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REVIEW 3 major objections 3 minor 64 references

RELISH: LLM REgression with a Latent Iterative State Head

T0 review · 3 major / 3 minor · reviewed 2026-07-13 · grok-4.5

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Pith's one-line read RELISH turns frozen LLM token features into accurate scalar predictions with a tiny iterative attention head, beating three standard families of text-regression methods.

desk verdict The supplied body is the wrong paper (QSP phase estimation, 2604.01205), so RELISH’s empirical claims cannot be audited from what we have. read the letter →

arxiv 2604.01206 v2 pith:TPFJB7IL submitted 2026-04-01 cs.CL cs.LG

Yiheng Su , Matthew Lease This is my paper · ORCID
classification cs.CLcs.LG
keywords textregressionlargelanguagemodelsparameter-efficientlearningcross-attentionheadfrozenbackbonescalarpredictionpredictive
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper argues that text regression with large language models should not treat numbers as text to decode or as many sampled generations to average. Instead, RELISH predicts a scalar directly from frozen LLM token representations by repeatedly refining a small learned latent state with cross-attention over those tokens, then mapping the final state with a linear regressor. Across six datasets, four backbones, and two training regimes, the method is claimed to outperform autoregressive decoding, regression-aware inference, and prior predictive heads while adding only about 3.4–3.7 million trainable parameters—roughly 0.01–0.04% overhead, far less than LoRA-style adapters that scale with model size. A sympathetic reader cares because it offers a path to strong numeric prediction from LLMs without expensive backbone fine-tuning or awkward number-as-text decoding.

What carries the argument

The Latent Iterative State Head: a small learned latent vector is refined over multiple steps by cross-attending to frozen token-level LLM representations; the final state is mapped to a scalar by a linear regressor.

What would settle it

On the paper’s six datasets and four frozen backbones, check whether RELISH’s error is consistently lower than strong baselines from autoregressive decoding, regression-aware inference, and existing predictive heads at the stated ~3.4–3.7M trainable-parameter budget; if not, or if gains vanish when the backbone stays frozen, the central claim fails.

Watch

Extended reading notes

Core claim

RELISH shows that iterative cross-attention refinement of a learned latent state over frozen LLM token representations, followed by a linear map, yields better text-regression accuracy than the main competing LLM regression families while remaining highly parameter-efficient on frozen backbones.

Load-bearing premise

The scalar target is already encoded well enough in frozen LLM token features that a small iterative attention head plus a linear map can recover accurate point estimates without training the backbone.

Editorial extensions

If this is right

  • Text regression can treat the LLM as a frozen feature encoder and put almost all trainable capacity in a lightweight head.
  • Number-as-text decoding and multi-sample aggregation are not required for competitive scalar prediction from LLMs.
  • Parameter overhead for regression can stay roughly constant (~3–4M) rather than growing with backbone size as LoRA does.
  • The same head design is claimed to transfer across multiple datasets, backbones, and two LLM training regimes.

Reading between the lines

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

  • If frozen features already carry the signal, similar iterative latent heads may help other continuous prediction tasks (ranking scores, risk, prices) without full fine-tuning.
  • Failure modes would concentrate where the target depends on information not linearly or attention-accessible in frozen last-layer tokens—e.g., rare numeric formats or deep multi-hop arithmetic.
  • A natural next test is whether deeper iteration or multi-layer latent states keep improving after the reported head size, or hit a plateau set by frozen representation quality.
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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

3 major / 3 minor

Summary. The submission is titled and abstracted as RELISH, a lightweight head for text regression that iteratively refines a learned latent state via cross-attention over frozen LLM token representations and maps the final state to a scalar with a linear regressor. The abstract claims consistent gains over three families of LLM regression methods (autoregressive decoding, regression-aware inference, and existing predictive heads) across six datasets, four LLM backbones, and two training regimes, with only ~3.4–3.7M trainable parameters (0.01–0.04% overhead) on frozen backbones—less than LoRA-based alternatives. The body supplied with the submission, however, is an entirely different manuscript: “Programmable Signal Design for Quantum Phase Estimation via Quantum Signal Processing” (arXiv:2604.01205, quant-ph), which develops QSP-based max–min signal design, a sensitivity-efficiency parameter κ, an iterative QSP-PE algorithm, and numerical comparisons to robust phase estimation. No RELISH architecture, equations, datasets, metrics, or ablations appear in the full text.

Significance. If the abstract’s claims for RELISH were supported by a matching manuscript—fair baselines, ablations of the iterative latent state, and reproducible parameter counts—the work would be of clear interest to the LLM regression and parameter-efficient adaptation communities: a frozen-backbone head with sub-0.05% overhead that beats both decoding-based and head-based families would be a useful practical contribution. That significance cannot be assessed from the materials provided, because the scientific content of the body is quantum phase estimation, not text regression. The QSP-PE paper itself is a coherent contribution in its own field, but it is not the paper under review as RELISH.

major comments (3)
  1. Title/abstract vs. full text: The abstract and paper_id identify RELISH (cs.CL, LLM text regression). The full manuscript is instead Programmable Signal Design for Quantum Phase Estimation via QSP (arXiv:2604.01205). There is no description of a latent iterative state head, cross-attention over token representations, linear regressor, six datasets, four LLM backbones, or the three baseline families. The central empirical claim of the abstract is therefore completely unsupported by the body and cannot be refereed.
  2. Unauditable architecture and efficiency claims: The abstract asserts ~3.4–3.7M trainable parameters (0.01–0.04% overhead) and superiority to LoRA (0.26–0.42%). The body contains no RELISH parameter table, latent dimension, iteration count, or training protocol on frozen LLMs. Without those sections, the parameter-efficiency and “consistently outperforms” claims are not checkable and cannot ground acceptance.
  3. Missing experimental evidence for the strongest claim: No tables, metrics, statistical tests, or ablations for text regression appear. The numerical figures and theorems in the body (e.g., κ vs. RPE, Theorem 1 on Heisenberg scaling, Algorithms 1/S1/S2) address quantum phase estimation, not LLM regression. A load-bearing evaluation of RELISH is impossible from this package.
minor comments (3)
  1. The abstract alone is clear and well written; if a correct RELISH manuscript is resubmitted, the abstract can largely stand with only standard tightening of claims to match tables.
  2. Code link https://github.com/SamSoup/RELISH is cited in the abstract but cannot substitute for a matching methods/results section in the journal submission.
  3. The attached QSP-PE manuscript has its own presentation issues (e.g., duplicate [42] notes, mixed figure encoding in Fig. 1 caption text) but those are irrelevant to a RELISH decision.

Circularity Check

0 steps flagged · score 0.0 of 10

No circular derivation in RELISH: available claims are empirical outperformance and parameter counts, not results forced by definition or self-citation.

full rationale

Only the RELISH abstract is available for the claimed paper (arXiv:2604.01206); the supplied full manuscript body is a different work (QSP phase estimation, arXiv:2604.01205) and cannot be used as RELISH’s derivation chain. Within the RELISH abstract, the central claims are empirical—consistent gains over three LLM-regression families across six datasets, four backbones, and two regimes, plus a stated trainable-parameter overhead (~3.4–3.7M; 0.01–0.04%) versus LoRA. There is no equation that defines a quantity in terms of the quantity it purports to predict, no fitted parameter re-labeled as a first-principles prediction, no uniqueness theorem imported from overlapping authors, and no ansatz smuggled in via self-citation. The architecture description (iterative latent state refined by cross-attention over frozen token representations, then a linear map) is a design choice, not a circular identity. Circularity burden is therefore zero on the material that can be audited; missing method/tables is an evidence gap, not circularity.

Assumptions & free parameters 1 free parameters · 3 assumptions · 1 invented entities

Abstract-only review of RELISH. Load-bearing premises are standard ML practice plus the architectural bet that frozen token features + iterative latent cross-attention suffice for scalar regression. No free parameters or invented physical entities appear in the abstract; training hyperparameters and dataset choices would be free parameters in a full paper but are not specified here.

free parameters (1)
  • Trainable head size / latent dimension and iteration count (unspecified)
    Abstract reports ~3.4–3.7M trainable parameters but does not fix latent width, number of refinement steps, or other head hyperparameters that determine capacity and the reported overhead.
assumptions (3)
  • domain assumption Frozen LLM token-level representations contain usable information for continuous targets without updating backbone weights.
    Central to the frozen-backbone design claimed in the abstract.
  • ad hoc to paper Cross-attention iterative refinement of a latent state plus a linear map is an adequate inductive bias for text regression.
    This is the paper’s architectural postulate; success is empirical, not derived from a theorem in the abstract.
  • domain assumption Standard supervised regression evaluation on the (unnamed in abstract detail) six datasets is a fair comparison across the three baseline families.
    Outperformance claims rest on that experimental protocol, which is not inspectable here.
invented entities (1)
  • RELISH latent iterative state head
    purpose: Map frozen LLM token representations to scalar predictions via iterative cross-attention state refinement and a linear regressor.
    The named architecture is the paper’s main construct; independent evidence would be external replications or theory, not provided in the abstract.

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Cite this review

Pith. "Pith review of RELISH: LLM REgression with a Latent Iterative State Head." pith.science (2026). https://pith.science/paper/TPFJB7IL

@misc{pith2026260401206,
  author       = {Pith},
  title        = {Pith review of: RELISH: LLM REgression with a Latent Iterative State Head},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/TPFJB7IL}},
  note         = {Machine review of arXiv:2604.01206}
}
abstract

We present RELISH (REgression with a Latent Iterative State Head), a novel, lightweight architecture designed for text regression with large language models. Rather than decoding numeric targets as text or aggregating multiple generated outputs, RELISH predicts scalar values directly from frozen LLM representations by iteratively refining a learned latent state through cross-attention over token-level representations, and then mapping the final state to a point estimate with a linear regressor. Across six datasets, four LLM backbones, and two LLM training regimes, RELISH consistently outperforms prior baselines from all three major LLM regression families, including autoregressive decoding, regression-aware inference, and existing predictive head methods. Despite these gains, RELISH remains highly parameter-efficient, requiring only $\sim$3.4-3.7M trainable parameters across frozen LLM backbones (only 0.01-0.04$\%$ additional overhead), far less than LoRA-based alternatives that grow with model size (0.26-0.42$\%$). Our code is available at https://github.com/SamSoup/RELISH.

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

64 extracted references · 8 canonical work pages

  1. [1]

    (b) End-to-end signal programming framework

    In contrast, QSP enables programmable signal transformations, allowing the signal to be tailored to a lo- cal confidence interval and achieving near-optimal sensitivity κ≈1. (b) End-to-end signal programming framework. Start- ing from a current estimate, the method designs an optimal signal by solving a max-min problem, implements it using a QSP circuit, ...

  2. [2]

    By contrast, the versatility of QSP-based signals enables substantially larger uniform slope over the same interval, leading to higher sensitivity efficiency and improved constant factors in estimation precision. III. ALGORITHM AND PERFORMANCE GUARANTEE We develop an iterative phase estimation procedure based on progressive refinement of both the estimato...

  3. [3]

    (c) Minimum derivative lower boundLas a function of query depthd, evaluated at three target phasesθ∈ {0.32,0.80,1.25} and shrinkage factorsζ∈ {1,2,5}

    (b) Sensitivity efficiencyκas a function of shrinkage factorζ.κincreases monotonically withζ, and this improvement is uniform across all target phasesθ 0. (c) Minimum derivative lower boundLas a function of query depthd, evaluated at three target phasesθ∈ {0.32,0.80,1.25} and shrinkage factorsζ∈ {1,2,5}. For each combination ofθ andζ,Lis plotted againstda...

  4. [4]

    (c) Optimized signal functionsf(θ) of QSP-PE (top) and RPE (bottom), with their corresponding Fourier mode decompositions shown at the lower right

    At each depth, QSP-PE estimates are more tightly concentrated aroundθ ⋆, directly accounting for the lower MSE observed in (a). (c) Optimized signal functionsf(θ) of QSP-PE (top) and RPE (bottom), with their corresponding Fourier mode decompositions shown at the lower right. The QSP-PE signal achieves near-optimal sensitivity efficiencyκ= 0.915 and is con...

  5. [5]

    Bardin, Rami Barends, Andreas Bengts- son, Sergio Boixo, Michael Broughton, Bob B

    Frank Arute, Kunal Arya, Ryan Babbush, Dave Ba- con, Joseph C. Bardin, Rami Barends, Andreas Bengts- son, Sergio Boixo, Michael Broughton, Bob B. Buck- ley, David A. Buell, Brian Burkett, Nicholas Bush- nell, Yu Chen, Zijun Chen, Yu-An Chen, Ben Chiaro, Roberto Collins, Stephen J. Cotton, William Court- ney, Sean Demura, Alan Derk, Andrew Dunsworth, Danie...

    arXiv 2020

  6. [6]

    Simulated quantum computa- tion of molecular energies.Science, 309(5741):1704–1707, 2005

    Al´ an Aspuru-Guzik, Anthony D Dutoi, Peter J Love, and Martin Head-Gordon. Simulated quantum computa- tion of molecular energies.Science, 309(5741):1704–1707, 2005

    2005

  7. [7]

    Achiev- ing Heisenberg scaling with maximally entangled states: An analytic upper bound for the attainable root-mean- square error.Physical Review A, 102(4):042613, October

    Federico Belliardo and Vittorio Giovannetti. Achiev- ing Heisenberg scaling with maximally entangled states: An analytic upper bound for the attainable root-mean- square error.Physical Review A, 102(4):042613, October

  8. [8]

    URLhttps: //link.aps.org/doi/10.1103/PhysRevA.102.042613

    doi:10.1103/PhysRevA.102.042613. URLhttps: //link.aps.org/doi/10.1103/PhysRevA.102.042613

    work page doi:10.1103/physreva.102.042613

Show all 64 references
  1. [9]

    D. W. Berry, B. L. Higgins, S. D. Bartlett, M. W. Mitchell, G. J. Pryde, and H. M. Wiseman. How to perform the most accurate possible phase measurements. Physical Review A, 80(5):052114, November 2009. doi: 10.1103/PhysRevA.80.052114. URLhttps://link.aps. org/doi/10.1103/PhysR...

    2009 doi

  2. [10]

    Cambridge university press, 2004

    Stephen Boyd and Lieven Vandenberghe.Convex opti- mization. Cambridge university press, 2004

    2004

  3. [11]

    Childs, Yuan Su, Minh C

    Andrew M. Childs, Yuan Su, Minh C. Tran, Nathan Wiebe, and Shuchen Zhu. Theory of Trotter Error with Commutator Scaling.Physi- cal Review X, 11(1):011020, February 2021. doi: 10.1103/PhysRevX.11.011020. URLhttps://link.aps. org/doi/10.1103/PhysRevX.11.011020

    2021 doi

  4. [12]

    Cortes and Stephen K

    Cristian L. Cortes and Stephen K. Gray. Quantum Krylov subspace algorithms for ground- and excited-state energy estimation.Physical Review A, 105(2):022417, February 2022. doi:10.1103/PhysRevA.105.022417. URLhttps://link.aps.org/doi/10.1103/PhysRevA. 105.022417

    2022 doi

  5. [13]

    Even Shorter Quantum Circuit for Phase Estimation on Early Fault-Tolerant Quantum Computers with Applications to Ground-State Energy Estimation.PRX Quantum, 4(2):020331, May 2023

    Zhiyan Ding and Lin Lin. Even Shorter Quantum Circuit for Phase Estimation on Early Fault-Tolerant Quantum Computers with Applications to Ground-State Energy Estimation.PRX Quantum, 4(2):020331, May 2023. doi: 10.1103/PRXQuantum.4.020331. URLhttps://link. aps.org/doi/10.1103/P...

    2023 doi

  6. [14]

    Multi-level quantum signal processing with applications to ground state preparation using fast-forwarded Hamiltonian evolution, June 2024

    Yulong Dong and Lin Lin. Multi-level quantum signal processing with applications to ground state preparation using fast-forwarded Hamiltonian evolution, June 2024. URLhttp://arxiv.org/abs/2406.02086. arXiv:2406.02086 [quant-ph]

    2024 arXiv

  7. [15]

    Birgitta Whaley, and Lin Lin

    Yulong Dong, Xiang Meng, K. Birgitta Whaley, and Lin Lin. Efficient phase-factor evaluation in quantum sig- nal processing.Physical Review A, 103(4):042419, April

  8. [16]

    URLhttps: //link.aps.org/doi/10.1103/PhysRevA.103.042419

    doi:10.1103/PhysRevA.103.042419. URLhttps: //link.aps.org/doi/10.1103/PhysRevA.103.042419

    doi

  9. [17]

    Yulong Dong, Lin Lin, and Yu Tong. Ground-State Preparation and Energy Estimation on Early Fault- Tolerant Quantum Computers via Quantum Eigenvalue Transformation of Unitary Matrices.PRX Quantum, 3(4):040305, October 2022. ISSN 2691-3399. doi: 10.1103/PRXQuantum.3.040305. URLh...

    2022 doi

  10. [18]

    Gross, and Murphy Yuezhen Niu

    Yulong Dong, Jonathan A. Gross, and Murphy Yuezhen Niu. Optimal low-depth quantum signal-processing phase estimation.Nature Communications, 16(1):1504, February 2025. ISSN 2041-1723. doi:10.1038/s41467- 025-56724-x. URLhttps://www.nature.com/articles/ s41467-025-56724-x

    2025 doi

  11. [19]

    Mueller, and Juan Miguel Arrazola

    Stepan Fomichev, Kasra Hejazi, Modjtaba Shokrian Zini, Matthew Kiser, Joana Fraxanet, Pablo Anto- nio Moreno Casares, Alain Delgado, Joonsuk Huh, Arne-Christian Voigt, Jonathan E. Mueller, and Juan Miguel Arrazola. Initial State Preparation for Quantum Chemistry on Quantum Com...

    2024 doi

  12. [20]

    Quantum singular value transformation and be- yond: exponential improvements for quantum matrix arithmetics

    Andr´ as Gily´ en, Yuan Su, Guang Hao Low, and Nathan Wiebe. Quantum singular value transformation and be- yond: exponential improvements for quantum matrix arithmetics. InProceedings of the 51st Annual ACM SIGACT Symposium on Theory of Computing, pages 193–204, June 2019. doi...

    2019 doi

  13. [21]

    Quantum Metrology.Physical Re- view Letters, 96(1):010401, January 2006

    Vittorio Giovannetti, Seth Lloyd, and Lorenzo Maccone. Quantum Metrology.Physical Re- view Letters, 96(1):010401, January 2006. doi: 10.1103/PhysRevLett.96.010401. URLhttps:// link.aps.org/doi/10.1103/PhysRevLett.96.010401

    2006 doi

  14. [22]

    Advances in quantum metrology.Nature Pho- tonics, 5(4):222–229, April 2011

    Vittorio Giovannetti, Seth Lloyd, and Lorenzo Mac- cone. Advances in quantum metrology.Nature Pho- tonics, 5(4):222–229, April 2011. ISSN 1749-4893. doi: 10.1038/nphoton.2011.35. URLhttps://www.nature. com/articles/nphoton.2011.35

    2011 doi

  15. [23]

    Gurobi Optimizer Reference Manual, 2026

    Gurobi Optimization, LLC. Gurobi Optimizer Reference Manual, 2026. URLhttps://www.gurobi.com

    2026

  16. [24]

    Wiseman, and Dominic W

    Wojciech G´ orecki, Rafa l Demkowicz-Dobrza´ nski, Howard M. Wiseman, and Dominic W. Berry. $\ensuremath{\pi}$-Corrected Heisenberg Limit. Physical Review Letters, 124(3):030501, January 2020. doi:10.1103/PhysRevLett.124.030501. URLhttps:// link.aps.org/doi/10.1103/PhysRevLett...

    2020 doi

  17. [25]

    Erenay Karacan, Yanbin Chen, and Christian B. Mendl. Enhancing Scalability of Quantum Eigenvalue Transfor- mation of Unitary Matrices for Ground State Prepa- ration through Adaptive Finer Filtering.Quantum, 9:1624, February 2025. doi:10.22331/q-2025-02-06-

    2025 doi

  18. [26]

    URLhttps://quantum-journal.org/papers/ q-2025-02-06-1624/

    2025

  19. [27]

    Shelby Kimmel, Guang Hao Low, and Theodore J. Yoder. Robust calibration of a universal single- qubit gate set via robust phase estimation.Phys- ical Review A, 92(6):062315, December 2015. doi: 10.1103/PhysRevA.92.062315. URLhttps://link.aps. org/doi/10.1103/PhysRevA.92.062315

    2015 doi

  20. [28]

    Emanuel Knill, Gerardo Ortiz, and Rolando D. Somma. Optimal quantum measurements of expectation values of observables.Physical Review A, 75(1):012328, January

  21. [29]

    URLhttps: //link.aps.org/doi/10.1103/PhysRevA.75.012328

    doi:10.1103/PhysRevA.75.012328. URLhttps: //link.aps.org/doi/10.1103/PhysRevA.75.012328

    doi

  22. [30]

    Bernstein–szeg˝ o inequality for trigonometric polynomials inL p, 0≤p≤ ∞, with the 7 classical value of the best constant.Journal of Approxi- mation Theory, 276:105713, 2022

    Anastasiya O Leont’eva. Bernstein–szeg˝ o inequality for trigonometric polynomials inL p, 0≤p≤ ∞, with the 7 classical value of the best constant.Journal of Approxi- mation Theory, 276:105713, 2022

    2022

  23. [31]

    Guang Hao Low and Isaac L. Chuang. Optimal Hamiltonian Simulation by Quantum Signal Process- ing.Physical Review Letters, 118(1):010501, Jan- uary 2017. ISSN 0031-9007, 1079-7114. doi: 10.1103/PhysRevLett.118.010501. URLhttps://link. aps.org/doi/10.1103/PhysRevLett.118.010501

    2017 doi

  24. [32]

    Guang Hao Low and Isaac L. Chuang. Hamiltonian Simulation by Qubitization.Quantum, 3:163, July

  25. [33]

    URLhttps:// quantum-journal.org/papers/q-2019-07-12-163/

    doi:10.22331/q-2019-07-12-163. URLhttps:// quantum-journal.org/papers/q-2019-07-12-163/

    2019 doi

  26. [34]

    Yoder, and Isaac L

    Guang Hao Low, Theodore J. Yoder, and Isaac L. Chuang. Methodology of Resonant Equiangular Com- posite Quantum Gates.Physical Review X, 6(4):041067, December 2016. doi:10.1103/PhysRevX.6.041067. URL https://link.aps.org/doi/10.1103/PhysRevX.6. 041067

    2016 doi

  27. [35]

    Rab, Giorgio Milani, Nicol` o Spagnolo, Nathan Wiebe, and Fabio Sciarrino

    Alessandro Lumino, Emanuele Polino, Adil S. Rab, Giorgio Milani, Nicol` o Spagnolo, Nathan Wiebe, and Fabio Sciarrino. Experimental Phase Esti- mation Enhanced by Machine Learning.Physi- cal Review Applied, 10(4):044033, October 2018. doi:10.1103/PhysRevApplied.10.044033. URL ...

    2018 doi

  28. [36]

    Encoded Quantum Signal Processing for Heisenberg- Limited Metrology, March 2026

    Carlos Ortiz Marrero, Rui Jie Tang, and Nathan Wiebe. Encoded Quantum Signal Processing for Heisenberg- Limited Metrology, March 2026. URLhttps://arxiv. org/abs/2603.22798v1

    2026

  29. [37]

    Martyn, Zane M

    John M. Martyn, Zane M. Rossi, Andrew K. Tan, and Isaac L. Chuang. Grand Unification of Quantum Algorithms.PRX Quantum, 2(4):040203, December

  30. [38]

    URLhttps: //link.aps.org/doi/10.1103/PRXQuantum.2.040203

    doi:10.1103/PRXQuantum.2.040203. URLhttps: //link.aps.org/doi/10.1103/PRXQuantum.2.040203

    doi

  31. [39]

    Generalized Quantum Signal Processing.PRX Quantum, 5 (2):020368, June 2024

    Danial Motlagh and Nathan Wiebe. Generalized Quantum Signal Processing.PRX Quantum, 5 (2):020368, June 2024. ISSN 2691-3399. doi: 10.1103/PRXQuantum.5.020368. URLhttps://link. aps.org/doi/10.1103/PRXQuantum.5.020368

    2024 doi

  32. [40]

    Neill, T

    C. Neill, T. McCourt, X. Mi, Z. Jiang, M. Y. Niu, W. Mruczkiewicz, I. Aleiner, F. Arute, K. Arya, J. Ata- laya, R. Babbush, J. C. Bardin, R. Barends, A. Bengts- son, A. Bourassa, M. Broughton, B. B. Buckley, D. A. Buell, B. Burkett, N. Bushnell, J. Campero, Z. Chen, B. Chiaro,...

    2021 doi

  33. [41]

    On low- depth algorithms for quantum phase estimation.Quan- tum, 7:1165, November 2023

    Hongkang Ni, Haoya Li, and Lexing Ying. On low- depth algorithms for quantum phase estimation.Quan- tum, 7:1165, November 2023. doi:10.22331/q-2023-11- 06-1165. URLhttps://quantum-journal.org/papers/ q-2023-11-06-1165/

    2023 doi

  34. [42]

    Note1.https://github.com/dongsnaq/ QPE-Phase-Estimation

  35. [43]

    O’Brien, Stefano Polla, Nicholas C

    Thomas E. O’Brien, Stefano Polla, Nicholas C. Rubin, William J. Huggins, Sam McArdle, Ser- gio Boixo, Jarrod R. McClean, and Ryan Bab- bush. Error Mitigation via Verified Phase Estima- tion.PRX Quantum, 2(2):020317, May 2021. doi: 10.1103/PRXQuantum.2.020317. URLhttps://link. ...

    2021 doi

  36. [44]

    QSPPACK: Quantum Signal Process- ing Package

    QSPPACK Team. QSPPACK: Quantum Signal Process- ing Package. User Manual:https://qsppack.gitbook. io/qsppack. GitHub Repository:https://github.com/ qsppack/qsppack

  37. [45]

    Yelin, and Roel Van Beeumen

    Yizhi Shen, Alex Buzali, Hong-Ye Hu, Katherine Klymko, Daan Camps, Susanne F. Yelin, and Roel Van Beeumen. Efficient Measurement-Driven Eigenen- ergy Estimation with Classical Shadows.PRX Quantum, 7(1):010328, February 2026. doi:10.1103/74s6-3jsz. URL https://link.aps.org/doi/...

    2026 doi

  38. [46]

    M. D. Shulman, S. P. Harvey, J. M. Nichol, S. D. Bartlett, A. C. Doherty, V. Umansky, and A. Yacoby. Suppress- ing qubit dephasing using real-time Hamiltonian esti- mation.Nature Communications, 5(1):5156, October

  39. [47]

    doi:10.1038/ncomms6156

    ISSN 2041-1723. doi:10.1038/ncomms6156. URL https://www.nature.com/articles/ncomms6156

    doi

  40. [48]

    Stair, Cristian L

    Nicholas H. Stair, Cristian L. Cortes, Robert M. Par- rish, Jeffrey Cohn, and Mario Motta. Stochastic quan- tum Krylov protocol with double-factorized Hamiltoni- ans.Physical Review A, 107(3):032414, March 2023. doi:10.1103/PhysRevA.107.032414. URLhttps://link. aps.org/doi/10....

    2023 doi

  41. [49]

    On the en- ergy landscape of symmetric quantum signal process- ing.Quantum, 6:850, November 2022

    Jiasu Wang, Yulong Dong, and Lin Lin. On the en- ergy landscape of symmetric quantum signal process- ing.Quantum, 6:850, November 2022. doi:10.22331/q- 2022-11-03-850. URLhttps://quantum-journal.org/ papers/q-2022-11-03-850/

    2022 doi

  42. [50]

    Efficient Bayesian Phase Estimation.Physical Re- view Letters, 117(1):010503, June 2016

    Nathan Wiebe and Chris Granade. Efficient Bayesian Phase Estimation.Physical Re- view Letters, 117(1):010503, June 2016. doi: 10.1103/PhysRevLett.117.010503. URLhttps:// link.aps.org/doi/10.1103/PhysRevLett.117.010503

    2016 doi

  43. [51]

    Demonstrating Bayesian quan- tum phase estimation with quantum error detection

    Kentaro Yamamoto, Samuel Duffield, Yuta Kikuchi, and David Mu˜ noz Ramo. Demonstrating Bayesian quan- tum phase estimation with quantum error detection. Physical Review Research, 6(1):013221, February 2024. doi:10.1103/PhysRevResearch.6.013221. URLhttps: //link.aps.org/doi/10....

    2024 doi

  44. [52]

    Dreiling, Dan Gresh, Cameron Foltz, Michael Mills, Steven A

    Kentaro Yamamoto, Yuta Kikuchi, David Amaro, Ben Criger, Silas Dilkes, Ciar´ an Ryan-Anderson, Andrew Tranter, Joan M. Dreiling, Dan Gresh, Cameron Foltz, Michael Mills, Steven A. Moses, Peter E. Siegfried, Maxwell D. Urmey, Justin J. Burau, Aaron Hankin, Do- minic Lucchetti, ...

    2025 arXiv

  45. [53]

    Note1.https://github.com/dongsnaq/ QPE-Phase-Estimation. Supplementary Material for Programmable Signal Design for Quantum Phase Estimation via Quantum Signal Processing Zikang Jia,1 Suying Liu,2,3, and Yulong Dong4 1Department of Mathematics, University of Michigan, Ann Arbor...

    2026

  46. [54]

    1, are based on the Hadamard test

    Hadamard-test-based quantum phase estimation and its signal representation Standard methods for quantum phase estimation (QPE), as illustrated by the circuit in Fig. 1, are based on the Hadamard test. In this construction, repeated queries to the Hamiltonian time-evolution ope...

  47. [55]

    As a result, a constant gap from the optimal value is preserved due to the use of a fixed complementary signal pair

    More importantly, the signal family itself is fixed throughout the iterative estimation process, so prior information from earlier stages is not used to adapt the signal. As a result, a constant gap from the optimal value is preserved due to the use of a fixed complementary si...

  48. [56]

    The algorithm interleaves oracles to the Hamiltonian with a sequence of phase-modulation gates whose angles encode the desired transformation

    Transformation functions of quantum signal processing based phase estimation (QSP-PE) QSP is a powerful quantum algorithmic primitive for performing universal function transformations of an input Hamiltonian [14, 23, 28]. The algorithm interleaves oracles to the Hamiltonian wi...

  49. [57]

    Signal class and problem formulation of QSP-PE As stated in Theorem 3, the corresponding signal class consists of cosine transforms with definite parity, given by bounded trigonometric polynomials. This can be equivalently written as follows Gd := ( g(θ) = dX k=0 ak cos(kθ) :a...

  50. [58]

    (S15) is formulated as a max-min optimization over the admissible signal class Fd

    Structure of the optimal design problem The optimal design principle in Eq. (S15) is formulated as a max-min optimization over the admissible signal class Fd. Since any admissible signal is the square of a transformation functiong∈ G d, the derivative offadmits a special struc...

  51. [59]

    One can then enforce a uniformly lower bounded sensitivity by imposing inequality constraints on a dense set of sampled points inI

    Relaxed optimization reformulation A brute-force way to tackle the optimal design principle in Theorem 5 is to parametrize the transformation function gby its Fourier coefficients. One can then enforce a uniformly lower bounded sensitivity by imposing inequality constraints on...

  52. [60]

    We demonstrate that the optimal signal is attained over a bounded confidence interval, as shown in Fig

    Numerical results of optimal signal design In this section, we numerically evaluate the performance of optimal signals constructed via the design principle in Algorithm S1. We demonstrate that the optimal signal is attained over a bounded confidence interval, as shown in Fig. ...

  53. [61]

    The procedure iteratively refines a confidence interval forθestimation using optimized signals with bounded derivatives and resource-aware confidence updates

    Iterative refinement scheme We consider an adaptive iterative estimator for a parameterθunder a resource schedule{(d k, mk)}k≥0, whered k is the query depth andm k is the number of measurement shots at stepk. The procedure iteratively refines a confidence interval forθestimati...

  54. [62]

    Therefore, estimating the unknown parameter by inverting the measurement outcome is 11 straightforward: we can recoverθby locating the intersection point on the signal curve

    Classical post-processing One important feature of our designed signal function is that it has a uniformly lower-bounded derivative on the confidence interval. Therefore, estimating the unknown parameter by inverting the measurement outcome is 11 straightforward: we can recove...

  55. [63]

    As a result, the total quantum resource cost is dominated by the final step, which suggests the optimal Heisenberg-limited scaling

    Heisenberg-limited quantum resource cost Recall that the depth schedule of our quantum algorithm is a geometric sequence. As a result, the total quantum resource cost is dominated by the final step, which suggests the optimal Heisenberg-limited scaling. In this subsection, we ...

  56. [64]

    As shown in Theorem 10, each post-processing step requires a total number of basic floating-point operations that scales linearly with the depth parameter

    Classical computational cost of post-processing Thanks to the local monotonicity of the signal function, the classical post-processing can be carried out efficiently via bisection method. As shown in Theorem 10, each post-processing step requires a total number of basic floati...

Pith tools

Reviewed July 13, 2026 · model on record in the stance chip above.