Pith. sign in

REVIEW 1 major objections 1 minor 82 references

Mixed Dicke state ansatz encodes equality and inequality constraints directly into VQE circuits, removing penalty terms

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

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

T0 review · grok-4.3

2026-06-27 18:30 UTC pith:WBCMENTB

load-bearing objection The paper gives a mixed Dicke ansatz that encodes Hamming-weight equality and inequality constraints directly into the circuit so penalties can be dropped, with explicit constructions and portfolio tests that show an edge over random feasible search. the 1 major comments →

arxiv 2606.08504 v1 pith:WBCMENTB submitted 2026-06-07 quant-ph

Pure and mixed Dicke state ansatz for equality and inequality constraints in variational quantum eigensolver

J.V.S Scursulim This is my paper
classification quant-ph
keywords variational quantum eigensolverDicke statescombinatorial optimizationconstraint handlingHamming weightportfolio optimizationquantum algorithmsansatz design
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

The paper proposes a mixed Dicke state ansatz that preserves the feasible subspace for Hamming weight constrained combinatorial optimization problems. It structurally encodes both equality and inequality constraints into the quantum circuit itself rather than relying on tunable penalty terms in the objective function. The pure Dicke state is recovered as the special case for equality constraints alone, and the method extends to multiple constraint groups through tensor products. Validation on portfolio optimization shows the ansatz needs fewer objective evaluations than feasible-subspace random search as problem size grows. Hardware runs on IBM processors indicate that noise mitigation and transpilation remain open issues for deployment.

Core claim

We propose the first feasibility-preserving mixed Dicke state ansatz for Hamming weight constrained combinatorial optimization, extending the density matrix formalism to structurally encode equality and inequality constraints directly into the quantum circuit, thereby eliminating the need for penalty terms in the objective function. The proposed framework handles both constraint types, with the pure Dicke state ansatz recovered as a special case corresponding to equality constraints, and generalizes to multiple constraint groups via tensor products of individual pure or mixed Dicke states.

What carries the argument

The mixed Dicke state ansatz, which uses a density-matrix preparation over feasible Hamming-weight states to enforce constraints exactly within the circuit.

Load-bearing premise

Mixed Dicke states can be prepared exactly preserving the feasible subspace with circuit depth and gate count compatible with current hardware.

What would settle it

An explicit circuit realizing the mixed Dicke state that fails to maintain exact Hamming-weight feasibility or still requires penalty terms to reach feasible solutions would falsify the central claim.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • Both equality and inequality Hamming-weight constraints are enforced without any Lagrange-multiplier tuning.
  • The pure Dicke state emerges as the equality-constraint special case of the mixed construction.
  • Multiple independent constraint groups are handled by tensor-product composition of the individual states.
  • In portfolio optimization the ansatz requires fewer objective calls than feasible-subspace random search once the feasible space grows large.
  • The same structural encoding applies directly to any other combinatorial problem whose constraints are Hamming-weight restrictions.

Where Pith is reading between the lines

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

  • If the required preparation circuits remain shallow enough, the approach could support larger numbers of simultaneous constraints on near-term devices.
  • Pairing the ansatz with gradient-free optimizers other than CMA-ES might further cut the number of evaluations needed.
  • Similar density-matrix encodings could be explored for constraint families beyond Hamming weight.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

1 major / 1 minor

Summary. The manuscript proposes the first feasibility-preserving mixed Dicke state ansatz for variational quantum eigensolvers applied to Hamming-weight-constrained combinatorial optimization. It extends the density-matrix formalism to encode equality and inequality constraints directly into the circuit structure (recovering the pure Dicke case for equality constraints), generalizes to multiple constraint groups via tensor products of individual pure or mixed Dicke states, and thereby eliminates penalty terms. Explicit circuit constructions with depth and gate-count expressions are supplied; the approach is validated on three portfolio-optimization scenarios of increasing constraint complexity using CMA-ES, showing an advantage over random feasible-subspace search as the search space grows, together with hardware runs on IBM NISQ processors that flag remaining noise-mitigation issues.

Significance. If the supplied circuit constructions prepare the required mixed Dicke states with depths compatible with NISQ hardware while exactly preserving the feasible subspace, the work would constitute a meaningful advance in constrained VQAs by removing the need for Lagrange-multiplier tuning. Credit is due for the explicit unitary constructions, depth/gate-count formulas, and the numerical comparison to random feasible search that directly tests the scaling claim.

major comments (1)
  1. [Abstract / Validation] Abstract and validation description: the reported advantage over random feasible search (in number of objective-function calls as the feasible space grows) is presented without error bars, number of independent runs, or statistical tests; this weakens the evidential support for the central claim that the ansatz yields a clear, reproducible improvement.
minor comments (1)
  1. [Hardware experiments] Hardware experiments section: the acknowledgment that noise mitigation and transpilation remain open challenges is appropriate, but quantitative metrics (e.g., fidelity degradation or success-probability drop under realistic noise) would clarify the practical gap between the ideal ansatz and hardware performance.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the constructive comment regarding the statistical presentation of our validation results. We address this point below and will update the manuscript accordingly.

read point-by-point responses

  1. Referee: [Abstract / Validation] Abstract and validation description: the reported advantage over random feasible search (in number of objective-function calls as the feasible space grows) is presented without error bars, number of independent runs, or statistical tests; this weakens the evidential support for the central claim that the ansatz yields a clear, reproducible improvement.

    Authors: We agree that the current presentation of the numerical results lacks these statistical details, which limits the strength of the evidence for the claimed advantage. In the revised manuscript we will explicitly state the number of independent runs performed for each scenario, include error bars (standard deviation across runs) on the plots and tables comparing objective-function calls, and report the results of appropriate statistical tests (e.g., Wilcoxon rank-sum tests) to quantify the significance of the observed improvement over random feasible-subspace search. revision: yes

Circularity Check

0 steps flagged

No significant circularity

full rationale

The manuscript presents a direct structural proposal for a mixed Dicke state ansatz that encodes Hamming-weight equality and inequality constraints via explicit circuit constructions and tensor-product generalizations. No load-bearing step reduces by definition or by self-citation to its own inputs; the central claim rests on the explicit unitary mappings and hardware-validated depth expressions rather than on any fitted parameter renamed as a prediction or on an ansatz smuggled through prior self-work. The derivation chain is therefore self-contained as a construction, not a tautological reduction.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 1 invented entities

Central claim rests on the novel structural encoding via mixed Dicke states and density-matrix formalism; no explicit free parameters are stated in the abstract. The construction assumes standard quantum circuit composition rules and the existence of efficient state-preparation circuits for Dicke states.

axioms (1)
  • standard math Standard quantum mechanics and density-matrix formalism apply to the mixed states used in the ansatz.
    Invoked when extending the formalism to encode inequality constraints.
invented entities (1)
  • Mixed Dicke state ansatz no independent evidence
    purpose: To structurally encode inequality Hamming-weight constraints while preserving feasibility without penalties.
    Newly proposed construction; no independent evidence outside the paper is provided in the abstract.

pith-pipeline@v0.9.1-grok · 5783 in / 1266 out tokens · 29669 ms · 2026-06-27T18:30:50.170156+00:00 · methodology

0 comments
read the original abstract

Combinatorial optimization can be addressed with quantum computing through variational quantum algorithms, but a central challenge in this approach is to design an ansatz expressive enough to explore the feasible subspace of the Hilbert space where the optimal solution lies. Another major challenge is tuning the Lagrange multipliers in penalty terms to enforce feasibility and guarantee solution quality. To address both challenges, we propose the first feasibility-preserving mixed Dicke state ansatz for Hamming weight constrained combinatorial optimization, extending the density matrix formalism to structurally encode equality and inequality constraints directly into the quantum circuit, thereby eliminating the need for penalty terms in the objective function. The proposed framework handles both constraint types, with the pure Dicke state ansatz recovered as a special case corresponding to equality constraints, and generalizes to multiple constraint groups via tensor products of individual pure or mixed Dicke states. We validate the proposed approach in the context of combinatorial portfolio optimization across three experimental scenarios with increasing constraint complexity, using the CMA-ES optimizer and comparing its performance against random search with replacement restricted to the feasible subspace. As the feasible search space grows, the proposed ansatz demonstrates a clear advantage over random search in terms of the number of objective function calls required to identify high-quality solutions. Hardware experiments on IBM NISQ processors confirm that noise mitigation and circuit transpilation optimizations remain open challenges for practical deployment. The framework is general and directly applicable to other combinatorial optimization problems with Hamming weight constraints.

Figures

Figures reproduced from arXiv: 2606.08504 by J.V.S Scursulim.

Figure 1
Figure 1. Figure 1: An example of a quantum circuit that generates a pure Dicke state ansatz for VQE. In this figure, the circuit [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: An example of a quantum circuit that creates a mixture of Dicke states as an ansatz for VQE. In this figure, the [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Probability of finding the optimal solution [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Discrete efficient frontier for Scenarios I (left), II (center), and III (right), showing portfolios sampled from the [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Estimator standard deviation σ⟨O⟩ as a function of nshots illustrating the 1/ √ nshots decay. The dashed line indicates the noiseless statevector limit, recovered as nshots → ∞. In practice, we have access only to a finite sample of the probability distribution and must consider the effects of finite sampling on variational quantum algorithms. As illustrated in [PITH_FULL_IMAGE:figures/full_fig_p013_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Energy landscape ⟨H⟩ as a function of the variational parameters θ0 and θ1 for increasing number of measurement shots. As the number of shots increases, the landscape progressively smooths toward the noiseless statevector limit (nshots → ∞), illustrating the impact of finite sampling noise on the optimization surface. C Hardware experiments In order to assess the performance of the proposed ansatz on curre… view at source ↗

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

82 extracted references · 5 canonical work pages · 2 internal anchors

  1. [1]

    Rapid solution of problems by quantum computation.Proceedings of the Royal Society of London

    David Deutsch and Richard Jozsa. Rapid solution of problems by quantum computation.Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences, 439(1907):553–558, 1992

    1907

  2. [2]

    Quantum complexity theory

    Ethan Bernstein and Umesh Vazirani. Quantum complexity theory. InProceedings of the twenty-fifth annual ACM symposium on Theory of computing, pages 11–20, 1993

    1993

  3. [3]

    Algorithms for quantum computation: discrete logarithms and factoring

    Peter W Shor. Algorithms for quantum computation: discrete logarithms and factoring. InProceedings 35th annual symposium on foundations of computer science, pages 124–134. Ieee, 1994

    1994

  4. [4]

    A fast quantum mechanical algorithm for database search

    Lov K Grover. A fast quantum mechanical algorithm for database search. InProceedings of the twenty-eighth annual ACM symposium on Theory of computing, pages 212–219, 1996

    1996

  5. [5]

    Quantum algorithm for linear systems of equations

    Aram W Harrow, Avinatan Hassidim, and Seth Lloyd. Quantum algorithm for linear systems of equations. Physical review letters, 103(15):150502, 2009

    2009

  6. [6]

    Evidence for the utility of quantum computing before fault tolerance.Nature, 618(7965):500–505, 2023

    Youngseok Kim, Andrew Eddins, Sajant Anand, Ken Xuan Wei, Ewout Van Den Berg, Sami Rosenblatt, Hasan Nayfeh, Yantao Wu, Michael Zaletel, Kristan Temme, et al. Evidence for the utility of quantum computing before fault tolerance.Nature, 618(7965):500–505, 2023

    2023

  7. [7]

    Quantum computing for high-energy physics: State of the art and challenges.Prx quantum, 5(3):037001, 2024

    Alberto Di Meglio, Karl Jansen, Ivano Tavernelli, Constantia Alexandrou, Srinivasan Arunachalam, Christian W Bauer, Kerstin Borras, Stefano Carrazza, Arianna Crippa, Vincent Croft, et al. Quantum computing for high-energy physics: State of the art and challenges.Prx quantum, 5(3):037001, 2024

    2024

  8. [8]

    Quantum simulations of hadron dynamics in the schwinger model using 112 qubits.Physical Review D, 109(11):114510, 2024

    Roland C Farrell, Marc Illa, Anthony N Ciavarella, and Martin J Savage. Quantum simulations of hadron dynamics in the schwinger model using 112 qubits.Physical Review D, 109(11):114510, 2024

    2024

  9. [9]

    Observation of constructive interference at the edge of quantum ergodicity.Nature, 646(8086):825–830, 2025

    Dmitry A Abanin, Rajeev Acharya, Laleh Aghababaie-Beni, Georg Aigeldinger, Ashok Ajoy, Ross Alcaraz, Igor Aleiner, Trond I Andersen, Markus Ansmann, Frank Arute, et al. Observation of constructive interference at the edge of quantum ergodicity.Nature, 646(8086):825–830, 2025

    2025

  10. [10]

    Dynamical simulations of many-body quantum chaos on a quantum computer.Nature Physics, pages 1–6, 2026

    Laurin E Fischer, Matea Leahy, Andrew Eddins, Nathan Keenan, Davide Ferracin, Matteo AC Rossi, Youngseok Kim, Andre He, Francesca Pietracaprina, Boris Sokolov, et al. Dynamical simulations of many-body quantum chaos on a quantum computer.Nature Physics, pages 1–6, 2026. 9

    2026

  11. [11]

    Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets.nature, 549(7671):242–246, 2017

    Abhinav Kandala, Antonio Mezzacapo, Kristan Temme, Maika Takita, Markus Brink, Jerry M Chow, and Jay M Gambetta. Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets.nature, 549(7671):242–246, 2017

    2017

  12. [12]

    Quantum computational chemistry.Reviews of Modern Physics, 92(1):015003, 2020

    Sam McArdle, Suguru Endo, Alán Aspuru-Guzik, Simon C Benjamin, and Xiao Yuan. Quantum computational chemistry.Reviews of Modern Physics, 92(1):015003, 2020

    2020

  13. [13]

    Quantum algorithms for quantum chemistry and quantum materials science.Chemical reviews, 120(22):12685–12717, 2020

    Bela Bauer, Sergey Bravyi, Mario Motta, and Garnet Kin-Lic Chan. Quantum algorithms for quantum chemistry and quantum materials science.Chemical reviews, 120(22):12685–12717, 2020

    2020

  14. [14]

    Quantum computing enhanced computational catalysis.Physical Review Research, 3(3):033055, 2021

    Vera von Burg, Guang Hao Low, Thomas Häner, Damian S Steiger, Markus Reiher, Martin Roetteler, and Matthias Troyer. Quantum computing enhanced computational catalysis.Physical Review Research, 3(3):033055, 2021

    2021

  15. [15]

    A hybrid quantum computing pipeline for real world drug discovery.Scientific Reports, 14(1):16942, 2024

    Weitang Li, Zhi Yin, Xiaoran Li, Dongqiang Ma, Shuang Yi, Zhenxing Zhang, Chenji Zou, Kunliang Bu, Maochun Dai, Jie Yue, et al. A hybrid quantum computing pipeline for real world drug discovery.Scientific Reports, 14(1):16942, 2024

    2024

  16. [16]

    Implicit solvent sample-based quantum diagonalization.The Journal of Physical Chemistry B, 129(23):5788–5796, 2025

    Danil Kaliakin, Akhil Shajan, Fangchun Liang, and Kenneth M Merz Jr. Implicit solvent sample-based quantum diagonalization.The Journal of Physical Chemistry B, 129(23):5788–5796, 2025

    2025

  17. [17]

    Quantum optimization using variational algorithms on near-term quantum devices.Quantum Science and Technology, 3(3):030503, 2018

    Nikolaj Moll, Panagiotis Barkoutsos, Lev S Bishop, Jerry M Chow, Andrew Cross, Daniel J Egger, Stefan Filipp, Andreas Fuhrer, Jay M Gambetta, Marc Ganzhorn, et al. Quantum optimization using variational algorithms on near-term quantum devices.Quantum Science and Technology, 3(3):030503, 2018

    2018

  18. [18]

    Applying quantum algorithms to constraint satisfaction problems.Quantum, 3:167, 2019

    Earl Campbell, Ankur Khurana, and Ashley Montanaro. Applying quantum algorithms to constraint satisfaction problems.Quantum, 3:167, 2019

    2019

  19. [19]

    Quantum speedup of branch-and-bound algorithms.Physical Review Research, 2(1):013056, 2020

    Ashley Montanaro. Quantum speedup of branch-and-bound algorithms.Physical Review Research, 2(1):013056, 2020

    2020

  20. [20]

    Warm-starting quantum optimization.Quantum, 5:479, 2021

    Daniel J Egger, Jakub Mareˇcek, and Stefan Woerner. Warm-starting quantum optimization.Quantum, 5:479, 2021

    2021

  21. [21]

    Challenges and opportunities in quantum optimization.Nature Reviews Physics, 6(12):718–735, 2024

    Amira Abbas, Andris Ambainis, Brandon Augustino, Andreas Bärtschi, Harry Buhrman, Carleton Coffrin, Giorgio Cortiana, Vedran Dunjko, Daniel J Egger, Bruce G Elmegreen, et al. Challenges and opportunities in quantum optimization.Nature Reviews Physics, 6(12):718–735, 2024

    2024

  22. [22]

    Bias-field digitized counterdiabatic quantum algorithm for higher-order binary optimization

    Sebastián V Romero, Anne-Maria Visuri, Alejandro Gomez Cadavid, Anton Simen, Enrique Solano, and Naren- dra N Hegade. Bias-field digitized counterdiabatic quantum algorithm for higher-order binary optimization. Communications Physics, 8(1):348, 2025

    2025

  23. [23]

    Quantum approximate multi-objective optimization.Nature Computational Science, pages 1–10, 2025

    Ayse Kotil, Elijah Pelofske, Stephanie Riedmüller, Daniel J Egger, Stephan Eidenbenz, Thorsten Koch, and Stefan Woerner. Quantum approximate multi-objective optimization.Nature Computational Science, pages 1–10, 2025

    2025

  24. [24]

    Approximate quadratization of high-order hamiltonians for combinatorial quantum optimization.Physical Review Research, 8(2):023159, 2026

    Sabina Dr ˘agoi, Alberto Baiardi, and Daniel J Egger. Approximate quadratization of high-order hamiltonians for combinatorial quantum optimization.Physical Review Research, 8(2):023159, 2026

    2026

  25. [25]

    Quantum machine learning.Nature, 549(7671):195–202, 2017

    Jacob Biamonte, Peter Wittek, Nicola Pancotti, Patrick Rebentrost, Nathan Wiebe, and Seth Lloyd. Quantum machine learning.Nature, 549(7671):195–202, 2017

    2017

  26. [26]

    Quantum machine learning for quantum anomaly detection.Physical Review A, 97(4):042315, 2018

    Nana Liu and Patrick Rebentrost. Quantum machine learning for quantum anomaly detection.Physical Review A, 97(4):042315, 2018

    2018

  27. [27]

    Quantum convolutional neural networks.Nature Physics, 15(12):1273–1278, 2019

    Iris Cong, Soonwon Choi, and Mikhail D Lukin. Quantum convolutional neural networks.Nature Physics, 15(12):1273–1278, 2019

    2019

  28. [28]

    Supervised learning with quantum-enhanced feature spaces.Nature, 567(7747):209–212, 2019

    V ojtˇech Havlíˇcek, Antonio D Córcoles, Kristan Temme, Aram W Harrow, Abhinav Kandala, Jerry M Chow, and Jay M Gambetta. Supervised learning with quantum-enhanced feature spaces.Nature, 567(7747):209–212, 2019

    2019

  29. [29]

    Quantum machine learning in feature hilbert spaces.Physical review letters, 122(4):040504, 2019

    Maria Schuld and Nathan Killoran. Quantum machine learning in feature hilbert spaces.Physical review letters, 122(4):040504, 2019

    2019

  30. [30]

    Power of data in quantum machine learning.Nature communications, 12(1):2631, 2021

    Hsin-Yuan Huang, Michael Broughton, Masoud Mohseni, Ryan Babbush, Sergio Boixo, Hartmut Neven, and Jarrod R McClean. Power of data in quantum machine learning.Nature communications, 12(1):2631, 2021

    2021

  31. [31]

    Challenges and opportunities in quantum machine learning.Nature computational science, 2(9):567–576, 2022

    Marco Cerezo, Guillaume Verdon, Hsin-Yuan Huang, Lukasz Cincio, and Patrick J Coles. Challenges and opportunities in quantum machine learning.Nature computational science, 2(9):567–576, 2022

    2022

  32. [32]

    Covariant quantum kernels for data with group structure.Nature Physics, 20(3):479–483, 2024

    Jennifer R Glick, Tanvi P Gujarati, Antonio D Corcoles, Youngseok Kim, Abhinav Kandala, Jay M Gambetta, and Kristan Temme. Covariant quantum kernels for data with group structure.Nature Physics, 20(3):479–483, 2024

    2024

  33. [33]

    Quantum risk analysis.npj Quantum Information, 5(1):15, 2019

    Stefan Woerner and Daniel J Egger. Quantum risk analysis.npj Quantum Information, 5(1):15, 2019. 10

    2019

  34. [34]

    Quantum computing for finance: State-of-the-art and future prospects.IEEE Transactions on Quantum Engineering, 1:1–24, 2020

    Daniel J Egger, Claudio Gambella, Jakub Marecek, Scott McFaddin, Martin Mevissen, Rudy Raymond, Andrea Simonetto, Stefan Woerner, and Elena Yndurain. Quantum computing for finance: State-of-the-art and future prospects.IEEE Transactions on Quantum Engineering, 1:1–24, 2020

    2020

  35. [35]

    Option pricing using quantum computers.Quantum, 4:291, 2020

    Nikitas Stamatopoulos, Daniel J Egger, Yue Sun, Christa Zoufal, Raban Iten, Ning Shen, and Stefan Woerner. Option pricing using quantum computers.Quantum, 4:291, 2020

    2020

  36. [36]

    Credit risk analysis using quantum computers.IEEE transactions on computers, 70(12):2136–2145, 2020

    Daniel J Egger, Ricardo García Gutiérrez, Jordi Cahué Mestre, and Stefan Woerner. Credit risk analysis using quantum computers.IEEE transactions on computers, 70(12):2136–2145, 2020

    2020

  37. [37]

    Langeloh, V

    J.V .S Scursulim, G.M. Langeloh, V . L. Beltran, and et al. Multiclass portfolio optimization via variational quantum eigensolver with dicke state ansatz.Scientific Reports, 16(6208), 2026

    2026

  38. [38]

    Quantum computing in the nisq era and beyond.Quantum, 2:79, 2018

    John Preskill. Quantum computing in the nisq era and beyond.Quantum, 2:79, 2018

    2018

  39. [39]

    Extending the computational reach of a noisy superconducting quantum processor

    Abhinav Kandala, Kristan Temme, Antonio D Corcoles, Antonio Mezzacapo, Jerry M Chow, and Jay M Gam- betta. Extending the computational reach of a noisy superconducting quantum processor.arXiv preprint arXiv:1805.04492, 2018

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  40. [40]

    Digital zero noise extrapolation for quantum error mitigation

    Tudor Giurgica-Tiron, Yousef Hindy, Ryan LaRose, Andrea Mari, and William J Zeng. Digital zero noise extrapolation for quantum error mitigation. In2020 IEEE international conference on quantum computing and engineering (QCE), pages 306–316. IEEE, 2020

    2020

  41. [41]

    Scalable mitigation of measurement errors on quantum computers.PRX Quantum, 2(4):040326, 2021

    Paul D Nation, Hwajung Kang, Neereja Sundaresan, and Jay M Gambetta. Scalable mitigation of measurement errors on quantum computers.PRX Quantum, 2(4):040326, 2021

    2021

  42. [42]

    Model-free readout-error mitigation for quantum expectation values.Physical Review A, 105(3):032620, 2022

    Ewout Van Den Berg, Zlatko K Minev, and Kristan Temme. Model-free readout-error mitigation for quantum expectation values.Physical Review A, 105(3):032620, 2022

    2022

  43. [43]

    Filippov, M

    Sergei Filippov, Matea Leahy, Matteo AC Rossi, and Guillermo García-Pérez. Scalable tensor-network error mitigation for near-term quantum computing.arXiv preprint arXiv:2307.11740, 2023

    work page arXiv 2023

  44. [44]

    Probabilistic error cancellation with sparse pauli–lindblad models on noisy quantum processors.Nature physics, 19(8):1116–1121, 2023

    Ewout Van Den Berg, Zlatko K Minev, Abhinav Kandala, and Kristan Temme. Probabilistic error cancellation with sparse pauli–lindblad models on noisy quantum processors.Nature physics, 19(8):1116–1121, 2023

    2023

  45. [45]

    Scalable error mitigation for noisy quantum circuits produces competitive expectation values

    Youngseok Kim, Christopher J Wood, Theodore J Yoder, Seth T Merkel, Jay M Gambetta, Kristan Temme, and Abhinav Kandala. Scalable error mitigation for noisy quantum circuits produces competitive expectation values. Nature Physics, 19(5):752–759, 2023

    2023

  46. [46]

    Probabilistic error cancellation for dynamic quantum circuits.Physical Review A, 109(6):062617, 2024

    Riddhi S Gupta, Ewout Van Den Berg, Maika Takita, Diego Riste, Kristan Temme, and Abhinav Kandala. Probabilistic error cancellation for dynamic quantum circuits.Physical Review A, 109(6):062617, 2024

    2024

  47. [47]

    Eddins, M

    Andrew Eddins, Minh C Tran, and Patrick Rall. Lightcone shading for classically accelerated quantum error mitigation.arXiv preprint arXiv:2409.04401, 2024

    work page arXiv 2024

  48. [48]

    Improved quantum computation using operator backpropaga- tion.npj Quantum Information, 2026

    Bryce Fuller, Minh C Tran, Danylo Lykov, Caleb Johnson, Max Rossmannek, Ken Xuan Wei, Andre He, Youngseok Kim, DinhDuy Vu, Kunal Sharma, et al. Improved quantum computation using operator backpropaga- tion.npj Quantum Information, 2026

    2026

  49. [49]

    Optimizing the optimizer: decomposition techniques for quantum annealing.Quantum Machine Intelligence, 3(1):10, 2021

    Gideon Bass, Maxwell Henderson, Joshua Heath, and Joseph Dulny III. Optimizing the optimizer: decomposition techniques for quantum annealing.Quantum Machine Intelligence, 3(1):10, 2021

    2021

  50. [50]

    Variational quantum algorithms.Nature Reviews Physics, 3(9):625–644, 2021

    Marco Cerezo, Andrew Arrasmith, Ryan Babbush, Simon C Benjamin, Suguru Endo, Keisuke Fujii, Jarrod R McClean, Kosuke Mitarai, Xiao Yuan, Lukasz Cincio, et al. Variational quantum algorithms.Nature Reviews Physics, 3(9):625–644, 2021

    2021

  51. [51]

    A variational eigenvalue solver on a photonic quantum processor.Nature communications, 5(1):4213, 2014

    Alberto Peruzzo, Jarrod McClean, Peter Shadbolt, Man-Hong Yung, Xiao-Qi Zhou, Peter J Love, Alán Aspuru- Guzik, and Jeremy L O’brien. A variational eigenvalue solver on a photonic quantum processor.Nature communications, 5(1):4213, 2014

    2014

  52. [52]

    A Quantum Approximate Optimization Algorithm

    Edward Farhi, Jeffrey Goldstone, and Sam Gutmann. A quantum approximate optimization algorithm.arXiv preprint arXiv:1411.4028, 2014

    work page internal anchor Pith review Pith/arXiv arXiv 2014

  53. [53]

    Connecting ansatz expressibility to gradient magnitudes and barren plateaus.PRX quantum, 3(1):010313, 2022

    Zoë Holmes, Kunal Sharma, Marco Cerezo, and Patrick J Coles. Connecting ansatz expressibility to gradient magnitudes and barren plateaus.PRX quantum, 3(1):010313, 2022

    2022

  54. [54]

    Noise-induced barren plateaus in variational quantum algorithms.Nature communications, 12(1):6961, 2021

    Samson Wang, Enrico Fontana, Marco Cerezo, Kunal Sharma, Akira Sone, Lukasz Cincio, and Patrick J Coles. Noise-induced barren plateaus in variational quantum algorithms.Nature communications, 12(1):6961, 2021

    2021

  55. [55]

    Barren plateaus in variational quantum computing

    Martin Larocca, Supanut Thanasilp, Samson Wang, Kunal Sharma, Jacob Biamonte, Patrick J Coles, Lukasz Cincio, Jarrod R McClean, Zoë Holmes, and Marco Cerezo. Barren plateaus in variational quantum computing. Nature Reviews Physics, 7(4):174–189, 2025. 11

    2025

  56. [56]

    Challenges of variational quantum optimization with measurement shot noise.Physical Review A, 109(3):032408, 2024

    Giuseppe Scriva, Nikita Astrakhantsev, Sebastiano Pilati, and Guglielmo Mazzola. Challenges of variational quantum optimization with measurement shot noise.Physical Review A, 109(3):032408, 2024

    2024

  57. [57]

    Training variational quantum algorithms is np-hard.Physical review letters, 127(12):120502, 2021

    Lennart Bittel and Martin Kliesch. Training variational quantum algorithms is np-hard.Physical review letters, 127(12):120502, 2021

    2021

  58. [58]

    OUP Oxford, 2002

    Heinz-Peter Breuer and Francesco Petruccione.The theory of open quantum systems. OUP Oxford, 2002

    2002

  59. [59]

    Cambridge university press, 2010

    Michael A Nielsen and Isaac L Chuang.Quantum computation and quantum information. Cambridge university press, 2010

    2010

  60. [60]

    Variational quantum state eigensolver.npj Quantum Information, 8(1):113, 2022

    Marco Cerezo, Kunal Sharma, Andrew Arrasmith, and Patrick J Coles. Variational quantum state eigensolver.npj Quantum Information, 8(1):113, 2022

    2022

  61. [61]

    A universal variational quantum eigensolver for non-hermitian systems.Scientific Reports, 13(1):22313, 2023

    Huanfeng Zhao, Peng Zhang, and Tzu-Chieh Wei. A universal variational quantum eigensolver for non-hermitian systems.Scientific Reports, 13(1):22313, 2023

    2023

  62. [62]

    Hermitian-preserving ansatz and variational open quantum eigensolver.Physical Review A, 109(6):062608, 2024

    Zhong-Xia Shang. Hermitian-preserving ansatz and variational open quantum eigensolver.Physical Review A, 109(6):062608, 2024

    2024

  63. [63]

    Mixed state variational quantum eigensolver for the estimation of expectation values at finite temperature.arXiv preprint arXiv:2401.17194, 2024

    Giuseppe Clemente. Mixed state variational quantum eigensolver for the estimation of expectation values at finite temperature.arXiv preprint arXiv:2401.17194, 2024

    work page arXiv 2024

  64. [64]

    Feature selection on quantum computers.Quantum Machine Intelligence, 5(1):11, 2023

    Sascha Mücke, Raoul Heese, Sabine Müller, Moritz Wolter, and Nico Piatkowski. Feature selection on quantum computers.Quantum Machine Intelligence, 5(1):11, 2023

    2023

  65. [65]

    Financial risk management on a neutral atom quantum processor.Physical Review Research, 5(4):043117, 2023

    Lucas Leclerc, Luis Ortiz-Gutiérrez, Sebastián Grijalva, Boris Albrecht, Julia RK Cline, Vincent E Elfving, Adrien Signoles, Loïc Henriet, Gianni Del Bimbo, Usman Ayub Sheikh, et al. Financial risk management on a neutral atom quantum processor.Physical Review Research, 5(4):043117, 2023

    2023

  66. [66]

    Portfolio selection.The Journal of Finance, 7(1):77–91, 1952

    Harry Markowitz. Portfolio selection.The Journal of Finance, 7(1):77–91, 1952

    1952

  67. [67]

    Quantum bridge analytics i: a tutorial on formulating and using qubo models.Annals of Operations Research, 314(1):141–183, 2022

    Fred Glover, Gary Kochenberger, Rick Hennig, and Yu Du. Quantum bridge analytics i: a tutorial on formulating and using qubo models.Annals of Operations Research, 314(1):141–183, 2022

    2022

  68. [68]

    Ising formulations of many np problems.Frontiers in physics, 2:74887, 2014

    Andrew Lucas. Ising formulations of many np problems.Frontiers in physics, 2:74887, 2014

    2014

  69. [69]

    Cambridge university press, 2018

    David J Griffiths and Darrell F Schroeter.Introduction to quantum mechanics. Cambridge university press, 2018

    2018

  70. [70]

    Barry M Garraway. The dicke model in quantum optics: Dicke model revisited.Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 369(1939):1137–1155, 2011

    1939

  71. [71]

    Experimental realization of dicke states of up to six qubits for multiparty quantum networking

    Robert Prevedel, Gunther Cronenberg, Mark S Tame, Mauro Paternostro, Philip Walther, Mu-Seong Kim, and Anton Zeilinger. Experimental realization of dicke states of up to six qubits for multiparty quantum networking. Physical review letters, 103(2):020503, 2009

    2009

  72. [72]

    Multipartite entanglement and high-precision metrology.Physical Review A—Atomic, Molecular, and Optical Physics, 85(2):022322, 2012

    Géza Tóth. Multipartite entanglement and high-precision metrology.Physical Review A—Atomic, Molecular, and Optical Physics, 85(2):022322, 2012

    2012

  73. [73]

    Permutation-invariant quantum coding for quantum deletion channels

    Yingkai Ouyang. Permutation-invariant quantum coding for quantum deletion channels. In2021 IEEE Interna- tional Symposium on Information Theory (ISIT), pages 1499–1503. IEEE, 2021

    2021

  74. [74]

    Quantum storage in quantum ferromagnets.Physical Review B, 103(14):144417, 2021

    Yingkai Ouyang. Quantum storage in quantum ferromagnets.Physical Review B, 103(14):144417, 2021

    2021

  75. [75]

    Heralded linear optical generation of dicke states.New Journal of Physics, 28(5):054501, 2026

    Minhyeok Kang, Jaehee Kim, William J Munro, Seungbeom Chin, and Joonsuk Huh. Heralded linear optical generation of dicke states.New Journal of Physics, 28(5):054501, 2026

    2026

  76. [76]

    Variational quantum eigensolver with linear depth problem-inspired ansatz for solving portfolio optimization in finance.Science China Information Sciences, 68(8):180504, 2025

    Shengbin Wang, Peng Wang, Guihui Li, Shubin Zhao, Dongyi Zhao, Jing Wang, Yuan Fang, Menghan Dou, Yongjian Gu, Yu-Chun Wu, et al. Variational quantum eigensolver with linear depth problem-inspired ansatz for solving portfolio optimization in finance.Science China Information Sciences, 68(8):180504, 2025

    2025

  77. [77]

    Springer, 2007

    Maximilian Schlosshauer.Decoherence and the quantum-to-classical transition. Springer, 2007

    2007

  78. [78]

    Cambridge University Press, 2015

    Steven Weinberg.Lectures on quantum mechanics. Cambridge University Press, 2015

    2015

  79. [79]

    Alexander V Grayver and Alexey V Kuvshinov. Exploring equivalence domain in nonlinear inverse problems using covariance matrix adaption evolution strategy (cmaes) and random sampling.Geophysical Journal International, 205(2):971–987, 2016

    2016

  80. [80]

    A direct search optimization method that models the objective and constraint functions by linear interpolation

    Michael JD Powell. A direct search optimization method that models the objective and constraint functions by linear interpolation. InAdvances in optimization and numerical analysis, pages 51–67. Springer, 1994

    1994

Showing first 80 references.