. arXiv:1803.00026 [cond-mat]

    Pith/arXiv arXiv 2019

  25. [25]

    A Quantum Approximate Optimization Algorithm,

    E. Farhi, J. Goldstone, and S. Gutmann, “A Quantum Approximate Optimization Algorithm,” Nov. 2014. arXiv:1411.4028 [quant-ph]

    Pith/arXiv arXiv 2014

  26. [26]

    Quantum Supremacy through the Quantum Approximate Optimization Algorithm,

    E. Farhi and A. W. Harrow, “Quantum Supremacy through the Quantum Approximate Optimization Algorithm,” Oct. 2019. arXiv:1602.07674 [quant-ph]

    arXiv 2019

  27. [27]

    A Review on Quantum Approximate Optimization Algorithm and its Variants,

    K. Blekos, D. Brand, A. Ceschini, C.-H. Chou, R.-H. Li, K. Pandya, and A. Summer, “A Review on Quantum Approximate Optimization Algorithm and its Variants,”Physics Reports, vol. 1068, pp. 1–66, June

  28. [28]

    arXiv:2306.09198 [quant-ph]

    arXiv

  29. [29]

    From the Quantum Approximate Optimization Algorithm to a Quantum Alternating Operator Ansatz,

    S. Hadfield, Z. Wang, B. O’Gorman, E. G. Rieffel, D. Venturelli, and R. Biswas, “From the Quantum Approximate Optimization Algorithm to a Quantum Alternating Operator Ansatz,”Algorithms, vol. 12, p. 34, Feb. 2019

    2019

  30. [30]

    Fermionic quantum approximate optimization algorithm,

    T. Yoshioka, K. Sasada, Y . Nakano, and K. Fujii, “Fermionic quantum approximate optimization algorithm,”Physical Review Research, vol. 5, p. 023071, May 2023

    2023

  31. [31]

    An adaptive variational algorithm for exact molecular simulations on a quantum computer,

    H. R. Grimsley, S. E. Economou, E. Barnes, and N. J. Mayhall, “An adaptive variational algorithm for exact molecular simulations on a quantum computer,”Nature Communications, vol. 10, p. 3007, July 2019

    2019

  32. [32]

    qubit-ADAPT-VQE: An adaptive algorithm for constructing hardware-efficient ansatze on a quantum processor,

    H. L. Tang, V . O. Shkolnikov, G. S. Barron, H. R. Grimsley, N. J. Mayhall, E. Barnes, and S. E. Economou, “qubit-ADAPT-VQE: An adaptive algorithm for constructing hardware-efficient ansatze on a quantum processor,”PRX Quantum, vol. 2, p. 020310, Apr. 2021. arXiv:1911.10205 [quant-ph]

    arXiv 2021

  33. [33]

    Overlap-ADAPT-VQE: practical quantum chemistry on quantum com- puters via overlap-guided compact Ans ¨atze,

    C. Feniou, M. Hassan, D. Traor ´e, E. Giner, Y . Maday, and J.-P. Piquemal, “Overlap-ADAPT-VQE: practical quantum chemistry on quantum com- puters via overlap-guided compact Ans ¨atze,”Communications Physics, vol. 6, p. 192, July 2023

    2023

  34. [34]

    How to really measure operator gradients in ADAPT-VQE,

    P. G. Anastasiou, N. J. Mayhall, E. Barnes, and S. E. Economou, “How to really measure operator gradients in ADAPT-VQE,” Sept. 2023. arXiv:2306.03227 [quant-ph]

    Pith/arXiv arXiv 2023

  35. [35]

    An Optimal Framework for Constructing Lie-Algebra Generator Pools: Application to Variational Quantum Eigensolvers for Chemistry,

    Y . Viswanathan, O. Adjoua, C. Feniou, S. Badreddine, and J.-P. Pique- mal, “An Optimal Framework for Constructing Lie-Algebra Generator Pools: Application to Variational Quantum Eigensolvers for Chemistry,” Dec. 2025. arXiv:2511.22593 [quant-ph]

    arXiv 2025

  36. [36]

    Reducing the resources required by ADAPT- VQE using coupled exchange operators and improved subroutines,

    M. Ram ˆoa, P. G. Anastasiou, L. P. Santos, N. J. Mayhall, E. Barnes, and S. E. Economou, “Reducing the resources required by ADAPT- VQE using coupled exchange operators and improved subroutines,”npj Quantum Information, vol. 11, no. 1, p. 86, 2025

    2025

  37. [37]

    TETRIS-ADAPT-VQE: An adaptive algorithm that yields shallower, denser circuit ans ¨atze,

    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,”Physical Review Research, vol. 6, no. 1, p. 013254, 2024

    2024

  38. [38]

    Geo-ADAPT-VQE: Quantum infor- mation metric-aware circuit optimization for quantum chemistry,

    M. A. Sohail and T. Koike-Akino, “Geo-ADAPT-VQE: Quantum infor- mation metric-aware circuit optimization for quantum chemistry,” 2026

    2026

  39. [39]

    Variational Quantum Linear Solver,

    C. Bravo-Prieto, R. LaRose, M. Cerezo, Y . Subasi, L. Cincio, and P. J. Coles, “Variational Quantum Linear Solver,” June 2020. arXiv:1909.05820 [quant-ph]

    arXiv 2020

  40. [40]

    Variational algorithms for linear algebra,

    X. Xu, J. Sun, S. Endo, Y . Li, S. C. Benjamin, and X. Yuan, “Variational algorithms for linear algebra,”Science Bulletin, vol. 66, pp. 2181–2188, Nov. 2021

    2021

  41. [41]

    Near term algorithms for linear systems of equations,

    A. Pellow-Jarman, I. Sinayskiy, A. Pillay, and F. Petruccione, “Near term algorithms for linear systems of equations,”Quantum Information Processing, vol. 22, p. 258, June 2023

    2023

  42. [42]

    Performance study of variational quantum linear solver with an improved ansatz for reservoir flow equations,

    X. Rao, “Performance study of variational quantum linear solver with an improved ansatz for reservoir flow equations,”Physics of Fluids, vol. 36, p. 047104, Apr. 2024

    2024

  43. [43]

    Efficient Variational Quantum Linear Solver for Structured Sparse Matrices,

    A. Gnanasekaran and A. Surana, “Efficient Variational Quantum Linear Solver for Structured Sparse Matrices,” Apr. 2024. arXiv:2404.16991 [quant-ph]

    arXiv 2024

  44. [44]

    Identifying Bottle- necks of NISQ-friendly HHL algorithms,

    M. A. Marfany, A. Sakhnenko, and J. M. Lorenz, “Identifying Bottle- necks of NISQ-friendly HHL algorithms,” June 2024. arXiv:2406.06288 [quant-ph]

    arXiv 2024

  45. [45]

    Quantum measurements and the Abelian Stabilizer Problem,

    A. Y . Kitaev, “Quantum measurements and the Abelian Stabilizer Problem,” Nov. 1995. arXiv:quant-ph/9511026

    Pith/arXiv arXiv 1995

  46. [46]

    Grand Unification of Quantum Algorithms,

    J. M. Martyn, Z. M. Rossi, A. K. Tan, and I. L. Chuang, “Grand Unification of Quantum Algorithms,”PRX Quantum, vol. 2, p. 040203, Dec. 2021

    2021

  47. [47]

    Ground state preparation and energy estimation on early fault-tolerant quantum computers via quantum eigenvalue transformation of unitary matrices,

    Y . Dong, L. Lin, and Y . Tong, “Ground state preparation and energy estimation on early fault-tolerant quantum computers via quantum eigenvalue transformation of unitary matrices,”PRX Quantum, vol. 3, p. 040305, Oct. 2022. arXiv:2204.05955 [physics, physics:quant-ph]

    arXiv 2022

  48. [48]

    Quantum Signal Processing Based Grover’s Adaptative Search Oracle for High Order Unconstrained Binary Optimization Problems,

    R. OLLIVE and S. LOUISE, “Quantum Signal Processing Based Grover’s Adaptative Search Oracle for High Order Unconstrained Binary Optimization Problems,” in2024 IEEE International Conference on Quantum Computing and Engineering (QCE), vol. 02, pp. 256–261, Sept. 2024

    2024

  49. [49]

    Numerical Error Extraction by Quantum Measurement Algorithm,

    C. Ronfaut, R. Ollive, and S. Louise, “Numerical Error Extraction by Quantum Measurement Algorithm,” Feb. 2026. arXiv:2602.01927 [quant-ph]

    arXiv 2026

  50. [50]

    Gate Efficient Composition of Hamiltonian Simulation and Block-Encoding with its Application on HUBO, Chem- istry and Finite Difference Method,

    R. Ollive and S. Louise, “Gate Efficient Composition of Hamiltonian Simulation and Block-Encoding with its Application on HUBO, Chem- istry and Finite Difference Method,” in2025 IEEE International Parallel and Distributed Processing Symposium Workshops (IPDPSW), pp. 519– 528, June 2025

    2025

  51. [51]

    A Theory of Trotter Error with Commutator Scaling,

    A. M. Childs, Y . Su, M. C. Tran, N. Wiebe, and S. Zhu, “A Theory of Trotter Error with Commutator Scaling,”Physical Review X, vol. 11, p. 011020, Feb. 2021. arXiv:1912.08854 [cond-mat, physics:physics, physics:quant-ph]

    arXiv 2021

  52. [52]

    Coupled-cluster theory in quantum chemistry,

    R. J. Bartlett and M. Musiał, “Coupled-cluster theory in quantum chemistry,”Reviews of Modern Physics, vol. 79, pp. 291–352, Feb. 2007

    2007

  53. [53]

    Quantum approximate optimization is computationally uni- versal,

    S. Lloyd, “Quantum approximate optimization is computationally uni- versal,” Dec. 2018. arXiv:1812.11075 [quant-ph]

    Pith/arXiv arXiv 2018

  54. [54]

    On the univer- sality of the quantum approximate optimization algorithm,

    M. MORALES, J. BIAMONTE, and Z. ZIMBORAS, “On the univer- sality of the quantum approximate optimization algorithm,”Quantum Information Processing, Aug. 2020. APPENDIX A. Cost-Function Structure By linearity, the expectation value of the operator on a quantum state (or the inner product of two states around the operator) can be computed via a weighted sum...

    2020

  55. [55]

    The original proposal shows instances for which it behaves well

    Quantum Approximate Optimization Algorithm:QAOA is a specific case for binary optimization problems. The original proposal shows instances for which it behaves well

  56. [56]

    It uses the mixing Hamiltonian dHM =Pnbqb−1 i=0 bXi and cHp a diagonal Hamiltonian, often corresponding to an Ising problem

    and [23] provided complexity-theoretic explanations of the hardness of modeling this algorithm classically. It uses the mixing Hamiltonian dHM =Pnbqb−1 i=0 bXi and cHp a diagonal Hamiltonian, often corresponding to an Ising problem. These two Hamiltonians can be implemented exactly. QAOA is one of the most studied VQA. [24, Table 1] provides a summary of ...

  57. [57]

    Hamiltonian Variational Ansatz:Is the generalization of the previous technique to arbitrary Hamiltonians: initially for quantum systems (Fermi-Hubbard) diagonalization [16], asso- ciate resource estimation [17], impact of errors [18], optimiza- tion guarantee [19], more general problems [20], and quantum state preparation [21]. When applied to a chemical ...

  58. [58]

    We implemented the quantum circuit construction and statevector simulations using the Qiskit and Qiskit Nature software stacks

    System Generation and Software Stack:To compute all electronic structure quantities and the Hartree-Fock method, we used the classical PySCF driver. We implemented the quantum circuit construction and statevector simulations using the Qiskit and Qiskit Nature software stacks. For the finite-shot executions, we used Qiskit’s V2 Primitives (SamplerV2) and t...

  59. [59]

    For the Fermionic-ADAPT-VQE, we kept all excitations as an Hamiltonian simulated operator

    Operator Pools:The adaptive pools were derived from Unitary Coupled-Cluster Singles and Doubles (UCCSD) ex- citation operators. For the Fermionic-ADAPT-VQE, we kept all excitations as an Hamiltonian simulated operator. For the Qubit-ADAPT-VQE, we decomposed the fermionic operators to extract individual Pauli strings. To optimize the pool size, we discarde...

  60. [60]

    For the shot simulation, we used the SPSA optimizer

    Optimisation and measurement strategies:For the exact- statevector simulations, the parameter optimization (θ, ϕ, δ) was performed globally at each iteration using the L-BFGS- B algorithm with a gradient tolerance of10 −5. For the shot simulation, we used the SPSA optimizer. The SPSA algorithm was configured with automatic calibration of the learning rate...