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REVIEW 3 major objections 4 minor 76 references

Perspectives on Utilization of Measurements in Quantum Algorithms

T0 review · 3 major / 4 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read This review argues that measurement is an active, first-class component of quantum algorithm design, not a passive readout step, and that the coming generation of error-prone quantum algorithms will hinge on sophisticated measurement…

desk verdict A useful taxonomy of measurement roles in quantum algorithms, but the sweeping claim that measurement is neglected does not survive its own scope choice. read the letter →

arxiv 2507.04325 v1 pith:GPADB6W4 submitted 2025-07-06 quant-ph

Valter Uotila , Ilmo Salmenperä , Leo Becker , Arianne Meijer - van de Griend , Aakash Ravindra Shinde , Jukka K. Nurminen This is my paper
classification quant-ph MSC 81P1581P6868Q12 PACS 03.65.Ta03.67.-a
keywords quantummeasurementPOVMmid-circuitdynamiccircuitscircuitcuttingerrormitigationbarrenplateausvariationalalgorithms
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper tries to shift how quantum algorithm designers think about measurement: instead of a final readout step, measurement is an active operation that can encode problem structure, modify the quantum state mid-circuit, and solve hardware challenges. The authors organize measurement use into three categories—static circuits, dynamic circuits, and measurement schemes aimed at quantum computing's own problems—and review concrete algorithms in each. Their central message is that measurement design deserves attention at every level of algorithm development because the most novel and error-prone quantum algorithms will likely require sophisticated measurement schemes. A sympathetic reader finishes with a map of where measurements already carry computational weight and where they are still treated as an afterthought.

What carries the argument

The organizing device is a three-way classification of measurement roles—static, dynamic, and challenge-driven. Its technical workhorses are projective (PVM) measurements, POVM measurements (including informationally complete and SIC-POVMs), and mid-circuit measurements, which the paper models as quantum instruments that return both a classical outcome and a transformed quantum state. These tools carry the argument: PVMs define observables that encode problem structure, IC-POVMs make state reconstruction and noise cancellation possible through formulas like $\rho = \sum_k \mathrm{Tr}(\rho E_k) D_k$, and quasiprobability decompositions such as $U = \sum_i a_i F_i$ let circuit cutting simulate nonlocal gates with local measurements.

What would settle it

A systematic survey of quantum algorithm papers from the last three years that counts how often a new algorithm's design depends on mid-circuit or adaptive measurements would settle the claim; if most novel algorithms already treat measurement as a central design element, the paper's central message would be wrong.

Watch

Extended reading notes

Core claim

The review's core claim is that measurement is not just a passive way to read out a quantum computation; it is an active component that shapes what a quantum device can compute. The evidence is organized around three roles: in static circuits, measurements deliver the result but also encode the optimization objective (as in QAOA and VQE) and can themselves induce barren plateaus when the measured observable is global; in dynamic circuits, mid-circuit measurements can reduce circuit depth, enable state preparation and teleportation, and turn a static QFT into a shallow classically controlled routine; and for hardware challenges, measurement-based schemes such as wire and gate cutting and tensor-network error mitigation use projective and informationally complete measurements to make near-term devices more capable. If the claim is right, future algorithm designers should treat measurement-scheme design as a first-class task alongside gate design.

Load-bearing premise

The review's sample of measurement applications is representative enough of quantum algorithm design that the observed neglect of measurement is real, rather than a side effect of the subfields the authors chose to survey.

Editorial extensions

If this is right

  • Quantum algorithm development should include measurement-scheme design as a first-class task, on par with designing gates and state preparation.
  • Mid-circuit measurements can make circuits dramatically shallower: the quantum Fourier transform drops from $O(n^2)$ two-qubit gates to $O(n)$ classically controlled single-qubit operations.
  • Classical communication between circuit cuts lowers sampling overhead, reducing wire cutting from $4^{2n}$ to $(2^{n+1}-1)^2$ and gate cutting from $9^n$ to $4^n$ for CNOT gates.
  • Measurement choice is a trainability factor: global observables create barren plateaus even in simple, non-entangling variational circuits.
  • Informationally complete POVMs followed by tensor-network postprocessing form an error-mitigation layer that can extend the reach of noisy hardware.

Reading between the lines

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

  • A consequence the authors do not spell out: if measurement design is a real algorithmic resource, then quantum compilation should treat mid-circuit measurements and measurement shots as costs in their own right, leading to measurement-aware optimization of circuits.
  • The review leaves out or barely touches measurement-based quantum computing, magic-state injection, and fully adaptive circuits; those areas already put measurement at the center, so a wider net might soften the claim that measurements are neglected.
  • A concrete testable extension is to vary measurement bases or measurement locations in a fixed variational quantum machine learning circuit and compare learning curves, turning measurement choice into an explicit hyperparameter.
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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 / 4 minor

Summary. This paper is a review/perspective on the role of measurement operations in quantum algorithms. It introduces basic measurement theory (PVMs, POVMs, SIC-POVMs, mid-circuit measurements), proposes a three-part taxonomy of measurement uses—static circuits, dynamic circuits, and measurement-based solutions to NISQ challenges—and surveys applications including variational algorithms, barren plateaus, learned measurements, state preparation, teleportation, circuit cutting, and error mitigation. The paper's central message is that measurement is often treated as a passive final readout, but should instead be considered an active, first-class component of quantum algorithm design.

Significance. If the central claim were properly scoped, the paper would be a useful organizational and pedagogical contribution: the static/dynamic/challenges taxonomy is intuitive, and the survey collects many relevant applications in one place. The paper does not introduce new derivations, fitting loops, or self-referential claims, so there is no circularity concern; the sole self-citation ([52]) is peripheral. Its main value is as a perspective piece that may help researchers think about measurement design earlier in algorithm development. However, the breadth of the central normative claim is not currently supported by the evidence presented, and one core theoretical example contains a mathematical error, so the paper needs revision before it can be recommended for publication.

major comments (3)
  1. [Abstract and Section I] The central claim that 'measurement operations are frequently not at the center of the quantum algorithm design' is not supported by the evidence presented, because the review is built on a 'selected set' of applications collected without stated inclusion criteria, and it omits the most measurement-centric paradigms. Measurement-based quantum computing is mentioned only in passing in Section IV-B, fault-tolerant magic-state injection appears only through references [68]–[71] in Section V-A2, and adaptive circuits appear only as a state-preparation example ([48]). In MBQC and in teleportation-based fault tolerance, measurement is the primary computational resource rather than a final readout, so these omissions make the asserted neglect an artifact of the chosen variational/NISQ/distributed subfields. The authors should either explicitly restrict the claim (for example, to variational and NISQ-era algorithm design) or extend the review to cover measurement-centric paradigms so that the field-level conclusion is supported.
  2. [Section II-B1] The single-qubit SIC-POVM example is mathematically incorrect as printed. The text says that four operators are defined, but the first entry is written as the ket |0⟩ rather than an operator, the label E2 is repeated, no E4 appears, and the operators are not normalized so that they satisfy the stated SIC condition Tr(E_i E_j)=1/(d+1) (in fact, for a proper qubit SIC-POVM one needs E_i=(1/2)|ψ_i⟩⟨ψ_i|, giving Tr(E_i E_j)=1/12, not 1/3). Because this example is used to illustrate informationally complete POVMs, a core concept of the background section, it should be corrected before publication.
  3. [Figure 2 and Section III-B3] The original numerical experiment in Figure 2 is not reproducible as presented: no code, random seed, axis labels, or error bars are provided, yet the text draws the strong conclusion that the barren plateau 'happens only because of the global observable.' Since this is an original simulation rather than a re-plot of published data, the authors should provide the data or code, or replace the figure with a pointer to the existing analytical results in [38] and [39].
minor comments (4)
  1. [Section III-B1] The sentence 'there is a high probability of measuring the expectation value −2' is imprecise: one measures eigenvalues, not expectation values; the intended statement is that the state should be prepared so that the outcome −2 occurs with high probability.
  2. [Section V-A] The overhead scalings are not typeset clearly: '42n', '(2n+1 − 1)2', '9n', and '4n' should read 4^{2n}, (2^{n+1}−1)^2, 9^n, and 4^n, respectively. Please ensure the exponents appear correctly in the final version.
  3. [Table III] The symbols Pz and S in the gate-cutting decomposition are not defined in the text; please define them (e.g., Pz = |0⟩⟨0| and S as the phase gate) so that the table is self-contained.
  4. [Section III-B2] The subsection title says 'Non-linear activation functions via measurements', but the described method from [34] approximates the activation function using linear operations during the circuit and measures only at the end; the connection to measurement should be clarified or the title adjusted.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the paper is a qualitative review whose claims are organizational and supported by external literature, not by a fitted or self-referential derivation.

full rationale

This is a survey and position paper, not a derivation. There is no chain of equations in which a claimed prediction is equivalent to an input by construction. Section II presents standard textbook material on PVM and POVM measurements, cited to Nielsen and Chuang and to Wilde; the IC-POVM reconstruction formulas in Equations 15 and 16 are taken from the external reference [14] and are used only to explain an existing error-mitigation method. The wire-cutting identity in Equation 19 and the gate-cutting quasiprobability decomposition in Table III are likewise quoted from external literature and are not introduced as novel predictions. No parameter is fitted to a subset of data and then reported as a prediction, and no uniqueness theorem from the authors' prior work is invoked to force a choice. The only self-citation in the paper, reference [52] by first author Uotila, is used for the standard observation that state teleportation is a special case of gate teleportation with U = I and as an implementation pointer for gate-teleportation-based circuit cutting; neither use is load-bearing for the paper's central message that measurement deserves more attention in quantum algorithm design. A scope concern—that the review omits measurement-centric paradigms such as measurement-based quantum computing, fault-tolerant magic-state injection, and adaptive circuits—is a legitimate criticism of the breadth of the survey, but it is not a circularity: the central claim is a qualitative synthesis of selected topics, not a result made true by definition. The paper's own statement that it collected 'crucial measurement-related applications' (Section I) explicitly indicates a selective review rather than a systematic derivation, and selectivity is a validity issue, not a circular one. Therefore no circular step is present.

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

The review invokes standard quantum mechanical postulates and results from cited papers. It introduces no free parameters and no invented entities. Its central message depends on the representativeness of its literature selection, not on any fitted quantity or new theoretical object.

assumptions (5)
  • standard math Born rule: the probability of outcome lambda is p(lambda) = <phi|P_lambda|phi>.
    Invoked in Section II-A and used throughout for expectation values and measurement statistics.
  • standard math Spectral decomposition of Hermitian observables as O = sum_lambda lambda P_lambda.
    Used in Section II-A to define projective measurements and their projectors.
  • standard math POVM elements are positive and sum to the identity.
    Presented as Equations 9 and 10 in Section II-B; underlies all POVM applications in the review.
  • standard math Post-measurement state update rule for projective measurements.
    Given as Equation 4 in Section II-A and used for mid-circuit measurements, teleportation, and state preparation.
  • domain assumption Correctness of cited overhead results for circuit cutting and error mitigation.
    Complexity claims such as 4^2n and 9^n are taken from references [55]-[56] and not re-derived; the review's comparisons depend on them.

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Cite this review

Pith. "Pith review of Perspectives on Utilization of Measurements in Quantum Algorithms." pith.science (2026). https://pith.science/paper/GPADB6W4

@misc{pith2026250704325,
  author       = {Pith},
  title        = {Pith review of: Perspectives on Utilization of Measurements in Quantum Algorithms},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/GPADB6W4}},
  note         = {Machine review of arXiv:2507.04325}
}
read the original abstract

Measurement is a fundamental operation in quantum computing and has many important use cases in quantum algorithms. This article provides a comprehensive overview of the basic measurement operations in quantum computing and represents a selected set of their applications in quantum algorithms. Our goal is to provide one of the first algorithmic overviews of measurement processes in quantum computing. From the quantum information-theoretical perspective, measurements are either a method to access the result of a quantum computation or a technique to modify a quantum state. We also identify measurement-based methods to solve quantum computational challenges, such as error mitigation and circuit cutting. We discuss three main categories of measurements: performing measurements in static quantum circuits, modifying the quantum state in dynamic quantum circuits via measurements, and addressing challenges in quantum computing with measurements. Based on the reviewed topics, the measurement operations are frequently not at the center of the quantum algorithm design. However, the most novel and error-prone quantum algorithms will likely require sophisticated measurement schemes. Thus, the central message of this article is to broaden the view of measurement operations and highlight their importance at every level of quantum algorithm design.

Figures

Figures reproduced from arXiv: 2507.04325 by the authors.

Figure 1
Figure 1. Quantum circuit for an n-qubit system with RY (θi) rotations followed by a global observable Z⊗n [PITH_FULL_IMAGE:figures/full_fig_p007_1.png] view at source ↗
Figure 2
Figure 2. We computed the variances of expectation values from the circuit in [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 3
Figure 3. Circuit that implements gate teleportation through gate [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figures from the paper (3 more)
Figure 4
Figure 4. Figure 4: Conceptual idea behind wire cutting: the selected wire is cut, and [PITH_FULL_IMAGE:figures/full_fig_p009_4.png]
Figure 5
Figure 5. Figure 5: Conceptual idea behind gate cutting: the green gates are cut, and the [PITH_FULL_IMAGE:figures/full_fig_p009_5.png]
Figure 6
Figure 6. Figure 6: Quantum-classical circuit implements an example of a tensor network [PITH_FULL_IMAGE:figures/full_fig_p010_6.png]

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Works this paper leans on

76 extracted references · 48 canonical work pages

  1. [52]

    Gate teleportation in noisy quantum networks with the squidasm simulator,

    V . Uotila, “Gate teleportation in noisy quantum networks with the squidasm simulator,” in 2024 IEEE International Conference on Quan- tum Computing and Engineering (QCE) , vol. 02, 2024, pp. 161–166

    work page 2024

  2. [68]

    Application of a resource theory for magic states to fault-tolerant quantum computing,

    M. Howard and E. Campbell, “Application of a resource theory for magic states to fault-tolerant quantum computing,” Physical Review Letters, vol. 118, no. 9, p. 090501, Mar. 2017

    work page 2017

  3. [71]

    Quantifying quantum speedups: Improved classical simulation from tighter magic monotones,

    J. R. Seddon, B. Regula, H. Pashayan, Y . Ouyang, and E. T. Campbell, “Quantifying quantum speedups: Improved classical simulation from tighter magic monotones,” PRX Quantum, vol. 2, no. 1, p. 010345, Mar. 2021

    work page 2021

  4. [48]

    Experimental demonstration of the advantage of adaptive quantum circuits,

    M. Foss-Feig, A. Tikku, T.-C. Lu, K. Mayer, M. Iqbal, T. M. Gatterman, J. A. Gerber, K. Gilmore, D. Gresh, A. Hankin, N. Hewitt, C. V . Horst, M. Matheny, T. Mengle, B. Neyenhuis, H. Dreyer, D. Hayes, T. H. Hsieh, and I. H. Kim, “Experimental demonstration of the advantage of adaptive quantum circuits,” 2023. [Online]. Available: https://arxiv.org/abs/2302.03029

    arXiv 2023

  5. [38]

    A lie algebraic theory of barren plateaus for deep parameterized quantum circuits,

    M. Ragone, B. N. Bakalov, F. Sauvage, A. F. Kemper, C. Ortiz Marrero, M. Larocca, and M. Cerezo, “A lie algebraic theory of barren plateaus for deep parameterized quantum circuits,” Nature Communications , vol. 15, no. 1, p. 7172, Aug. 2024

    work page 2024

  6. [39]

    Does provable absence of barren plateaus imply classical simulability? or, why we need to rethink variational quantum computing,

    M. Cerezo, M. Larocca, D. Garc ´ıa-Mart´ın, N. L. Diaz, P. Braccia, E. Fontana, M. S. Rudolph, P. Bermejo, A. Ijaz, S. Thanasilp, E. R. Anschuetz, and Z. Holmes, “Does provable absence of barren plateaus imply classical simulability? or, why we need to rethink variational quantum computing,” no. arXiv:2312.09121, Mar. 2024, arXiv:2312.09121 [quant-ph]. [O...

    arXiv 2024

  7. [1]

    Algorithms for quantum computation: discrete logarithms and factoring,

    P. Shor, “Algorithms for quantum computation: discrete logarithms and factoring,” in Proceedings 35th Annual Symposium on Foundations of Computer Science, 1994, pp. 124–134

    1994

  8. [2]

    A fast quantum mechanical algorithm for database search,

    L. K. Grover, “A fast quantum mechanical algorithm for database search,” in Proceedings of the twenty-eighth annual ACM symposium on Theory of Computing , ser. STOC ’96. New York, NY , USA: Association for Computing Machinery, Jul. 1996, p. 212–219. [Online]. Available: https://dl.acm.org/doi/10.1145/237814.237866

    arXiv 1996

Show all 76 references
  1. [3]

    Is quantum advantage the right goal for quantum machine learning?

    M. Schuld and N. Killoran, “Is quantum advantage the right goal for quantum machine learning?” PRX Quantum , vol. 3, no. 3, p. 030101, Jul. 2022, arXiv:2203.01340 [quant-ph]

    2022 arXiv

  2. [4]

    The standard model of quantum measurement theory: History and applications,

    P. Busch and P. Lahti, “The standard model of quantum measurement theory: History and applications,” Foundations of Physics, vol. 26, no. 7, p. 875–893, Jul. 1996, arXiv:quant-ph/9603020

    1996 arXiv

  3. [5]

    Jacobs, Quantum Measurement Theory and its Applications

    K. Jacobs, Quantum Measurement Theory and its Applications. Cambridge: Cambridge University Press,

  4. [6]

    Ma- terials challenges and opportunities for quantum computing hardware,

    N. P. de Leon, K. M. Itoh, D. Kim, K. K. Mehta, T. E. Northup, H. Paik, B. S. Palmer, N. Samarth, S. Sangtawesin, and D. W. Steuerman, “Ma- terials challenges and opportunities for quantum computing hardware,” Science, vol. 372, no. 6539, p. eabb2823, Apr. 2021

    2021

  5. [7]

    Fault-tolerant quantum computation,

    P. Shor, “Fault-tolerant quantum computation,” in Proceedings of 37th Conference on Foundations of Computer Science , 1996, pp. 56–65

    1996

  6. [8]

    Preskill, FAULT-TOLERANT QUANTUM COMPUTATION

    J. Preskill, FAULT-TOLERANT QUANTUM COMPUTATION. WORLD SCIENTIFIC, Oct. 1998, p. 213–269. [Online]. Available: http: //www.worldscientific.com/doi/abs/10.1142/9789812385253 0008

    1998 doi

  7. [9]

    A theory of fault-tolerant quantum computation,

    D. Gottesman, “A theory of fault-tolerant quantum computation,” Phys- ical Review A , vol. 57, no. 1, p. 127–137, Jan. 1998, arXiv:quant- ph/9702029

    1998

  8. [10]

    M. A. Nielsen and I. L. Chuang, Quantum computation and quantum information, 10th ed. Cambridge; New York: Cambridge University Press, 2010

    2010

  9. [11]

    M. M. Wilde, Quantum Information Theory , 2nd ed. Cambridge University Press, Nov. 2016. [Online]. Available: https://www. cambridge.org/core/product/identifier/9781316809976/type/book

    2016

  10. [12]

    Informationally complete measurements and group representation,

    G. M. D’Ariano, P. Perinotti, and M. F. Sacchi, “Informationally complete measurements and group representation,” Journal of Optics B: Quantum and Semiclassical Optics , vol. 6, no. 6, p. S487, May 2004

    2004

  11. [13]

    Dual-frame optimization for informationally complete quantum measurements,

    L. E. Fischer, T. Dao, I. Tavernelli, and F. Tacchino, “Dual-frame optimization for informationally complete quantum measurements,” Physical Review A , vol. 109, no. 6, p. 062415, Jun. 2024

    2024

  12. [14]

    Scalable tensor-network error mitigation for near-term quantum computing,

    S. Filippov, M. Leahy, M. A. C. Rossi, and G. Garc ´ıa-P´erez, “Scalable tensor-network error mitigation for near-term quantum computing,” no. arXiv:2307.11740, Jul. 2023, arXiv:2307.11740 [quant-ph]. [Online]. Available: http://arxiv.org/abs/2307.11740

    2023 arXiv

  13. [15]

    Sym- metric informationally complete quantum measurements,

    J. M. Renes, R. Blume-Kohout, A. J. Scott, and C. M. Caves, “Sym- metric informationally complete quantum measurements,” Journal of Mathematical Physics, vol. 45, no. 6, p. 2171–2180, Jun. 2004

    2004

  14. [16]

    Characterizing midcircuit measurements on a superconducting qubit using gate set tomography,

    K. Rudinger, G. J. Ribeill, L. C. Govia, M. Ware, E. Nielsen, K. Young, T. A. Ohki, R. Blume-Kohout, and T. Proctor, “Characterizing midcircuit measurements on a superconducting qubit using gate set tomography,” Phys. Rev. Appl. , vol. 17, p. 014014, Jan 2022. [Online]. Availa...

    2022 doi

  15. [17]

    An operational approach to quantum probability,

    E. B. Davies and J. T. Lewis, “An operational approach to quantum probability,” Communications in Mathematical Physics , vol. 17, no. 3, p. 239–260, Sep. 1970

    1970

  16. [18]

    Dynamic quantum circuit compilation,

    K. Fang, M. Zhang, R. Shi, and Y . Li, “Dynamic quantum circuit compilation,” 2023. [Online]. Available: https://arxiv.org/abs/2310. 11021

    2023

  17. [19]

    Quantum algorithm zoo,

    S. Jordan, “Quantum algorithm zoo,” 2025, accessed: 2025-02-22. [Online]. Available: https://quantumalgorithmzoo.org/

    2025

  18. [20]

    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, no. 9, p. 625–644, Sep. 2021

    2021

  19. [21]

    Better than classical? the subtle art of benchmarking quantum machine learning models,

    J. Bowles, S. Ahmed, and M. Schuld, “Better than classical? the subtle art of benchmarking quantum machine learning models,” no. arXiv:2403.07059, Mar. 2024, arXiv:2403.07059 [quant-ph]. [Online]. Available: http://arxiv.org/abs/2403.07059

    2024 arXiv

  20. [22]

    Single-shot quantum machine learning,

    E. Recio-Armengol, J. Eisert, and J. J. Meyer, “Single-shot quantum machine learning,” Phys. Rev. A , vol. 111, p. 042420, Apr

  21. [23]

    Qnlp in practice: Running compositional models of meaning on a quantum computer,

    R. Lorenz, A. Pearson, K. Meichanetzidis, D. Kartsaklis, and B. Coecke, “Qnlp in practice: Running compositional models of meaning on a quantum computer,” Journal of Artificial Intelligence Research , vol. 76, p. 1305–1342, Apr. 2023

    2023

  22. [24]

    Challenges and opportunities in quantum optimization,

    A. Abbas, A. Ambainis, B. Augustino, A. B ¨artschi, H. Buhrman, C. Coffrin, G. Cortiana, V . Dunjko, D. J. Egger, B. G. Elmegreen, N. Franco, F. Fratini, B. Fuller, J. Gacon, C. Gonciulea, S. Gribling, S. Gupta, S. Hadfield, R. Heese, G. Kircher, T. Kleinert, T. Koch, G. Korpa...

    2024 arXiv

  23. [25]

    A quantum approximate optimization algorithm,

    E. Farhi, J. Goldstone, and S. Gutmann, “A quantum approximate optimization algorithm,” arXiv:1411.4028 [quant-ph] , Nov. 2014, arXiv: 1411.4028. [Online]. Available: http://arxiv.org/abs/1411.4028

    2014 arXiv

  24. [26]

    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, Jul. 2014

    2014

  25. [27]

    Variational quantum optimization with multibasis encodings,

    T. L. Patti, J. Kossaifi, A. Anandkumar, and S. F. Yelin, “Variational quantum optimization with multibasis encodings,” Phys. Rev. Res. , vol. 4, p. 033142, Aug 2022. [Online]. Available: https://link.aps.org/ doi/10.1103/PhysRevResearch.4.033142

    2022 doi

  26. [28]

    Towards large-scale quantum optimiza- tion solvers with few qubits,

    M. Sciorilli, L. Borges, T. L. Patti, D. Garc ´ıa-Mart´ın, G. Camilo, A. Anandkumar, and L. Aolita, “Towards large-scale quantum optimiza- tion solvers with few qubits,” Nature Communications, vol. 16, no. 1, p. 476, Jan. 2025

    2025

  27. [29]

    Ising formulations of many np problems,

    A. Lucas, “Ising formulations of many np problems,” Frontiers in Physics, vol. 2, 2014, arXiv:1302.5843 [cond-mat]. [Online]. Available: http://arxiv.org/abs/1302.5843

    2014 arXiv

  28. [30]

    Approximation capabilities of multilayer feedforward net- works,

    K. Hornik, “Approximation capabilities of multilayer feedforward net- works,” Neural Networks, vol. 4, no. 2, p. 251–257, Jan. 1991

    1991

  29. [31]

    A simple quantum neural net with a periodic activation function,

    A. Daskin, “A simple quantum neural net with a periodic activation function,” in 2018 IEEE International Conference on Systems, Man, and Cybernetics (SMC) , Oct. 2018, p. 2887–2891, arXiv:1804.07633 [quant-ph]. [Online]. Available: http://arxiv.org/abs/1804.07633

    2018 arXiv

  30. [32]

    Quantum neuron: an elementary building block for machine learning on quantum computers,

    Y . Cao, G. G. Guerreschi, and A. Aspuru-Guzik, “Quantum neuron: an elementary building block for machine learning on quantum computers,” no. arXiv:1711.11240, Nov. 2017, arXiv:1711.11240 [quant-ph]. [Online]. Available: http://arxiv.org/abs/1711.11240

    2017 arXiv

  31. [33]

    An artificial neuron implemented on an actual quantum processor,

    F. Tacchino, C. Macchiavello, D. Gerace, and D. Bajoni, “An artificial neuron implemented on an actual quantum processor,” npj Quantum Information, vol. 5, no. 1, p. 1–8, Mar. 2019

    2019

  32. [34]

    Quantum activation functions for quantum neural networks,

    M. Maronese, C. Destri, and E. Prati, “Quantum activation functions for quantum neural networks,” Quantum Information Processing , vol. 21, no. 4, p. 128, Mar. 2022

    2022

  33. [35]

    Barren plateaus in quantum neural network training landscapes,

    J. R. McClean, S. Boixo, V . N. Smelyanskiy, R. Babbush, and H. Neven, “Barren plateaus in quantum neural network training landscapes,”Nature Communications, vol. 9, no. 1, p. 4812, Nov. 2018

    2018

  34. [36]

    Attention is not all you need: pure attention loses rank doubly exponentially with depth,

    Y . Dong, J.-B. Cordonnier, and A. Loukas, “Attention is not all you need: pure attention loses rank doubly exponentially with depth,” in Proceedings of the 38th International Conference on Machine Learning. PMLR, Jul. 2021, p. 2793–2803. [Online]. Available: https://proceedin...

    2021

  35. [37]

    Deep residual learning for image recognition,

    K. He, X. Zhang, S. Ren, and J. Sun, “Deep residual learning for image recognition,” in 2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR) , Jun. 2016, p. 770–778. [Online]. Available: https://ieeexplore.ieee.org/document/7780459

    2016

  36. [40]

    An adaptive optimizer for measurement-frugal variational algorithms,

    J. M. K ¨ubler, A. Arrasmith, L. Cincio, and P. J. Coles, “An adaptive optimizer for measurement-frugal variational algorithms,” Quantum, vol. 4, p. 263, May 2020

    2020

  37. [41]

    Group-invariant quantum machine learning,

    M. Larocca, F. Sauvage, F. M. Sbahi, G. Verdon, P. J. Coles, and M. Cerezo, “Group-invariant quantum machine learning,” PRX Quan- tum, vol. 3, no. 3, p. 030341, Sep. 2022

    2022

  38. [42]

    Cost function dependent barren plateaus in shallow parametrized quantum circuits,

    M. Cerezo, A. Sone, T. V olkoff, L. Cincio, and P. J. Coles, “Cost function dependent barren plateaus in shallow parametrized quantum circuits,” Nature Communications, vol. 12, no. 1, p. 1791, Mar. 2021

    2021

  39. [43]

    Layerwise learning for quantum neural networks,

    A. Skolik, J. R. McClean, M. Mohseni, P. Van Der Smagt, and M. Leib, “Layerwise learning for quantum neural networks,” Quantum Machine Intelligence, vol. 3, no. 1, p. 5, Jun. 2021

    2021

  40. [44]

    Learning to measure: Adaptive informationally complete generalized measurements for quantum algorithms,

    G. Garc ´ıa-P´erez, M. A. C. Rossi, B. Sokolov, F. Tacchino, P. K. Barkoutsos, G. Mazzola, I. Tavernelli, and S. Maniscalco, “Learning to measure: Adaptive informationally complete generalized measurements for quantum algorithms,” PRX Quantum, vol. 2, no. 4, p. 040342, Nov. 20...

    2021 arXiv

  41. [45]

    Equivalence checking of dynamic quantum circuits,

    X. Hong, Y . Feng, S. Li, and M. Ying, “Equivalence checking of dynamic quantum circuits,” in Proceedings of the 41st IEEE/ACM International Conference on Computer-Aided Design , ser. ICCAD ’22. New York, NY , USA: Association for Computing Machinery, 2022. [Online]. Available...

    2022

  42. [46]

    Quantum fourier transform using dynamic circuits,

    E. B ¨aumer, V . Tripathi, A. Seif, D. Lidar, and D. S. Wang, “Quantum fourier transform using dynamic circuits,” Phys. Rev. Lett., vol. 133, p. 150602, Oct 2024. [Online]. Available: https: //link.aps.org/doi/10.1103/PhysRevLett.133.150602

    2024 doi

  43. [47]

    Efficient long-range entanglement using dynamic circuits,

    E. B ¨aumer, V . Tripathi, D. S. Wang, P. Rall, E. H. Chen, S. Majumder, A. Seif, and Z. K. Minev, “Efficient long-range entanglement using dynamic circuits,” PRX Quantum, vol. 5, p. 030339, Aug 2024. [Online]. Available: https://link.aps.org/doi/10.1103/PRXQuantum.5.030339

    2024 doi

  44. [49]

    Variational quantum regression algorithm with encoded data structure,

    C. C. J. Wang and R. S. Bennink, “Variational quantum regression algorithm with encoded data structure,” 2024. [Online]. Available: https://arxiv.org/abs/2307.03334

    2024 arXiv

  45. [50]

    Demonstrating the viability of universal quantum computation using teleportation and single-qubit operations,

    D. Gottesman and I. L. Chuang, “Demonstrating the viability of universal quantum computation using teleportation and single-qubit operations,” Nature, vol. 402, no. 67606760, p. 390–393, Nov. 1999

    1999

  46. [51]

    A one-way quantum computer,

    R. Raussendorf and H. J. Briegel, “A one-way quantum computer,” Physical Review Letters , vol. 86, no. 22, p. 5188–5191, May 2001

    2001

  47. [53]

    Trading classical and quantum computational resources,

    S. Bravyi, G. Smith, and J. Smolin, “Trading classical and quantum computational resources,” Physical Review X , vol. 6, no. 2, p. 021043, Jun. 2016, arXiv:1506.01396 [quant-ph]

    2016 arXiv

  48. [54]

    Doubling the size of quantum simulators by entanglement forging,

    A. Eddins, M. Motta, T. P. Gujarati, S. Bravyi, A. Mezzacapo, C. Had- field, and S. Sheldon, “Doubling the size of quantum simulators by entanglement forging,” PRX Quantum , vol. 3, no. 1, p. 010309, Jan. 2022

    2022

  49. [55]

    Optimal wire cutting with classical communication,

    L. Brenner, C. Piveteau, and D. Sutter, “Optimal wire cutting with classical communication,” no. arXiv:2302.03366, Feb. 2023, arXiv:2302.03366 [quant-ph]. [Online]. Available: http://arxiv.org/abs/ 2302.03366

    2023

  50. [56]

    Circuit knitting with classical commu- nication,

    C. Piveteau and D. Sutter, “Circuit knitting with classical commu- nication,” IEEE Transactions on Information Theory , p. 1–1, 2024, arXiv:2205.00016 [quant-ph]

    2024 arXiv

  51. [57]

    Simulating large quantum circuits on a small quantum computer,

    T. Peng, A. W. Harrow, M. Ozols, and X. Wu, “Simulating large quantum circuits on a small quantum computer,” Physical Review Letters , vol. 125, no. 15, p. 150504, Oct. 2020

    2020

  52. [58]

    Qiskit addon: circuit cutting,

    A. M. Bra ´nczyk, A. Carrera Vazquez, D. J. Egger, B. Fuller, J. Gacon, J. R. Garrison, J. R. Glick, C. Johnson, S. Joshi, E. Pednault, C. D. Pemmaraju, P. Rivero, I. Shehzad, and S. Woerner, “Qiskit addon: circuit cutting,” https://github.com/Qiskit/qiskit-addon-cutting, 2024

    2024

  53. [59]

    Constructing a virtual two-qubit gate by sampling single-qubit operations,

    K. Mitarai and K. Fujii, “Constructing a virtual two-qubit gate by sampling single-qubit operations,” New Journal of Physics , vol. 23, no. 2, p. 023021, Feb. 2021, arXiv:1909.07534 [quant-ph]

    2021 arXiv

  54. [60]

    Fast quantum circuit cutting with randomized measurements,

    A. Lowe, M. Medvidovi ´c, A. Hayes, L. J. O’Riordan, T. R. Brom- ley, J. M. Arrazola, and N. Killoran, “Fast quantum circuit cutting with randomized measurements,” Quantum, vol. 7, p. 934, Mar. 2023, arXiv:2207.14734 [quant-ph]

    2023 arXiv

  55. [61]

    Overhead for simulating a non-local channel with local channels by quasiprobability sampling,

    K. Mitarai and K. Fujii, “Overhead for simulating a non-local channel with local channels by quasiprobability sampling,” Quantum, vol. 5, p. 388, Jan. 2021, arXiv:2006.11174 [quant-ph]

    2021 arXiv

  56. [62]

    Error mitigation for short- depth quantum circuits,

    K. Temme, S. Bravyi, and J. M. Gambetta, “Error mitigation for short- depth quantum circuits,” Physical Review Letters , vol. 119, no. 18, p. 180509, Nov. 2017

    2017

  57. [63]

    Practical quantum error mitigation for near-future applications,

    S. Endo, S. C. Benjamin, and Y . Li, “Practical quantum error mitigation for near-future applications,” Physical Review X, vol. 8, no. 3, p. 031027, Jul. 2018

    2018

  58. [64]

    Error mitigation extends the computational reach of a noisy quantum processor,

    A. Kandala, K. Temme, A. D. C ´orcoles, A. Mezzacapo, J. M. Chow, and J. M. Gambetta, “Error mitigation extends the computational reach of a noisy quantum processor,” Nature, vol. 567, no. 7749, p. 491–495, Mar. 2019

    2019

  59. [65]

    Error mitigation for universal gates on encoded qubits,

    C. Piveteau, D. Sutter, S. Bravyi, J. M. Gambetta, and K. Temme, “Error mitigation for universal gates on encoded qubits,” Physical Review Letters, vol. 127, no. 20, p. 200505, Nov. 2021

    2021

  60. [66]

    Quasiprobability decomposi- tions with reduced sampling overhead,

    C. Piveteau, D. Sutter, and S. Woerner, “Quasiprobability decomposi- tions with reduced sampling overhead,”npj Quantum Information, vol. 8, no. 1, p. 1–9, Feb. 2022

    2022

  61. [67]

    Estimating outcome probabilities of quantum circuits using quasiprobabilities,

    H. Pashayan, J. J. Wallman, and S. D. Bartlett, “Estimating outcome probabilities of quantum circuits using quasiprobabilities,” Physical Review Letters, vol. 115, no. 7, p. 070501, Aug. 2015

    2015

  62. [69]

    Quantifying magic for multi-qubit operations,

    J. R. Seddon and E. T. Campbell, “Quantifying magic for multi-qubit operations,” Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences , vol. 475, no. 2227, p. 20190251, Jul. 2019

    2019

  63. [70]

    Robustness of magic and symmetries of the stabiliser polytope,

    M. Heinrich and D. Gross, “Robustness of magic and symmetries of the stabiliser polytope,” Quantum, vol. 3, p. 132, Apr. 2019

    2019

  64. [72]

    Error mitigation for variational quantum algorithms through mid- circuit measurements,

    L. Botelho, A. Glos, A. Kundu, J. A. Miszczak, ¨O. Salehi, and Z. Zim- bor´as, “Error mitigation for variational quantum algorithms through mid- circuit measurements,” Physical Review A , vol. 105, no. 2, p. 022441, Feb. 2022, arXiv:2108.10927 [quant-ph]

    2022 arXiv

  65. [73]

    Tensor networks in a nutshell,

    J. Biamonte and V . Bergholm, “Tensor networks in a nutshell,” 2017. [Online]. Available: https://arxiv.org/abs/1708.00006

    2017 arXiv

  66. [74]

    [Online]

    Algorithmiq. [Online]. Available: https://docs.quantum.ibm.com/guides/ docs.quantum.ibm.com/guides/algorithmiq-tem

  67. [2014]

    Available: https://www.cambridge.org/ core/books/quantum-measurement-theory-and-its-applications/ 120E32FFBEBF6EE0F6EC6F84D51DC907

    [Online]. Available: https://www.cambridge.org/ core/books/quantum-measurement-theory-and-its-applications/ 120E32FFBEBF6EE0F6EC6F84D51DC907

  68. [2025]

    Available: https://link.aps.org/doi/10.1103/PhysRevA

    [Online]. Available: https://link.aps.org/doi/10.1103/PhysRevA. 111.042420

    doi

Pith tools

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