Pith. sign in

REVIEW 3 major objections 5 minor 1 cited by

Networked Quantum Services

T0 review · 3 major / 5 minor · reviewed 2026-08-07 · deepseek-v4-flash

Pith's one-line read The paper argues that networked quantum services form a distinct field—combining small quantum processors over classical and quantum links—and provides a structured survey of architectures, software, and hardware implementations.

desk verdict A useful but uneven survey of networked quantum services; the taxonomy is fine, the hardware tables are not. read the letter →

arxiv 2505.23074 v1 pith:ZD2VAPC5 submitted 2025-05-29 quant-ph

classification quant-ph
keywords networkedquantumservicesnetworkingdistributedcomputingmachinelearningcloudprogramminglanguageserrorcorrectioninternet
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 review sets out to give the first comprehensive map of networked quantum services: ways of delivering computation, communication, and security to users by connecting quantum computers, repeaters, and memories over quantum and classical channels. The authors argue that this is a distinct field that existing surveys touch only piecemeal, since distributed quantum computing, quantum cloud, quantum machine learning, programming languages, and the quantum internet are usually treated separately rather than as one service stack. The paper organizes the field by architecture (multichip, circuit distribution, and circuit splitting), by software layer (languages, SDKs, APIs, and standardization), and by implementation basis (channels, repeaters, error correction, and memories). It concludes that networked operation is how small noisy intermediate-scale quantum (NISQ) machines can be pooled into scalable, fault-tolerant computation, provided three requirements are met: precise synchronization, efficient error correction, and memories with sufficient coherence time. If the map holds, it gives practitioners a shared vocabulary and a checklist for what must be standardized before quantum services become a real utility.

What carries the argument

The load-bearing organizing device is the classification of networked quantum services by which communication resources distant quantum processing units can use. Multichip execution keeps circuits local and combines outputs classically; circuit distribution assumes quantum communication and distributes a decomposed circuit across nodes; circuit splitting assumes only classical communication and cuts the circuit, as in gate-cutting or wire-cutting. This taxonomy is what lets the survey place dozens of algorithms, compilers, and experimental demonstrations into one structure. Secondary machinery includes the layered architectures for quantum computers and distributed computation, the data-splitting versus circuit-splitting distinction for distributed quantum neural networks, and the fidelity-based quality model in which entanglement purification improves fidelity from $F' = F_0^2/p_S$ with $p_S = F_0^2 + (1-F_0)^2$, making entangled states usable only above a threshold $F_{\rm thr}$.

What would settle it

Choose any row in Table 15 or Table 18 and check the stated gate error rate or coherence time against the cited primary paper or the vendor's current specification sheet; if a value is off by an order of magnitude, the survey's implementation-basis tables are not a reliable quantitative record and the map's hardware layer would need source-level verification.

Watch

Extended reading notes

Core claim

The central claim is that networked quantum services are a coherent emerging category whose core idea is to combine several smaller quantum processing units in parallel, then merge their outputs by post-processing, with classical communication always available and quantum communication available in some variants. The paper establishes a three-way taxonomy: multichip approaches need no quantum communication between circuits; circuit distribution cuts a large circuit across distant nodes that share entangled links; circuit splitting runs subcircuits with only classical coordination. On top of this, the review classifies distributed quantum machine learning into data splitting versus circuit splitting, surveys the quantum software stack from languages and SDKs to API gateways and OpenAPI-based service descriptions, and reviews the physical basis of quantum channels, repeaters, quantum memories, and error correction. It draws the practical conclusion that all devices in a quantum network must meet three conditions—synchronization, error-correction coding, and adequate memory coherence—and that network generations can be typed by how they handle loss and errors (Types I–III), with end-to-end Bell pairs per second and fidelity thresholds as service-level quality measures.

Load-bearing premise

The survey's quantitative tables (gate error rates and coherence times) present hardware numbers without a primary source attached to each row, so the entire survey's implementation picture stands on vendor-reported figures that the text does not independently verify.

Editorial extensions

If this is right

  • If the taxonomy is adopted, any proposed networked quantum service can be classified by its quantum-communication capability, which determines which algorithms, compilers, and error-management methods apply.
  • Distributed execution over many small QPUs becomes a credible near-term path: it avoids the high gate counts and decoherence of a single large machine and allows low-complexity error correction in each node.
  • Interoperability, not raw qubit count, is the next bottleneck: without standardized APIs, service descriptions, and programming interfaces, quantum services cannot be combined across vendors.
  • Quantum networks will evolve in generations, with Type I using distillation and two-way classical communication, Type II using quantum error correction, and Type III using QEC for both loss and errors without classical side-information, each trading rate, complexity, and hardware demands.
  • Fidelity-aware service quality can be engineered: end-to-end Bell pairs per second plus a fidelity threshold gives a concrete quality-of-service contract for networked quantum services.

Reading between the lines

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

  • The paper leaves implicit that the same three-way split by quantum-communication availability could organize distributed quantum sensing, where some protocols need shared entanglement and others coordinate classically.
  • The tables of processor error rates and memory coherence times, if each entry were tied to a primary source, would become a yearly trackable benchmark of whether network-component requirements are being met; the paper stops short of providing that provenance.
  • The fidelity-threshold model suggests a testable service-engineering rule: a quantum cloud could advertise a distribution of delivered Bell-pair fidelities and route jobs to paths whose purified fidelity exceeds the application threshold, making QoS a measurable contract rather than a hardware specification.
  • The networked-beats-monolithic argument leads to a testable prediction: a distributed computation over smaller QPUs should show slower fidelity decay than a single larger QPU at the same total gate count, provided synchronization overhead stays below the error-reduction gain.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 5 minor

Summary. This survey reviews the emerging area of networked quantum services: the use of quantum computers and quantum networking to provide services such as distributed quantum computing, networked quantum machine learning, blind quantum computation, quantum cloud platforms, and quantum-enhanced sensing. It organizes the material around architectural concepts (multichip, circuit distribution, circuit splitting), software and programming-language support, standardization efforts, and an implementation basis covering quantum channels, repeaters, error correction, and quantum memories. The stated novel contribution is a compact and comprehensive state-of-the-art overview with structured tables and a discussion of open problems.

Significance. Read as a curated overview, the paper has real value: the related-work comparison is broad, the taxonomy of distributed-computing approaches is useful, and the separation of data splitting from circuit splitting in quantum neural networks is a helpful organizing device. Because the paper makes no technical derivations, its soundness rests on the accuracy of its factual claims and tables. The paper's own advertised contribution, 'well structured, easy-to-access tables,' is weakened by internal contradictions and by state-of-the-art numbers that lack primary sources. If the tables are corrected and sourced, the survey could be a useful entry point for readers entering this field; in its present form, the hardware-performance tables cannot be relied on without external checking.

major comments (3)
  1. [Table 15 and §3.2] Table 15 is internally inconsistent with the timeline given in §3.2. The table dates Google Sycamore to 2020, but §3.2 states that Google announced its 53-qubit processor in 2019; it dates IBM Hummingbird to 2023, while §3.2 places that processor in 2020; and it dates IBM Eagle to 2019, while §3.2 places the 127-qubit processor in 2021. Since Section 1.1 presents the tables as a central contribution of the survey, these date errors make the table unusable as a reliable hardware map and need to be corrected against primary sources.
  2. [Table 15 and §5.4] The error-rate column in Table 15 is presented without any definition of the reported metric (single-qubit versus two-qubit gate error, median versus best qubit, and whether values are percentages or fractions), and no primary source is cited in the table or in the surrounding text. The statement in §5.4 that 'the current ε error rate (%) of quantum gates is in the range of ε ≈ 0.01' is ambiguous: if 0.01 means percent, it matches only the last row of the table, and the claimed 'two orders of magnitude improvement in the last few years' is not substantiated by the table. The table should state the metric, the unit, and a source for each row or be removed.
  3. [§5.4 and Table 18] The text in §5.4 says that the highest achievable coherence times in quantum network hardware are 'in the range of few seconds to few minutes,' but Table 18 lists a single ion qubit with ~1 hour coherence time and a single trapped ion qubit with ~10 min. The summary statement directly contradicts the table it refers to; either the text or the table must be corrected.
minor comments (5)
  1. [§5.2] The claim that physical qubit numbers are 'increasing exponentially (2^n) every year' and that the state space grows 'super-exponentially (2^{2n})' is imprecise and appears to conflate the qubit count with its exponential growth; please rephrase with a concrete source and the correct formula.
  2. [§3.2 and Table 11] In §3.2, Google's 2019 processor is described as 53-qubit, while Table 11 lists Google Cloud as 54 qubits; clarify whether the table refers to the same device or a different generation.
  3. [§5.3] The phrase 'TheF fidelity' appears to be a typo for 'The fidelity'.
  4. [§2 and §6] There are several proofreading errors, including 'an comprehensive overview' in §2 and 'coincidence' instead of 'coincide' in §6; the manuscript would benefit from a careful language pass.
  5. [Figure 3 and Figure 6] The relations Σ_i w_i QC_i = QC and Σ_i c_i PQC_i = PQC are used in the figure captions, but the meaning of the weights w_i and c_i is never defined; please state what these coefficients represent.

Circularity Check

0 steps flagged · score 0.0 of 10

No circular reasoning identified: the paper is a literature survey without a derivation chain, and its self-citations are used as background summaries rather than load-bearing premises.

full rationale

The manuscript is a review of networked quantum services; it makes no predictions and derives no quantities from fitted parameters. Its claims are organizational and comparative: it categorizes architectures, summarizes prior results, and provides tables. Self-citations (e.g., Refs. [12,45,56-58]) appear in the related-work discussion and in tables as pointers to earlier publications, but no argument depends on accepting the authors' own prior results as a premise. The claim that no existing survey specifically addresses networked quantum services is supported by the comparative table of related surveys, not by a self-referential chain. The most significant weakness is Table 15, whose gate-error rows and release dates lack primary citations and contradict the text in Section 3.2 (e.g., the Eagle is dated 2019 in the table but the text says the 127-qubit processor was released in 2021, and the Hummingbird is dated 2023 in the table while the text says it was announced in 2020); this undermines verifiability and accuracy, but it is a correctness and external-evidence problem, not circularity. Therefore the paper is not circular.

Assumptions & free parameters 0 free parameters · 1 assumptions · 0 invented entities

The survey introduces no free parameters, no new entities, and no derivations. It relies on the accuracy of the cited primary literature, especially for the quantitative tables that summarize hardware capabilities and network protocols.

assumptions (1)
  • domain assumption Cited experimental results and performance numbers are accurately reported by the original sources.
    The survey aggregates numbers (e.g., Table 15 gate error rates, Table 18 coherence times) from primary literature without independent verification.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Networked Quantum Services." pith.science (2026). https://pith.science/paper/ZD2VAPC5

@misc{pith2026250523074,
  author       = {Pith},
  title        = {Pith review of: Networked Quantum Services},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/ZD2VAPC5}},
  note         = {Machine review of arXiv:2505.23074}
}
read the original abstract

The intense growth of quantum computation and communication allows the development of advanced solutions and services. Networked quantum services are provided for the users via quantum computers and quantum networking. Here, we review the fundamental concepts and recent achievements of networked quantum services. We present a comprehensive study of the state of the art, the different technologies, platforms and applications. We analyze the implementation basis and identify key challenges.

Figures

Figures reproduced from arXiv: 2505.23074 by the authors.

Figure 1
Figure 1. A hierarchical quantum internet architecture for networked quantum services in compliance [PITH_FULL_IMAGE:figures/full_fig_p008_1.png] view at source ↗
Figure 2
Figure 2. Layer architectures. (a) Layer architecture of a quantum computer (general gate-model [PITH_FULL_IMAGE:figures/full_fig_p009_2.png] view at source ↗
Figure 3
Figure 3. Distributed quantum computer architectures. (a) Multichip: the [PITH_FULL_IMAGE:figures/full_fig_p015_3.png] view at source ↗
Figures from the paper (4 more)
Figure 4
Figure 4. Figure 4: A distributed CNOT gate realized by two QPUs between distant quantum states [PITH_FULL_IMAGE:figures/full_fig_p015_4.png]
Figure 5
Figure 5. Figure 5: Schematic model of a VQA. The classical data [PITH_FULL_IMAGE:figures/full_fig_p017_5.png]
Figure 6
Figure 6. Figure 6: Data splitting and circuit splitting in distributed quantum neural networks. (a) Data [PITH_FULL_IMAGE:figures/full_fig_p018_6.png]
Figure 7
Figure 7. Figure 7: A QUDIO model for VQAs. The nodes are trained in parallel using a PQC or a quantum [PITH_FULL_IMAGE:figures/full_fig_p018_7.png]

Discussion (0). Sign in to comment.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Intelligence-Guided Adaptive Purification for DDoS-Resilient Quantum Networks: A CUDA-Q based Study

    quant-ph 2026-07 conditional novelty 5.0 of 10

    IDS-driven adaptive purification in a simulated 8-node quantum repeater chain restores fidelity-qualified entanglement delivery under SSDP-induced degradation (0.098 to 0.344 above-target; oracle 0.335).

Reference graph

Works this paper leans on

290 extracted references · 44 canonical work pages · cited by 1 Pith paper

  1. [1]

    C. H. Bennett, S. J. Wiesner (1992). Communication via 1- and 2-particle operators on Einstein-Podolsky-Rosen states. Phys. Rev. Lett. , 69:2881-2884. https://doi.org/10.1103/PhysRevLett.69.2881

  2. [2]

    C. H. Bennett, G. Brassard, C. Crepeau, R. Jozsa, A. Peres, W. K. Wootters (1993). Teleporting an unknown quantum state via dual classic and Einstein-Podolsky-Rosen channels. Phys. Rev. Lett., 70:1895-1899. https://doi.org/10.1103/PhysRevLett.70.1895. 32 Networked Quantum Services

  3. [3]

    Imre and M

    S. Imre and M. Berces (2021). Entanglement-Based Competition Resolution in Distributed Sys- tems. IEEE Access, vol. 9, pp. 10253-10262. https://doi.org/10.1109/ACCESS.2021.3050271

  4. [4]

    P. W. Shor (2002). Introduction to quantum algorithms. AMS PSAPM , 58:143-159. https://doi.org/10.48550/arXiv.quant-ph/0005003

  5. [5]

    Jozsa (1998)

    R. Jozsa (1998). Quantum algorithms and the Fourier transform. Proc. Roy. Soc. London Ser. A , 454:323-337. https://doi.org/10.1098/rspa.1998.0163

  6. [6]

    Imre (2007)

    S. Imre (2007). Quantum Existence Testing and Its Application for Finding Extreme Val- ues in Unsorted Databases. IEEE Transactions on Computers , vol. 56, no. 5, pp. 706-710. https://doi.org/10.1109/TC.2007.1032

  7. [7]

    Gyongyosi, S

    L. Gyongyosi, S. Imre, H. V. Nguyen (2018). A Survey on Quantum Channel Capacities. IEEE Communications Surveys and Tutorials , Volume: 20, Issue: 2. https://doi.org/10.1109/COMST.2017.2786748

  8. [8]

    Q. A. Memon, M. Al Ahmad and M. Pecht, M (2024). Quantum Computing: Navigating the Future of Computation, Challenges, and Technological Breakthroughs. Quantum Rep. 6, pp. 627–663. https://doi.org/10.3390/quantum6040039

Show all 290 references
  1. [9]

    Z. Yang, M. Zolanvari, and R. Jain (2023). A survey of important issues in quantum computing and communications. IEEE Communications and Surveys Tutorials , vol. 25, no. 2, pp. 1059-1094. https://doi.org/10.1109/COMST.2023.3254481

  2. [10]

    H. Sahu, H. P. Gupta (2023). Quantum Computing Toolkit From Nuts and Bolts to Sack of Tools. arXiv:2302.08884. https://doi.org/10.48550/arXiv.2302.08884

  3. [11]

    Singh, R

    P. Singh, R. Dasgupta, A. Singh et al (2024). A Survey on Available Tools and Technologies Enabling Quantum Computing. IEEE Access , pp. 57974-57991. https://doi.org/10.1109/ACCESS.2024.3388005

  4. [12]

    Gyongyosi and S

    L. Gyongyosi and S. Imre (2019). A Survey on Quantum Computing Technology.Computer Science Review, Volume 31, pp. 51-71. https://doi.org/10.1016/j.cosrev.2018.11.002

  5. [13]

    S. S. Gill et al (2021). Quantum Computing: A Taxonomy, Systematic Review and Future Direc- tions. Software: Practice and Experience. https://doi.org/10.1002/spe.3039

  6. [14]

    E. Chae, J. Choi, J. Kim (2024). An elementary review on basic principles and developments of qubits for quantum computing. Nano Convergence, 11:11. https://doi.org/10.1186/s40580-024- 00418-5

  7. [15]

    Bochkarev, R

    A. Bochkarev, R. Heese, S. Jager et al (2024). Quantum Computing for Discrete Optimization: A Highlight of Three Technologies. arXiv:2409.01373. https://doi.org/10.48550/arXiv.2409.01373

  8. [16]

    Y. Li, M. Tian, G. Liu, C. Peng, and L. Jiao (2020). Quantum optimization and quantum learning: A survey. IEEE Access, vol. 8, pp. 23 568-23 593. https://doi.org/10.1109/ACCESS.2020.2970105

  9. [17]

    Kusyk, S

    J. Kusyk, S. M. Saeed, and M. U. Uyar (2021). Survey on quantum circuit compilation for noisy intermediate-scale quantum computers: Artificial intelligence to heuristics. IEEE Transactions on Quantum Engineering, vol. 2, pp. 1-16. https://doi.org/10.1109/TQE.2021.3068355

  10. [18]

    Upama, M

    P. Upama, M. J. Hossain Faruk, M. Nazim, M. Masum, H. Shahriar, G. Uddin, S. Barzanjeh, A. Rahman, and S. Ahamed (2022). Evolution of Quantum Computing: A Systematic Survey on the Use of Quantum Computing Tools. 2022 IEEE Computers, Software, and Applications Conference. https...

  11. [19]

    F. V. Massoli, L. Vadicamo, G. Amato, and F. Falchi (2022). A leap among quan- tum computing and quantum neural networks: A survey. ACM Comput. Surv. , 55, 5. https://doi.org/10.1145/3529756

  12. [20]

    S. B. Ramezani, A. Sommers, H. K. Manchukonda, S. Rahimi, and A. Amirlatifi (2020). Machine learning algorithms in quantum computing: A survey. 2020 International Joint Conference on Neural Networks (IJCNN) , pp. 1-8. https://doi.org/10.1109/IJCNN48605.2020.9207714

  13. [21]

    Peral-Garcia et al (2024)

    D. Peral-Garcia et al (2024). Systematic literature review: Quantum machine learning and its applications. Computer Science Review , https://doi.org/10.1016/j.cosrev.2024.100619

  14. [22]

    M. D. Garcia, A. M. Romero (2024). Survey on Computational Applications of Tensor Network Simulations. IEEE Access , DOI: 10.1109/ACCESS.2024.3519676. https://doi.org/10.1109/ACCESS.2024.3519676. Laszlo Gyongyosi and Sandor Imre 33

  15. [23]

    Ayral, P

    T. Ayral, P. Besserve, D. Lacroix, E. A. R. Guzman (2023). Quantum comput- ing with and for many-body physics. The European Physical Journal A , 59, 227. https://doi.org/10.1140/epja/s10050-023-01141-1

  16. [24]

    Moguel, J

    E. Moguel, J. R. and V. Garcia-Alonso (2022). Quantum service-oriented computing: cur- rent landscape and challenges. Software Quality Journal , Volume 30, pages 983–1002. https://doi.org/10.1007/s11219-022-09589-y

  17. [25]

    M. A. Serrano, J. A. Cruz-Lemus, R.-P. Castillo and M. Piattini (2022). Quantum Software Com- ponents and Platforms: Overview and Quality Assessment. ACM Comput. Surveys, 55, 8 pp. 1-31. https://doi.org/10.1145/3548679

  18. [26]

    A. A. Khan, A. Ahmad, M. Waseem, P. Liang, M. Fahmideh, T. Mikkonen, and P. Abrahamsson (2023). Software architecture for quantum computing systems - A systematic review. Journal of Systems and Software 201, 111682. https://doi.org/10.1016/j.jss.2023.111682

  19. [27]

    Jimnez-Navajas, F

    L. Jimnez-Navajas, F. Bhler, F. Leymann et al (2024). Quantum Software Development: A Survey. Quantum Information and Computation, 24, 7-8, 0609-0642. https://doi.org/10.26421/qic24.7-8-4

  20. [28]

    Garhwal, M

    S. Garhwal, M. Ghorani, and A. Ahmad (2021). Quantum programming language: A systematic review of research topic and top cited languages. Archives of Computational Methods in Engineer- ing vol. 28, pp. 289-310. https://doi.org/10.1007/s11831-019-09372-6

  21. [29]

    Dwivedi, M

    K. Dwivedi, M. Haghparast, T. Mikkonen (2024). Quantum software engineering and quan- tum software development lifecycle: a survey. Cluster Computing , Volume 27, pp. 7127.7145. https://doi.org/10.1007/s10586-024-04362-1

  22. [30]

    Cuomo, M

    D. Cuomo, M. Caleffi (2020). Towards a distributed quantum computing ecosystem.IET Quantum Communication 1, 1 pp. 3–8. https://doi.org/10.1049/iet-qtc.2020.0002

  23. [31]

    Caleffi, M

    M. Caleffi, M. Amoretti, D. Ferrari et al (2024). Distributed Quantum Computing: A Survey. Computer Networks , 254, 110672. https://doi.org/10.1016/j.comnet.2024.110672

  24. [32]

    Barrala, F

    D. Barrala, F. J. Cardamab, G. Diaz et al (2024). Review of Distributed Quantum Com- puting. From single QPU to High Performance Quantum Computing. arXiv:2404.01265v1. https://doi.org/10.48550/arXiv.2404.01265

  25. [33]

    J. C. Boschero, N. M. P. Neumann, W. van der Schoot, T. Sijpesteijn, R. Wezeman (2024). Distributed Quantum Computing: Applications and Challenges. arXiv:2410.00609. https://doi.org/10.48550/arXiv.2410.00609

  26. [34]

    G. M. Jones, H.-A. Jacobsen (2024). Distributed Quantum Computing for Chemical Applica- tions. 2024 IEEE International Conference on Quantum Computing and Engineering (QCE) . https://doi.org/10.1109/QCE60285.2024.10270

  27. [35]

    Pira and C

    L. Pira and C. Ferrie (2023). An Invitation to Distributed Quantum Neural Networks. Quantum Machine Intelligence , https://doi.org/10.1007/s42484-023-00114-3

  28. [36]

    H. T. Nguyen, P. Krishnan, D. Krishnaswamy et al (2024). Quantum Cloud Computing: A Review, Open Problems, and Future Directions. arXiv:2404.11420. https://doi.org/10.48550/arXiv.2404.11420

  29. [37]

    Moguel, J

    E. Moguel, J. Garcia-Alonso, J. M. Murillo (2024). Development and Deployment of Quantum Services. In: I. Exman et al.(eds.), Quantum Software , Springer. https://doi.org/10.1007/978-3- 031-64136-7 8

  30. [38]

    Phillipson (2023)

    F. Phillipson (2023). Quantum Computing in Telecommunication-A Survey. Mathematics, 2023, 11(15), 3423; https://doi.org/10.3390/math11153423

  31. [39]

    Baseri, V

    Y. Baseri, V. Chouhan, A. Ghorbani (2024). Cybersecurity in the Quantum Era: Assessing the Impact of Quantum Computing on Infrastructure. arXiv:2404.10659. https://doi.org/10.48550/arXiv.2404.10659

  32. [40]

    Dutta, A

    H. Dutta, A. K. Bhuyan (2024). Quantum Communication: From Fundamentals to Recent Trends, Challenges and Open Problems. arXiv:2406.04492. https://doi.org/10.48550/arXiv.2406.04492

  33. [41]

    Z. Li, K. Xue, J. Li, L. Chen, R. Li, Z. Wang, et al (2023). Entanglement-assisted quantum net- works: Mechanics, enabling technologies, challenges, and research directions. IEEE Communica- tions Surveys and Tutorials , 25, 4 pp. 2133-2189. https://doi.org/10.1109/COMST.2023.3294240

  34. [42]

    Mehic et al (2023)

    M. Mehic et al (2023). Quantum Cryptography in 5G Networks: A Comprehen- 34 Networked Quantum Services sive Overview. IEEE Communications Surveys and Tutorials , Volume: 26, Issue: 1, https://doi.org/10.1109/COMST.2023.3309051

  35. [43]

    A. B. Popa, P. G. Popescu (2024). The Future of QKD Networks. arXiv:2407.00877. https://doi.org/10.48550/arXiv.2407.00877

  36. [44]

    Abane, M

    A. Abane, M. Cubeddu, V. S. Mai, A. Battou (2025). Entanglement Routing in Quantum Networks: A Comprehensive Survey. IEEE Transactions on Quantum Engineering , pp. 1-36. https://doi.org/10.1109/TQE.2025.3541123

  37. [45]

    Gyongyosi, S

    L. Gyongyosi, S. Imre (2022). Advances in the Quantum Internet. Communications of the ACM , Volume 65, Issue 8, pp. 52-63. https://doi.org/10.1145/3524455

  38. [46]

    Wehner, D

    S. Wehner, D. Elkouss, R. Hanson (2018). Quantum internet: A vision for the road ahead. Science 362, 6412. https://doi.org/10.1126/science.aam9288

  39. [47]

    Y. Li. et al (2024). A Survey of Quantum Internet Protocols From a Layered Perspective. IEEE Communications Surveys and Tutorials , Volume: 26, Issue: 3. https://doi.org/10.1109/COMST.2024.3361662

  40. [48]

    J. Ang, G. Carini, Y. Chen, I. Chuang et al (2024). Architectures for Multinode Superconducting Quantum Computers. ACM Transactions on Quantum Computing , Volume 5, Issue 3, pp. 1-59. https://doi.org/10.1145/3674151

  41. [49]

    Barz et al (2012)

    S. Barz et al (2012). Demonstration of blind quantum computing. Science, vol. 335, 6066, pp. 303-308. https://doi.org/10.1126/science.1214707

  42. [50]

    Ruiting et al (2021)

    S. Ruiting et al (2021). Verifiable Multi-Party Universal Blind Quantum Computing in Distributed Networks. Chinese Journal of Electronics , vol. 30, no. 4, pp. 712-718. https://dx.doi.org/10.1049/cje.2021.05.013

  43. [51]

    Mantri, C

    A. Mantri, C. Perez-Delgado and J. Fitzsimons (2013). Optimal blind quantum computation.Phys- ical Review Letters, vol. 111, no. 23, p. 230502. https://doi.org/10.1103/PhysRevLett.111.230502

  44. [52]

    J. I. Cirac, A. K. Ekert, S. F. Huelga, C. Macchiavello (1999). Distributed quantum computation over noisy channels. Phys. Rev. A 59. 4249-4254. https://doi.org/10.1103/PhysRevA.59.4249

  45. [53]

    Collins, N

    D. Collins, N. Linden, S. Popescu (2001). Nonlocal content of quantum operations.Physical Review A 64, 7. https://doi.org/10.1103/PhysRevA.64.032302

  46. [54]

    Eisert, K

    J. Eisert, K. Jacobs, P. Papadopoulos, M. B. Plenio (2000). Optimal local implementation of nonlocal quantum gates. Physical Review A 62 (5). https://doi.org/10.1103/PhysRevA.62.052317

  47. [55]

    Gidney, M

    C. Gidney, M. Ekera (2021). How to factor 2048 bit RSA integers in 8 hours using 20 million noisy qubits. Quantum 5 (2021). https://doi.org/10.22331/q-2021-04-15-433

  48. [56]

    Gyongyosi, S

    L. Gyongyosi, S. Imre (2018). Multiple Access Multicarrier Continuous-Variable Quantum Key Distribution. Chaos, Solitons and Fractals , 114, pp. 491-505. https://doi.org/10.1016/j.chaos.2018.07.006

  49. [57]

    Gyongyosi, S

    L. Gyongyosi, S. Imre (2020). Resource Prioritization and Balancing for the Quantum Internet. Scientific Reports, https://doi.org/DOI: 10.1038/s41598-020-78960-5

  50. [58]

    Gyongyosi, S

    L. Gyongyosi, S. Imre (2021). Scalable distributed gate-model quantum computers. Sci. Rep., 11,

  51. [59]

    H. Li, D. Qiu, L. Luo (2023). Distributed exact quantum algorithms for Deutsch-Jozsa problem. arXiv.2303.10663. https://doi.org/10.48550/arXiv.2303.10663

  52. [60]

    N. M. Neumann, R. van Houte, T. Attema (2020). Imperfect distributed quantum phase estimation. Computational Science-ICCS 2020 , Vol. 12142 of LNCS, Springer, pp. 605-615. https://doi.org/10.1007/978-3-030-50433-5 46

  53. [61]

    Y. Shi, T. Nguyen, S. Stein, T. Stavenger, M. Warner, M. Roetteler et al (2023). A reference implementation for a quantum message passing interface. Proc. of the SC’23 Workshops of The Int. Conf. on High Performance Computing , Network, Storage, and Analysis, ACM, New York, NY...

  54. [62]

    J. Tan, L. Xiao, D. Qiu, L. Luo, P. Mateus (2022). Distributed quantum algorithm for Simon’s problem. Physical Review A 106, 3. https://doi.org/10.1103/PhysRevA.106.032417

  55. [63]

    Van Meter, W

    R. Van Meter, W. J. Munro, K. Nemoto, K. M. Itoh (2008). Arithmetic on a distributed- memory quantum multicomputer. ACM J. on Emerging Technologies in Computing Systems 3, 4. Laszlo Gyongyosi and Sandor Imre 35 https://doi.org/10.1145/1324177.1324179

  56. [64]

    L. Xiao, D. Qiu, L. Luo, P. Mateus (2023). Distributed quantum-classical hybrid Shor’s algorithm. arXiv.2304.12100. https://doi.org/10.48550/arXiv.2304.12100

  57. [65]

    Zhang and Q

    Z. Zhang and Q. Zhuang (2021). Distributed quantum sensing. Quantum Science and Technology, vol. 6, no. 4, p. 043001. https://doi.org/10.1088/2058-9565/abd4c3

  58. [66]

    C. L. Degen, F. Reinhard, and P. Cappellaro (2017). Quantum sensing.Reviews of Modern Physics, vol. 89, no. 3, p. 035002. https://doi.org/10.1103/RevModPhys.89.035002

  59. [67]

    X. Zhou, D. Qiu, L. Luo (2023). Distributed Bernstein-Vazirani algorithm. Physica A: Statistical Mechanics and its Applications 629, 129209. https://doi.org/10.1016/j.physa.2023.129209

  60. [68]

    X. Zhou, D. Qiu, L. Luo (2023). Distributed exact Grover’s algorithm. Frontiers of Physics 18 (5) 1-25. https://doi.org/10.1007/s11467-023-1327-x

  61. [69]

    B. He, D. Zhang, S. W. Loke, S. Lin, L. Lu (2024). Building a Hierarchical Architecture and Com- munication Model for the Quantum Internet.IEEE Journal on Selected Areas in Communications, 42, 7. https://doi.org/10.1109/JSAC.2024.3380103

  62. [70]

    Kozlowski, S

    W. Kozlowski, S. Wehner, R. V. Meter, B. Rijsman, A. S. Cacciapuoti, M. Caleffi et al (2023). RFC 9340: Architectural principles for a quantum Internet , Internet Research Task Force (IRTF). https://doi.org/10.17487/RFC9340

  63. [71]

    Roffe (2019)

    J. Roffe (2019). Quantum Error Correction: An Introductory Guide. Contemporary Physics, Vol. 60, 3. https://doi.org/10.1080/00107514.2019.1667078

  64. [72]

    Paler, S

    A. Paler, S. J. Devitt (2015). An introduction to Fault-tolerant Quantum Com- puting. DAC’15 Proceedings of the 52nd Annual Design Automation Conference , 60. https://doi.org/10.1145/2744769.2747911

  65. [73]

    Heshami, D

    K. Heshami, D. G. England, P. C. Humphreys (2016). Quantum memories: emerg- ing applications and recent advances. Journal of Modern Optics 63, No. S3, S42-S65. https://doi.org/10.1080/09500340.2016.1148212

  66. [74]

    B. M. Terhal (2015). Quantum Error Correction for Quantum Memories. Rev. Mod. Phys. 87,

  67. [75]

    Bravyi, D

    S. Bravyi, D. Gosset, and R. Konig (2018). Quantum advantage with shallow circuits. Science 362, 308. https://doi.org/10.1126/science.aar3106

  68. [76]

    J. D. Hidary (2021). Quantum computing: an Applied Approach . Springer, ISBN-10: 3030832732

  69. [77]

    T. D. Ladd, F. Jelezko, R. Laflamme, Y. Nakamura, C. Monroe, and J. L. O’Brien (2010). Quantum computers. Nature, vol. 464, no. 7285, pp. 45–53. https://doi.org/10.1038/nature08812

  70. [78]

    AbuGhanem (2024)

    M. AbuGhanem (2024). Photonic Quantum Computers. arXiv:2409.08229. https://doi.org/10.48550/arXiv.2409.08229

  71. [79]

    Kjaergaard, M

    M. Kjaergaard, M. E. Schwartz, J. Braumuller, P. Krantz, J. I.-J. Wang, S. Gustavsson, and W. D. Oliver (2020). Superconducting qubits: Current state of play. Annual Review of Condensed Matter Physics, vol. 11, pp. 369–395. https://doi.org/10.1146/annurev-conmatphys-031119-050605

  72. [80]

    Arute et al (2019)

    F. Arute et al (2019). Quantum supremacy using a programmable superconducting processor. Nature, Vol 574. https://doi.org/10.1038/s41586-019-1666-5

  73. [81]

    Maurand, X

    R. Maurand, X. Jehl, D. Kotekar-Patil, A. Corna, H. Bohuslavskyi, R. Lavieville, L. Hutin, S. Barraud, M. Vinet, M. Sanquer et al (2016). A cmos silicon spin qubit. Nature communications, vol. 7, no. 1, p. 13575. https://doi.org/10.1038/ncomms13575

  74. [82]

    Henriet, L

    L. Henriet, L. Beguin, A. Signoles, T. Lahaye, A. Browaeys, G.-O. Reymond, and C. Jurczak (2020). Quantum computing with neutral atoms. Quantum, vol. 4, p. 327. https://doi.org/10.22331/q-2020-09-21-327

  75. [83]

    Gong, Z.-Y

    R.-Y. Gong, Z.-Y. He, C.-H. Yu, G.-F. Zhang, F. Nori, Z.-L. Xiang (2024). Tunable quantum router with giant atoms, implementing quantum gates, teleportation, non-reciprocity, and circulators. arXiv:2411.19307. https://doi.org/10.48550/arXiv.2411.19307

  76. [84]

    C. D. Bruzewicz, J. Chiaverini, R. McConnell, and J. M. Sage (2019). Trapped-ion quan- tum computing: Progress and challenges. Applied Physics Reviews , vol. 6, no. 2, p. 021314. https://doi.org/10.1063/1.5088164

  77. [85]

    Nayak, S

    C. Nayak, S. H. Simon, A. Stern, M. Freedman, and S. D. Sarma (2008). Non-abelian anyons 36 Networked Quantum Services and topological quantum computation. Reviews of Modern Physics , vol. 80, no. 3, p. 1083. https://doi.org/10.1103/RevModPhys.80.1083

  78. [86]

    Pezzagna, J

    S. Pezzagna, J. Meijer (2021). Quantum computer based on color centers in diamond. Appl. Phys. Rev. 8, 011308. https://doi.org/10.1063/5.0007444

  79. [87]

    L. M. K. Vandersypen et al (2001). Experimental realization of Shor’s quantum factoring algorithm using nuclear magnetic resonance. Nature 414, 883-887. https://doi.org/10.1038/414883a

  80. [88]

    L. M. K. Vandersypen, I. L. Chuang (2005). NMR Techniques for Quantum Control and Compu- tation. Rev. Mod. Phys. 76, 1037. https://doi.org/10.1103/RevModPhys.76.1037

  81. [89]

    N. C. Jones, R. Van Meter, A. G. Fowler, P. L. McMahon, J. Kim, T. D. Ladd, Y. Ya- mamoto (2012). Layered architecture for quantum computing. Phys. Rev. X , vol. 2, 031007. https://doi.org/10.1103/PhysRevX.2.031007

  82. [90]

    Rodrigo, S

    S. Rodrigo, S. Abadal, E. Alarcon et al (2021). On Double Full-Stack Communication- Enabled Architectures for Multicore Quantum Computers. IEEE Micro , 41, 48–56. https://doi.org/10.1109/MM.2021.3092706

  83. [91]

    Van Meter (2014)

    R. Van Meter (2014). Quantum Networking . ISBN 1118648927, 9781118648926, John Wiley and Sons Ltd

  84. [92]

    Illiano, M

    J. Illiano, M. Caleffi, A. Manzalini, A. S. Cacciapuoti (2022). Quantum Inter- net protocol stack: A comprehensive survey. Computer Networks 213, 109092. https://doi.org/10.1016/j.comnet.2022.109092

  85. [93]

    Z. Li, K. Xue, J. Li, N. Yu, J. Liu, D. S. L. Wei et al (2021). Building a large scale and wide- area quantum Internet based on an OSI-alike model. China Communications 18, 10, pp. 1-14. https://doi.org/10.23919/JCC.2021.10.001

  86. [94]

    Dahlberg, M

    A. Dahlberg, M. Skrzypczyk, T. Coopmans, L. Wubben, F. Rozpundefineddek, M. Pom- pili et al (2019). A link layer protocol for quantum networks. Proceedings of the ACM Special Interest Group on Data Communication , ACM, New York, NY, USA, pp. 159-173. https://doi.org/10.1145/33...

  87. [95]

    Pirker, W

    A. Pirker, W. Dur (2019). A quantum network stack and protocols for reliable entanglement-based networks. New Journal of Physics 21, 3. https://doi.org/10.1088/1367-2630/ab05f7

  88. [96]

    R. V. Meter, J. Touch (2013). Designing quantum repeater networks. IEEE Communications Magazine 51, 8 pp. 64-71. https://doi.org/10.1109/MCOM.2013.6576340

  89. [98]

    Preskill (2018)

    J. Preskill (2018). Quantum Computing in the NISQ era and beyond. Quantum 2, 79. https://doi.org/10.22331/q-2018-08-06-79

  90. [99]

    A. W. Harrow and A. Montanaro (2017). Quantum Computational Supremacy. Nature, vol 549, pages 203-209. https://doi.org/10.1038/nature23458

  91. [100]

    Aaronson and L

    S. Aaronson and L. Chen (2017). Complexity-theoretic foundations of quantum supremacy experi- ments. Proceedings of the 32nd Computational Complexity Conference, CCC ’17, pages 22:1-22:67. https://doi.org/10.4230/LIPIcs.CCC.2017.22

  92. [101]

    Farhi, J

    E. Farhi, J. Goldstone, S. Gutmann and H. Neven (2017). Quantum Algorithms for Fixed Qubit Architectures. arXiv:1703.06199v1. https://doi.org/10.48550/arXiv.1703.06199

  93. [102]

    Mastriani (2024)

    M. Mastriani (2024). Explaining the results of quantum mechanics via entanglement closed loop. Optical and Quantum Electronics , 56, 801. https://doi.org/10.1007/s11082-024-06393-9

  94. [103]

    Alexeev et al (2019)

    Y. Alexeev et al (2019). Quantum Computer Systems for Scientific Discovery. PRX Quantum 2, 017001. https://doi.org/10.1103/PRXQuantum.2.017001

  95. [104]

    Loncar et al (2019)

    M. Loncar et al (2019). Development of Quantum InterConnects for Next-Generation Information Technologies. PRX Quantum 2, 017002. https://doi.org/10.1103/PRXQuantum.2.017002

  96. [105]

    Foxen et al (2020)

    B. Foxen et al (2020). Demonstrating a Continuous Set of Two-qubit Gates for Near-term Quantum Algorithms. Phys. Rev. Lett , 125, 120504. https://doi.org/10.1103/PhysRevLett.125.120504

  97. [106]

    Ajagekar, T

    A. Ajagekar, T. Humble, and F. You (2020). Quantum Computing based Hybrid Solution Strate- gies for Large-scale Discrete-Continuous Optimization Problems. Computers and Chemical Engi- Laszlo Gyongyosi and Sandor Imre 37 neering Vol 132, 106630. https://doi.org/10.1016/j.compch...

  98. [107]

    Ajagekar and F

    A. Ajagekar and F. You (2019). Quantum computing for energy systems optimization: Challenges and opportunities. Energy, Volume 179, pp. 76-89. https://doi.org/10.1016/j.energy.2019.04.186

  99. [108]

    Harrigan et al (2020)

    M. Harrigan et al (2020). Quantum Approximate Optimization of Non-Planarusing eigenen- ergies Graph Problems on a Planar Superconducting Processor. Nature Physics 17, 332-336. https://doi.org/10.1038/s41567-020-01105-y

  100. [109]

    Rubin et al (2020)

    N. Rubin et al (2020). Hartree-Fock on a superconducting qubit quantum computer. Science 69 (6507), 1084-1089. https://doi.org/10.1126/science.abb9811

  101. [110]

    Farhi, J

    E. Farhi, J. Goldstone and S. Gutmann (2014). A Quantum Approximate Optimization Algorithm. arXiv:1411.4028v1. https://doi.org/10.48550/arXiv.1411.4028

  102. [111]

    Farhi, J

    E. Farhi, J. Goldstone, S. Gutmann and L. Zhou, L (2019). The Quantum Approximate Op- timization Algorithm and the Sherrington-Kirkpatrick Model at Infinite Size. Quantum 6, 759. https://doi.org/10.22331/q-2022-07-07-759

  103. [112]

    Farhi and H

    E. Farhi and H. Neven (2018). Classification with Quantum Neural Networks on Near Term Processors. arXiv:1802.06002v1. https://doi.org/10.48550/arXiv.1802.06002

  104. [114]

    K. A. Brown and T. Roser (2020). Towards storage rings as quantum computers. Phys. Rev. Accel. Beams 23, 054701. https://doi.org/10.1103/PhysRevAccelBeams.24.049901

  105. [115]

    J. Bae, P. M. Alsing, D. Ahn et al (2020). Quantum circuit optimization using quantum Karnaugh map. Sci Rep 10, 15651, https://doi.org/10.1038/s41598-020-72469-7

  106. [116]

    Li et al (2020)

    S. Li et al (2020). Programmable Unitary Operations for Orbital Angular Mo- mentum Encoded States. National Science Open , Volume 1, Issue 2: 20220019. https://doi.org/10.1360/nso/20220019

  107. [117]

    S. Bugu, F. Ozaydin and T. Kodera (2020). Surpassing the Classical Limit in Magic Square Game with Distant Quantum Dots Coupled to Optical Cavities. Sci Rep . DOI: https://doi.org/10.1038/s41598-020-79295-x

  108. [118]

    Teplukhin, B

    A. Teplukhin, B. Kendrick and D. Babikov (2020). Solving complex eigenvalue problems on a quantum annealer with applications to quantum scattering resonances. Phys. Chem. Chem. Phys . https://doi.org/10.1039/D0CP04272B

  109. [119]

    Lloyd (2018)

    S. Lloyd (2018). Quantum approximate optimization is computationally universal. arXiv:1812.11075. https://doi.org/10.48550/arXiv.1812.11075

  110. [120]

    Q. Zhu. et al (2022). Quantum computational advantage via 60-qubit 24-cycle random circuit sampling. Science bulletin , 67(3):240-245. https://doi.org/10.1016/j.scib.2021.10.017

  111. [121]

    Aaronson, A

    S. Aaronson, A. Arkhipov (2013). The computational complexity of linear optics. Theory of Com- puting, 9(4):143-252. https://doi.org/10.1145/1993636.1993682

  112. [122]

    Zhong et al (2020)

    H-S. Zhong et al (2020). Quantum computational advantage using photons. Science, 370(6523):1460-1463. https://doi.org/10.1126/science.abe8770

  113. [123]

    L. S. Madsen et al (2022). Quantum computational advantage with a programmable photonic processor. Nature, 606(7912):75-81. https://doi.org/10.1038/s41586-022-04725-x

  114. [124]

    Reiher, N

    M. Reiher, N. Wiebe, K. M. Svore et al (2017). Elucidating reaction mechanisms on quantum computers. Proc Natl Acad Sci 114:7555-7560. https://doi.org/10.1073/pnas.1619152114

  115. [125]

    Mandra and H

    S. Mandra and H. G. Katzgraber (2018). A deceptive step towards quantum speedup detection. Quantum Sci Technol, 3:04LT. https://doi.org/10.1088/2058-9565/aac8b2

  116. [126]

    Moret-Bonillo (2015)

    V. Moret-Bonillo (2015). Can artificial intelligence benefit from quantum computing? Prog Artif Intell, 3:89-105. https://doi.org/10.1007/s13748-014-0059-0

  117. [127]

    Yamakawa and M

    T. Yamakawa and M. Zhandry (2022). Verifiable quantum advantage without structure. 2022 IEEE 63rd Annual Symposium on Foundations of Computer Science (FOCS) , pages 69-74. https://doi.org/10.1145/3658665

  118. [128]

    T. F. Ronnow, Z. Wang, J. Job et al (2014). Defining and detecting quantum speedup. Science, 345:420-424. https://doi.org/10.1126/science.1252319. 38 Networked Quantum Services

  119. [129]

    Aaronson (2015)

    S. Aaronson (2015). Quantum Machine Learning Algorithms: Read the Fine Print. Nature Physics 11:291-293. https://doi.org/10.1038/nphys3272

  120. [130]

    Bharti, A

    K. Bharti, A. Cervera-Lierta, T. H. Kyaw, T. Haug, S. Alperin-Lea, A. Anand, M. Degroote, H. Heimonen, J. S. Kottmann, T. Menke, et al (2022). Noisy intermediate-scale quantum (NISQ) algorithms. Rev. Mod. Phys. 94, 015004. https://doi.org/10.1103/RevModPhys.94.015004

  121. [131]

    P. W. Shor (1994). Algorithms for quantum computation: discrete logarithms and fac- toring. Proceedings 35th Annual Symposium on Foundations of Computer Science 124-134. https://doi.org/10.1109/SFCS.1994.365700

  122. [132]

    V. S. Denchev, S. Boixo, S. V. Isakov et al (2016). What is the computational value of finite-range tunneling? Phys Rev X 6, 1-17. https://doi.org/10.1103/PhysRevX.6.031015

  123. [133]

    P. J. J. O’Malley et al (2016). Scalable Quantum Simulation of Molecular Energies. Phys Rev X , 6, 031007. https://doi.org/10.1103/PhysRevX.6.031007

  124. [134]

    Arute et al (2020)

    F. Arute et al (2020). Observation of separated dynamics of charge and spin in the Fermi-Hubbard model. arXiv:2010.07965. https://doi.org/10.48550/arXiv.2010.07965

  125. [135]

    Aleiner et al (2020)

    I. Aleiner et al (2020). Accurately computing electronic properties of materials using eigenenergies. arXiv:2012.00921. https://doi.org/10.1038/s41586-021-03576-2

  126. [136]

    Farhi, D

    E. Farhi, D. Gamarnik and S. Gutmann (2020). The Quantum Approximate Optimiza- tion Algorithm Needs to See the Whole Graph: A Typical Case. arXiv:2004.09002v1. https://doi.org/10.48550/arXiv.2004.09002

  127. [137]

    Farhi, D

    E. Farhi, D. Gamarnik and S. Gutmann (2020). The Quantum Approximate Optimiza- tion Algorithm Needs to See the Whole Graph: Worst Case Examples. arXiv:2005.08747. https://doi.org/10.48550/arXiv.2005.08747

  128. [138]

    Peruzzo et al (2014)

    A. Peruzzo et al (2014). A variational eigenvalue solver on a photonic quantum processor. Nat. Commun. 5, 4213. https://doi.org/10.1038/ncomms5213

  129. [139]

    Wecker, M

    D. Wecker, M. B. Hastings, and M. Troyer (2015). Progress towards practical quantum variational algorithms. Phys. Rev. A 92, 042303. https://doi.org/10.1103/PhysRevA.92.042303

  130. [141]

    Yuan et al (2019)

    X. Yuan et al (2019). Theory of variational quantum simulation. Quantum 3, 191. https://doi.org/10.22331/q-2019-10-07-191

  131. [143]

    Mitarai and K

    K. Mitarai and K. Fujii (2021). Constructing a virtual two-qubit gate by sampling single-qubit operations. New Journal of Physics 23. https://doi.org/10.1088/1367-2630/abd7bc

  132. [144]

    T. Peng, A. W. Harrow, M. Ozols, and X. Wu (2020). Simulating Large Quan- tum Circuits on a Small Quantum Computer. Physical Review Letters 125, 150504. https://doi.org/10.1103/PhysRevLett.125.150504

  133. [145]

    Brenner, C

    L. Brenner, C. Piveteau, D. Sutter (2023). Optimal wire cutting with classical communication. arXiv.2302.03366. https://doi.org/10.48550/arXiv.2302.03366

  134. [146]

    Gokhale, O

    P. Gokhale, O. Angiuli, Y. Ding, K. Gui, T. Tomesh, M. Suchara, et al (2019). Minimizing state preparations in variational quantum eigensolver by partitioning into commuting families. arXiv.1907.13623

  135. [147]

    Tilly, H

    J. Tilly, H. Chen, S. Cao, D. Picozzi, K. Setia, Y. Li, et al (2022). The variational quantum eigensolver: A review of methods and best practices. Physics Reports 986, 1–128. https://doi.org/10.1016/j.physrep.2022.08.003

  136. [148]

    Y. Wang, L. M. Sager-Smith, D. A. Mazziotti (2023). Quantum simulation of bosons with the contracted quantum eigensolver. New Journal of Physics 25, 10. https://doi.org/10.1088/1367- 2630/acf9c3

  137. [149]

    Schuld, V

    M. Schuld, V. Bergholm, C. Gogolin, J. Izaac, and N. Killoran (2019). Evaluating analytic gradi- ents on quantum hardware. Physical Review A 99. https://doi.org/10.1103/PhysRevA.99.032331. Laszlo Gyongyosi and Sandor Imre 39

  138. [150]

    A. J. McCaskey, D. I. Lyakh, E. F. Dumitrescu, S. S. Powers, T. S. Humble (2019). XACC: A system-level software infrastructure for heterogeneous quantum-classical computing. Quantum Science and Technology, Volume 5, Number 2. https://doi.org/10.1088/2058-9565/ab6bf6

  139. [151]

    A. J. McCaskey, T. Nguyen, A. Santana, D. Claudino, T. Kharazi, H. Finkel (2021). Extending C++ for heterogeneous quantum-classical computing. ACM Trans. on Quantum Computing 2, 2, 1–36. https://doi.org/10.1145/3462670

  140. [152]

    J. K. Lee, O. T. Brown, M. Bull, M. Ruefenacht, J. Doerfert, M. Klemm et al. (2023). Quantum task offloading with the openmp api. arXiv.2311.03210. https://doi.org/10.48550/arXiv.2311.03210

  141. [153]

    Gambetta (2022)

    J. Gambetta (2022). Quantum-centric supercomputing: The next wave of computing. URL: https: //www.ibm.com/quantum/blog/next-wave-quantum-centric-supercomputing

  142. [154]

    Gambetta (2023)

    J. Gambetta (2023). The hardware and software for the era of quantum utility is here . URL: https://www.ibm.com/quantum/blog/quantum-roadmap-2033

  143. [155]

    L. Liu, X. Dou (2021). QuCloud: A new qubit mapping mechanism for multiprogramming quantum computing in cloud environment. IEEE Int. Symposium on High-performance Computer Architec- ture (HPCA), IEEE, pp. 167–178. https://doi.org/10.1109/HPCA51647.2021.00024

  144. [156]

    L. Liu, X. Dou, QuCloud+ (2024). A holistic qubit mapping scheme for single/multi-programming on 2D/3D NISQ quantum computers. ACM Trans. on Architecture and Code Optimization 21, 1, 1–27. https://doi.org/10.1145/3631525

  145. [157]

    Bandic, C

    M. Bandic, C. G. Almudever, S. Feld (2023). Interaction graph-based characterization of quantum benchmarks for improving quantum circuit mapping techniques. Quantum Machine Intelligence 5, 1–30. https://doi.org/10.1007/s42484-023-00124-1

  146. [158]

    K. Li, D. Qiu, L. Li, S. Zheng, Z. Rong (2017). Application of distributed semiquan- tum computing model in phase estimation. Information Processing Letters 120, 23-29. https://doi.org/10.1016/j.ipl.2016.12.002

  147. [159]

    Tanaka, Y

    T. Tanaka, Y. Suzuki, S. Uno, R. Raymond, T. Onodera, N. Yamamoto (2021). Amplitude esti- mation via maximum likelihood on noisy quantum computer. Quantum Information Processing 20, 1-29. https://doi.org/10.1007/s11128-021-03215-9

  148. [160]

    Zhang, P

    K. Zhang, P. Rao, K. Yu, H. Lim, V. Korepin (2021). Implementation of efficient quan- tum search algorithms on NISQ computers. Quantum Information Processing , 20, 233. https://doi.org/10.1007/s11128-021-03165-2

  149. [161]

    G. Park, K. Zhang, K. Yu, V. Korepin (2023). Quantum multi-programming for Grover’s search. Quantum Information Processing 22, 1. https://doi.org/10.1007/s11128-022-03793-2

  150. [162]

    P. Das, S. S. Tannu, P. J. Nair, M. Qureshi (2019). A case for multiprogramming quantum comput- ers. Proceedings of the 52nd Annual IEEE/ACM International Symposium on Microarchitecture , pp. 291-303. https://doi.org/10.1145/3352460.3358287

  151. [163]

    S. Niu, A. Todri-Sanial (2023). Enabling multi-programming mechanism for quantum computing in the NISQ era. Quantum 7. https://doi.org/10.22331/q-2023-02-16-925

  152. [164]

    Ash-Saki, M

    A. Ash-Saki, M. Alam, S. Ghosh (2020). Analysis of crosstalk in NISQ devices and security im- plications in multi-programming regime. Proceedings of the ACM/IEEE International Symposium on Low Power Electronics and Design , pp. 25–30. https://doi.org/10.1145/3370748.3406570

  153. [165]

    Ohkura (2021)

    Y. Ohkura (2021). Crosstalk-aware NISQ multi-programming . Bachelor’s thesis, Faculty Policy Manage., Keio Univ., Tokyo, Japan

  154. [166]

    Parekh, A

    R. Parekh, A. Ricciardi, A. Darwish, and S. DiAdamo (2021). Quantum Algorithms and Simulation for Parallel and Distributed Quantum Computing. 2021 IEEE/ACM Second International Workshop on Quantum Computing Software (QCS) , pp. 9-19. https://doi.ieeecomputersociety.org/10.1109...

  155. [167]

    Andres-Martinez, C

    P. Andres-Martinez, C. Heunen (2019). Automated distribution of quan- tum circuits via hypergraph partitioning. Physical Review A 100, 3, 032308. https://doi.org/10.1103/PhysRevA.100.032308

  156. [168]

    Pastor, P

    A. Pastor, P. Escofet, S. B. Rached, E. Alarcon, P. Barlet-Ros, S. Abadal (2024). Circuit parti- tioning for multi-core quantum architectures with deep reinforcement learning. arXiv.2401.17976. 40 Networked Quantum Services https://doi.org/10.48550/arXiv.2401.17976

  157. [169]

    Akhremtsev, T

    Y. Akhremtsev, T. Heuer, P. Sanders, S. Schlag (2017). Engineering a direct k-way hypergraph partitioning algorithm. Proceedings of the Meeting on Algorithm Engineering and Experiments (ALENEX), SIAM, pp. 28-42. https://doi.org/10.1137/1.9781611974768.3

  158. [170]

    Schlag, T

    S. Schlag, T. Heuer, L. Gottesburen, Y. Akhremtsev, C. Schulz, P. Sanders (2023). High-quality hypergraph partitioning. ACM Journal of Experimental Algorithmics 27, 1-39. https://doi.org/10.1145/3529090

  159. [172]

    Andres-Martinez, T

    P. Andres-Martinez, T. Forrer, D. Mills, J.-Y. Wu, L. Henaut, K. Yamamoto et al (2023). Dis- tributing circuits over heterogeneous, modular quantum computing network architectures. Quan- tum Science and Technology, 9, 4. https://doi.org/10.1088/2058-9565/ad6734

  160. [173]

    R. G. Sundaram, H. Gupta, C. R. Ramakrishnan (2021). Efficient distribution of quantum circuits. 35th Int. Symp. on Distributed Computing (DISC) , Vol. 209 of Leibniz International Proceedings in Informatics (LIPIcs). https://doi.org/10.4230/LIPIcs.DISC.2021.41

  161. [174]

    R. G. Sundaram, H. Gupta, C. R. Ramakrishnan (2022). Distribution of quantum circuits over gen- eral quantum networks. 2022 IEEE Int. Conf. on Quantum Computing and Engineering (QCE) , pp. 415-425. https://doi.ieeecomputersociety.org/10.1109/QCE53715.2022.00063

  162. [175]

    R. G. Sundaram, H. Gupta (2023). Distributing quantum circuits using tele- portations. 2023 IEEE Int. Conf. on Quantum Software (QSW) , pp. 186-192. https://doi.ieeecomputersociety.org/10.1109/QSW59989.2023.00030

  163. [176]

    Davarzani, M

    Z. Davarzani, M. Zomorodi-Moghadam, M. Houshmand, M. Nouri-Baygi (2020). A dynamic pro- gramming approach for distributing quantum circuits by bipartite graphs. Quantum Information Processing 19, 9. https://doi.org/10.1007/s11128-020-02871-7

  164. [177]

    B. W. Kernighan, S. Lin (1970). An efficient heuristic procedure for partitioning graphs. The Bell system technical journal 49, 2, 291-307. https://doi.org/10.1002/j.1538-7305.1970.tb01770.x

  165. [178]

    Zomorodi-Moghadam, M

    M. Zomorodi-Moghadam, M. Houshmand, M. Houshmand (2018). Optimizing teleportation cost in distributed quantum circuits. International Journal of Theoretical Physics 57, 3, 848-861. https://doi.org/10.1007/s10773-017-3618-x

  166. [179]

    Houshmand, Z

    M. Houshmand, Z. Mohammadi, M. Zomorodi-Moghadam, M. Houshmand (2020). An evolution- ary approach to optimizing teleportation cost in distributed quantum computation. International Journal of Theoretical Physics 59, 4. https://doi.org/10.1007/s10773-020-04409-0

  167. [180]

    O. Daei, K. Navi, M. Zomorodi-Moghadam (2020). Optimized quantum circuit partitioning. In- ternational Journal of Theoretical Physics 59, 12, https://doi.org/3804-3820

  168. [181]

    Nikahd, N

    E. Nikahd, N. Mohammadzadeh, M. Sedighi, M. S. Zamani (2021). Automated window-based partitioning of quantum circuits. Physica Scripta 96, 3, 035102. 10.1088/1402-4896/abd57c

  169. [182]

    C. M. Fiduccia, R. M. Mattheyses (1982). A linear-time heuristic for improving net- work partitions. Papers on Twenty-five years of electronic design automation , pp. 175-181. https://doi.org/10.1109/DAC.1982.1585498

  170. [184]

    Clark, T

    J. Clark, T. Humble, H. Thapliyal (2023). TDAG: Tree-based directed acyclic graph partitioning for quantum circuits. Proceedings of the Great Lakes Symposium on VLSI 2023 , GLSVLSI ’23, ACM, New York, NY, USA, p. 587-592. https://doi.org/10.1145/3583781.3590234

  171. [185]

    T. Park, C. Y. Lee (1995). Algorithms for partitioning a graph. Computers and Industrial Engi- neering 28, 4, 899–909. https://doi.org/10.1016/0360-8352(95)00003-J

  172. [186]

    J. M. Baker, C. Duckering, A. Hoover, F. T. Chong (2020). Time-sliced quantum circuit partition- ing for modular architectures. 17th ACM Int. Conf. on Computing Frontiers 2020 Proceedings , ACM, pp. 98-107. https://doi.org/10.1145/3387902.3392617. Laszlo Gyongyosi and Sandor Imre 41

  173. [187]

    Escofet, A

    P. Escofet, A. Ovide, C. G. Almudever, E. Alarcon, S. Abadal (2023). Hungarian qubit assign- ment for optimized mapping of quantum circuits on multi-core architectures. IEEE Computer Architecture Letters. https://doi.org/10.1109/LCA.2023.3318857

  174. [188]

    Bandic, L

    M. Bandic, L. Prielinger, J. Nublein, A. Ovide, S. Rodrigo, S. Abadal et al (2023). Mapping quantum circuits to modular architectures with QUBO. 2023 IEEE Int. Conf. on Quantum Computing and Engineering (QCE) , Vol. 1, IEEE, pp. 790–801. https://doi.org/10.1109/QCE57702.2023.00094

  175. [190]

    L. K. Grover (1997). Quantum telecomputation. arXiv.quant-ph/9704012. https://doi.org/10.48550/arXiv.quant-ph/9704012

  176. [191]

    Gupta, A

    M. Gupta, A. Pathak (2007). A scheme for distributed quantum search through simultaneous state transfer mechanism. Annalen der Physik 16, 12, pp. 791–797. https://doi.org/10.1002/andp.200710265

  177. [192]

    Yimsiriwattana and S

    A. Yimsiriwattana and S. J. Lomonaco (2004). Distributed quantum computing: A distributed Shor algorithm. Quantum Information and Computation II , vol. 5436. International Society for Optics and Photonics, pp. 360–372. DOI: https://doi.org/10.1117/12.546504

  178. [193]

    Ekera, J

    M. Ekera, J. Hastad (2017). Quantum algorithms for computing short discrete logarithms and factoring RSA integers. in: T. Lange, T. Takagi (Eds.), Post-Quantum Cryptography, no. 10346 in LNCS, Springer, pp. 347-363. https://doi.org/10.1007/978-3-319-59879-6 20

  179. [194]

    Z.-Y. Chen, Q. Zhou, C. Xue, X. Yang, G.-C. Guo, and G.-P. Guo (2018). 64-Qubit Quantum Circuit Simulation. Science Bulletin 63, 964. https://doi.org/10.1016/j.scib.2018.06.007

  180. [195]

    Eddins, M

    A. Eddins, M. Motta, T. P. Gujarati, S. Bravyi, A. Mezzacapo, C. Hadfield, and S. Sheldon (2022). Doubling the size of quantum simulators by entanglement forging. PRX Quantum 3. https://doi.org/10.1103/PRXQuantum.3.010309

  181. [196]

    M. A. Perlin, Z. H. Saleem, M. Suchara, and J. C. Osborn (2021). Quantum Circuit Cut- ting with Maximum Likelihood Tomography. npj Quantum Information , Vol. 7, No. 1, pp. 64. https://doi.org/10.1038/s41534-021-00390-6

  182. [197]

    W. Tang, T. Tomesh, M. Suchara, J. Larson, and M. Martonosi (2021). CutQC: using small Quantum computers for large Quantum circuit evaluations. Proceedings of the 26th ACM Inter- national Conference on Architectural Support for Programming Languages and Operating Systems (ASPL...

  183. [198]

    Z. H. Saleem, T. Tomesh, M. A. Perlin, P. Gokhale, and M. Suchara (2021). Divide and Con- quer for Combinatorial Optimization and Distributed Quantum Computation. arXiv:2107.07532. https://doi.org/10.48550/arXiv.2107.07532

  184. [199]

    Lowe et al (2023)

    A. Lowe et al (2023). Fast quantum circuit cutting with randomized measurements. Quantum 7,

  185. [200]

    S. C. Marshall, C. Gyurik, and V. Dunjko (2022). High Dimensional Quantum Machine Learn- ing With Small Quantum Computers. arXiv:2203.13739. https://doi.org/10.22331/q-2023-08-09- 1078

  186. [201]

    Piveteau and D

    C. Piveteau and D. Sutter (2023). Circuit knitting with classical communica- tion. IEEE Transactions on Information Theory , DOI: 10.1109/TIT.2023.3310797. https://doi.org/10.1109/TIT.2023.3310797

  187. [202]

    Tuysuz et al (2021)

    C. Tuysuz et al (2021). Classical Splitting of Parametrized Quantum Circuits. Quantum Mach. Intell. 5, 34. https://doi.org/10.1007/s42484-023-00118-z

  188. [203]

    Mitarai and K

    K. Mitarai and K. Fujii (2021). Overhead for simulating a non-local channel with local channels by quasiprobability sampling. Quantum 5, 388. https://doi.org/10.22331/q-2021-01-28-388

  189. [204]

    Bravyi, G

    S. Bravyi, G. Smith, and J. A. Smolin (2016). Trading classical and quantum computational resources. Physical Review X 6. https://doi.org/10.1103/PhysRevX.6.021043

  190. [205]

    A. W. Harrow, A. Lowe (2025). Optimal quantum circuit cuts with application to clustered Hamil- tonian simulation. PRX Quantum 6, 010316. https://doi.org/10.1103/PRXQuantum.6.010316. 42 Networked Quantum Services

  191. [206]

    Z. Zhou, Y. Du, X. Tian, D. Tao (2023). QAOA-in-QAOA: Solving large-scale max- cut problems on small quantum machines. Physical Review Applied 19 (2) (2023) 024027. https://doi.org/10.1103/PhysRevApplied.19.024027

  192. [207]

    Fujii, K

    K. Fujii, K. Mizuta, H. Ueda, K. Mitarai, W. Mizukami, Y. O. Nakagawa (2022). Deep variational quantum eigensolver: A divide-and-conquer method for solving a larger problem with smaller size quantum computers. PRX Quantum 3. https://doi.org/10.1103/PRXQuantum.3.010346

  193. [208]

    S. C. Marshall, C. Gyurik, V. Dunjko (2023). High dimensional quantum machine learning with small quantum computers. Quantum 7. https://doi.org/10.22331/q-2023-08-09-1078

  194. [209]

    Gottesman, I

    D. Gottesman, I. L. Chuang (1999). Demonstrating the viability of universal quantum computation using teleportation and single-qubit operations. Nature 402 6760, 390–393. https://doi.org/10.1038/46503

  195. [210]

    Y. F. Huang, X. F. Ren, Y. S. Zhang, L. M. Duan, G. C. Guo (2004). Exper- imental teleportation of a quantum controlled-NOT gate. Physical Review Letters 93. https://doi.org/10.1103/PhysRevLett.93.240501

  196. [211]

    K. S. Chou, J. Z. Blumoff, C. S. Wang, P. C. Reinhold, C. J. Axline, Y. Y. Gao, et al. (2018). Deterministic teleportation of a quantum gate between two logical qubits. Nature 561, 7723, 368–373. https://doi.org/10.1038/s41586-018-0470-y

  197. [212]

    Y. Wan, D. Kienzler, S. Erickson, K. Mayer, T. Tan, J. Wu, et al (2019). Quantum gate teleportation between separated qubits in a trapped-ion processor. Science 364 875–878. https://doi.org/10.1126/science.aaw9415

  198. [213]

    Daiss, S

    S. Daiss, S. Langenfeld, S. Welte, E. Distante, P. Thomas, L. Hartung, et al (2021). A quantum-logic gate between distant quantum-network modules. Science 371, 6529, 614–617. https://doi.org/10.1126/science.abe3150

  199. [214]

    C. Qiao, Y. Zhao, G. Zhao, H. Xu (2022). Quantum Data Networking for Dis- tributed Quantum Computing: Opportunities and Challenges. Proceedings of the IEEE Conference on Computer Communications Workshop , New York, NY, USA, pp. 1–6. https://doi.org/10.1109/INFOCOMWKSHPS54753.2...

  200. [215]

    Z. Cho, Y. Son, H. Jeong et al (2022). A New Approach to Quantum Computing Multi-Qubit Generation and Development of Quantum Computing Platform with Magnetic Resonance Imaging Techniques. arXiv:2206.05932. https://doi.org/10.48550/arXiv.2206.05932

  201. [216]

    Alarcon, S

    E. Alarcon, S. Abadal, F. Sebastiano et al (2023). Scalable multi-chip quantum architec- tures enabled by cryogenic hybrid wireless/quantum-coherent network-in-package. Proceedings of the IEEE International Symposium on Circuits and Systems , Monterey, CA, USA, pp. 1–5. https:...

  202. [217]

    Zheng, C

    Y. Zheng, C. Zhai, D. Liu et al (2023). Multichip multidimensional quantum networks with en- tanglement retrievability. Science, 381, 221–226. https://doi.org/10.1126/science.adg9210

  203. [218]

    Field, A

    M. Field, A. Chen, B. Scharmann et al (2024). Modular superconducting-qubit architecture with a multichip tunable coupler. Phys. Rev. Appl. , 21, 054063. https://doi.org/10.1103/PhysRevApplied.21.054063

  204. [219]

    Stokes, J

    J. Stokes, J. Izaac, N. Killoran, G. Carleo (2020). Quantum Natural Gradient. Quantum 4, 269. https://doi.org/10.22331/q-2020-05-25-269

  205. [220]

    M. S. Alvarez-Alvarado, F. E. Alban-Chacon, E. A. Lamilla-Rubio et al (2021). Three novel quantuminspired swarm optimization algorithms using different bounded potential fields.Scientific Reports 11, 1, 11655. https://doi.org/10.1038/s41598-021-90847-7

  206. [221]

    Wierichs, J

    D. Wierichs, J. Izaac, C. Wang, C. Y.-Y. Lin (2022). General parameter-shift rules for quantum gradients. Quantum 6, 677. https://doi.org/10.22331/q-2022-03-30-677

  207. [222]

    E. R. Anschuetz, B. T. Kiani (2022). Quantum variational algorithms are swamped with traps. Nature Communications 13, 1, 7760. https://doi.org/10.1038/s41467-022-35364-5

  208. [223]

    Failde, J

    D. Failde, J. D. Viqueira, M. Mussa Juane, A. Gomez (2023). Using differential evolution to avoid local minima in variational quantum algorithms. Scientific Reports 13, 1 16230. https://doi.org/10.1038/s41598-023-43404-3

  209. [224]

    J. D. Viqueira, D. Failde, M. M. Juane, A. Gomez, D. Mera (2025). Density matrix emulation Laszlo Gyongyosi and Sandor Imre 43 of quantum recurrent neural networks for multivariate time series prediction. Mach. Learn.: Sci. Technol. 6, 015023. https://doi.org/10.1088/2632-2153/ad9431

  210. [225]

    Ferrari, S

    D. Ferrari, S. Carretta, M. Amoretti (2023). A Modular Quantum Compilation Frame- work for Distributed Quantum Computing. IEEE Trans. Quantum Eng. 2023, 4, 2500213. https://doi.org/10.1109/TQE.2023.3303935

  211. [226]

    Mukhanov, B

    O. Mukhanov, B. L. T. Plourde, A. Opremcak et al (2019). Scalable Quantum Com- puting Infrastructure Based on Superconducting Electronics. Proceedings of the IEEE International Electron Devices Meeting , San Francisco, CA, USA, pp. 31.2.1–31.2.4. https://doi.org/10.1109/IEDM19...

  212. [227]

    Baheri, Q

    B. Baheri, Q. Guan, S. Xu, V. Chaudhary (2022). SQCC: Smart Quantum Circuit Cutting. Pro- ceedings of the IEEE International Parallel and Distributed Processing Symposium Workshops , Lyon, France, pp. 614–615. https://doi.org/10.1109/IPDPSW55747.2022.00104

  213. [228]

    Smith, M

    K. Smith, M. Perlin, P. Gokhale et al (2023). Clifford-based Circuit Cutting for Quantum Simula- tion. Proceedings of the 50th Annual International Symposium on Computer Architecture, Orlando, FL, USA, pp. 1–13. https://doi.org/10.1145/3579371.3589352

  214. [229]

    El-Araby, N

    E. El-Araby, N. Mahmud, M. J. Jeng et al (2023). Towards Complete and Scalable Emulation of Quantum Algorithms on High-Performance Reconfigurable Computers. IEEE Trans. Comput. 72, 2350–2364. https://doi.org/10.1109/TC.2023.3248276

  215. [230]

    Andres, M

    E. Andres, M. P. Cuellar, G. Navarro (2023). Efficient Dimensionality Reduction Strategies for Quantum Reinforcement Learning. IEEE Access , 11, 104534–104553. https://doi.org/10.1109/ACCESS.2023.3318173

  216. [232]

    Schuld, I

    M. Schuld, I. Sinayskiy, and F. Petruccione (2014). The quest for a Quantum Neural Network. Quantum Information Processing 13. https://doi.org/10.1007/s11128-014-0809-8

  217. [233]

    K. Beer, D. Bondarenko, T. Farrelly, T. Osborne, R. Salzmann, D (2020). Scheiermann, and R. Wolf. Training deep quantum neural networks. Nature Communications 11, 808. https://doi.org/10.1038/s41467-020-14454-2

  218. [234]

    Cerezo, A

    M. Cerezo, A. Arrasmith, R. Babbush, S. C. Benjamin, S. Endo, K. Fujii, J. R. McClean, K. Mi- tarai, X. Yuan, L. Cincio, et al (2021). Variational Quantum Algorithms. Nature Reviews Physics 3, 625. https://doi.org/10.1038/s42254-021-00348-9

  219. [235]

    Mangini, F

    S. Mangini, F. Tacchino, D. Gerace, D. Bajoni, and C. Macchiavello (2021). Quan- tum computing models for artificial neural networks. Europhysics Letters 134, 10002. https://doi.org/10.1209/0295-5075/134/10002

  220. [236]

    Kandala, A

    A. Kandala, A. Mezzacapo, K. Temme, M. Takita, M. Brink, J. M. Chow, and J. M. Gambetta (2017). Hardware-efficient variational quantum eigensolver for small molecules and quantum mag- nets. Nature 549, 242. https://doi.org/10.1038/nature23879

  221. [237]

    Sweke, F

    R. Sweke, F. Wilde, J. Meyer, M. Schuld, P. K. Faehrmann, B. Meynard-Piganeau, and J. Eisert (2020). Stochastic gradient descent for hybrid quantum-classical optimization. Quantum 4, 314. https://doi.org/10.22331/q-2020-08-31-314

  222. [238]

    Biamonte et al (2017)

    J. Biamonte et al (2017). Quantum Machine Learning. Nature, 549, 195-202. https://doi.org/10.1038/nature23474

  223. [239]

    Yang et al (2017)

    Z.-C. Yang et al (2017). Optimizing Variational Quantum Algorithms Using Pontryagin’s Mini- mum Principle. Phys. Rev. X 7, 021027. https://doi.org/10.1103/PhysRevX.7.021027

  224. [240]

    Oh et al (2019)

    Y.-H. Oh et al (2019). Solving Multi-Coloring Combinatorial Optimization Problems Using Hybrid Quantum Algorithms. arXiv:1911.00595. https://doi.org/10.48550/arXiv.1911.00595

  225. [241]

    Biamonte (2021)

    J. Biamonte (2021). Universal variational quantum computation. Physical Review A , 103(3):L030401. https://doi.org/10.1103/PhysRevA.103.L030401

  226. [242]

    Havlicek et al (2019)

    V. Havlicek et al (2019). Supervised learning with quantum-enhanced feature spaces. Nature, 567(7747):209-212. https://doi.org/10.1038/s41586-019-0980-2

  227. [243]

    Manzano et al (2023)

    A. Manzano et al (2023). Parametrized Quantum Circuits and their approxima- 44 Networked Quantum Services tion capacities in the context of quantum machine learning. arXiv:2307.14792. https://doi.org/10.48550/arXiv.2307.14792

  228. [244]

    Dunjko, J

    V. Dunjko, J. M. Taylor, and H. J. Briegel (2016). Quantum-enhanced machine learning. Physical Review Letters 117. https://doi.org/10.1103/PhysRevLett.117.130501

  229. [245]

    Pira (2024)

    L. Pira (2024). The Fundamentals of Quantum Neural Networks. PhD Dissertation. University of Technology Sydney

  230. [246]

    Tang (2019)

    E. Tang (2019). A quantum-inspired classical algorithm for recommendation systems. Proceedings of the 51st Annual ACM SIGACT Symposium on Theory of Computing . https://doi.org/10.1145/3313276.3316310

  231. [247]

    Lloyd, M

    S. Lloyd, M. Mohseni, and P. Rebentrost (2013). Quantum algorithms for supervised and unsu- pervised machine learning. arXiv:1307.0411. https://doi.org/10.48550/arXiv.1307.0411

  232. [248]

    Giovannetti, S

    V. Giovannetti, S. Lloyd, and L. Maccone (2008). Architectures for a quantum random access memory. Physical Review A 78. https://doi.org/10.1103/PhysRevA.78.052310

  233. [249]

    Giovannetti, S

    V. Giovannetti, S. Lloyd, and L. Maccone (2008). Quantum Random Access Memory. Physical Review Letters 100. https://doi.org/10.1103/PhysRevLett.100.160501

  234. [250]

    Arunachalam, V

    S. Arunachalam, V. Gheorghiu, T. Jochym-O’Connor, M. Mosca, and P. V. Srinivasan (2015). On the robustness of bucket brigade quantum RAM. New Journal of Physics 17, 123010. https://doi.org/10.1088/1367-2630/17/12/123010

  235. [251]

    Gyongyosi and S

    L. Gyongyosi and S. Imre (2019). Training Optimization for Gate-Model Quantum Neural Net- works. Sci Rep., DOI: 10.1038/s41598-019-48892-w. https://doi.org/10.1038/s41598-019-48892-w

  236. [252]

    Carleo, I

    G. Carleo, I. Cirac, K. Cranmer, L. Daudet, M. Schuld, N. Tishby, L. Vogt-Maranto, and L. Zdeborova (2019). Machine learning and the physical sciences. Reviews of Modern Physics 91. https://doi.org/10.1103/RevModPhys.91.045002

  237. [253]

    Dawid, J

    A. Dawid, J. Arnold, B. Requena, A. Gresch, M. P lodzien, K. Donatella, K. A. Nicoli, P. Stornati, R. Koch, M. Buttner, et al (2022). Modern applications of machine learning in quantum sciences. arXiv:2204.04198. https://doi.org/10.48550/arXiv.2204.04198

  238. [254]

    Bukov, A

    M. Bukov, A. G. R. Day, D. Sels, P. Weinberg, A. Polkovnikov, and P. Mehta (2018). Reinforcement Learning in Different Phases of Quantum Control. Physical Review X 8. https://doi.org/10.1103/PhysRevX.8.031086

  239. [255]

    M. Y. Niu, S. Boixo, V. N. Smelyanskiy, and H. Neven (2019). Universal Quantum Control through Deep Reinforcement Learning. npj Quantum Information 5, 1. https://doi.org/10.1038/s41534- 019-0141-3

  240. [256]

    H. P. Nautrup, N. Delfosse, V. Dunjko, H. J. Briegel, and N. Friis (2019). Optimizing Quantum Er- ror Correction Codes with Reinforcement Learning. Quantum 3, 215. https://doi.org/10.22331/q- 2019-12-16-215

  241. [257]

    Torlai and R

    G. Torlai and R. G. Melko (2017). A Neural Decoder for Topological Codes. Physical Review Letters 119, 030501. https://doi.org/10.1103/PhysRevLett.119.030501

  242. [258]

    Torlai, G

    G. Torlai, G. Mazzola, J. Carrasquilla, M. Troyer, R. Melko, and G. Carleo (2018). Many-body quantum state tomography with neural networks. Nature Physics 14. https://doi.org/10.1038/s41567-018-0048-5

  243. [259]

    Xu and S

    Q. Xu and S. Xu (2018). Neural network state estimation for full quantum state tomography. arXiv:1811.06654. https://doi.org/10.1103/PhysRevA.106.012409

  244. [260]

    Sentis, A

    G. Sentis, A. Monras, R. Munoz Tapia, J. Calsamiglia, and E. Bagan (2019). Unsupervised Classification of Quantum Data. Physical Review X 9, 041029. https://doi.org/10.1103/PhysRevX.9.041029

  245. [261]

    Liu and P

    N. Liu and P. Rebentrost (2018). Quantum machine learning for quantum anomaly detection. Physical Review A 97, 042315. https://doi.org/10.1103/PhysRevA.97.042315

  246. [262]

    Wang et al (2021)

    S. Wang et al (2021). Noise-induced barren plateaus in variational quantum algorithms. Nature Communications, 12(1):6961. https://doi.org/10.1038/s41467-021-27045-6

  247. [263]

    J. R. McClean, S. Boixo, V. N. Smelyanskiy, R. Babbush, and H. Neven (2018). Bar- ren plateaus in quantum neural network training landscapes. Nature Communications 9. https://doi.org/10.1038/s41467-018-07090-4. Laszlo Gyongyosi and Sandor Imre 45

  248. [264]

    Cerezo, A

    M. Cerezo, A. Sone, T. Volko, L. Cincio, and P. J. Coles (2021). Cost Function Dependent Barren Plateaus in Shallow Parametrized Quantum Circuits. Nature Communications 12, 1. https://doi.org/10.1038/s41467-021-21728-w

  249. [266]

    Cerezo et al (2022)

    M. Cerezo et al (2022). Challenges and opportunities in quantum machine learning. Nature Com- putational Science, 2(9):567-576. https://doi.org/10.1038/s43588-022-00311-3

  250. [267]

    Herbst (2024)

    S. Herbst (2024). Beyond 0’s and 1’s: Exploring the Impact of Noise, Data Encoding, and Hyper- parameter Optimization in Quantum Machine Learning. Diploma Thesis , Technische Universitat Wien

  251. [268]

    Suchan (2024)

    D. Suchan (2024). Hyperparameter Tuning for Quantum Machine Learning.Diploma Thesis, Tech- nische Universitat Wien

  252. [270]

    Wiebe (2020)

    N. Wiebe (2020). Key questions for the quantum machine learner to ask themselves. New Journal of Physics 22, 091001. https://doi.org/10.1088/1367-2630/abac39

  253. [271]

    Ventura and T

    D. Ventura and T. Martinez (2000). Quantum Associative Memory. Information Sciences 126,

  254. [272]

    LaRose and B

    R. LaRose and B. Coyle (2020). Robust data encodings for quantum classifiers. Physical Review A 102. https://doi.org/10.1103/PhysRevA.102.032420

  255. [273]

    https://doi.org/10.1016/S0020-0255(99)00101-2

  256. [274]

    Huang, M

    H.-Y. Huang, M. Broughton, M. Mohseni, R. Babbush, S. Boixo, H. Neven, and J. R. McClean (2021). Power of data in quantum machine learning. Nature Communications 12. https://doi.org/10.1038/s41467-021-22539-9

  257. [275]

    Schuld and N

    M. Schuld and N. Killoran (2019). Quantum Machine Learning in Feature Hilbert Spaces. Phys. Rev. Lett. 122, 040504. https://doi.org/10.1103/PhysRevLett.122.040504

  258. [276]

    Skolik, J

    A. Skolik, J. R. McClean, M. Mohseni, P. van der Smagt, and M. Leib (2021). Layerwise learning for quantum neural networks. Quantum Machine Intelligence 3, 1. https://doi.org/10.1007/s42484- 020-00036-4

  259. [277]

    Schuld and F

    M. Schuld and F. Petruccione (2018). Supervised Learning with Quantum Computers , Springer, DOI: 10.1007/978-3-319-96424-9

  260. [278]

    Y. Du, Y. Qian, and D. Tao (2021). Accelerating variational quantum algorithms with multiple quantum processors. arXiv:2106.12819. https://doi.org/10.48550/arXiv.2106.12819

  261. [279]

    C. Cade, L. Mineh, A. Montanaro, and S. Stanisic (2020). Strategies for solving the Fermi-Hubbard model on near-term quantum computers. Physical Review B 102. https://doi.org/10.1103/PhysRevB.102.235122

  262. [280]

    Wiersema, C

    R. Wiersema, C. Zhou, Y. de Sereville, J. F. Carrasquilla, Y. B. Kim, and H. Yuen (2020). Explor- ing entanglement and optimization within the Hamiltonian Variational Ansatz. PRX Quantum 1. https://doi.org/10.1103/PRXQuantum.1.020319

  263. [281]

    T. Haug, C. N. Self, and M. S. Kim (2023). Quantum machine learning of large datasets using randomized measurements. Mach. Learn.: Sci. Technol. 4 015005. https://doi.org/10.1088/2632- 2153/acb0b4

  264. [282]

    Weigold, J

    M. Weigold, J. Barzen, F. Leymann, and M. Salm (2021). Expanding Data Encoding Patterns For Quantum Algorithms. 2021 IEEE 18th International Conference on Software Architecture Companion (ICSA-C), pp. 95-101. https://doi.org/10.1109/ICSA-C52384.2021.00025

  265. [283]

    Schuld, M

    M. Schuld, M. Fingerhuth and F. Petruccione (2017). Implementing a distance-based classifier with a quantum interference circuit. Europhysics Letters 119, 60002. https://doi.org/10.1209/0295- 5075/119/60002. 46 Networked Quantum Services

  266. [284]

    Romero, J.P

    J. Romero, J.P. Olson, and A. Aspuru-Guzik (2017). Quantum autoencoders for efficient compres- sion of quantum data. Quantum Science and Technology 2, 045001. https://doi.org/10.1088/2058- 9565/aa8072

  267. [285]

    Weigold, J

    M. Weigold, J. Barzen, F. Leymann, and M. Salm (2020). Data encoding patterns for quantum computing. Proceedings of the 27th Conference on Pattern Languages of Programs , https://doi.org/10.5555/3511065.3511068

  268. [286]

    Moretti, A

    R. Moretti, A. Giachero, V. Radescu, M. Grossi (2024). Enhanced feature en- coding and classification on distributed quantum hardware. arXiv:2412.01664. https://doi.org/10.48550/arXiv.2412.01664

  269. [287]

    Tomesh, P

    T. Tomesh, P. Gokhale, E. R. Anschuetz, and F. T. Chong (2021). Coreset Clustering on Small Quantum Computers. Electronics 10. https://doi.org/10.3390/electronics10141690

  270. [288]

    A. W. Harrow (2020). Small quantum computers and large classical data sets. arXiv:2004.00026. https://doi.org/10.48550/arXiv.2004.00026

  271. [289]

    M. H. Amin, E. Andriyash, J. Rolfe, B. Kulchytskyy, and R. Melko (2018). Quantum Boltzmann Machine. Phys. Rev. X 8, 021050. https://doi.org/10.1103/PhysRevX.8.021050

  272. [290]

    Y. Du, Y. Qian, X. Wu, D. Tao (2022). A distributed learning scheme for variational quantum algorithms. IEEE Trans. Quantum Eng. 3 1–16. https://doi.org/10.1109/TQE.2022.3175267

  273. [291]

    J. F. Fitzsimons (2017). Private quantum computation: an introduction to blind quantum com- puting and related protocols. npj Quantum Inf 3, 23. https://doi.org/10.1038/s41534-017-0025-3

  274. [292]

    Kaewpuang, M

    R. Kaewpuang, M. Xu, D. T. Hoang et al (2023). Elastic Entangled Pair and Qubit Resource Management in Quantum Cloud Computing. arXiv:2307.13185. https://doi.org/10.48550/arXiv.2307.13185

  275. [293]

    C. N. Self, K. E. Khosla, A. W. R. Smith, F. Sauvage, P. D. Haynes, J. Knolle, F. Mintert, and M. S. Kim (2021). Variational quantum algorithm with information sharing. npj Quantum Information 7. https://doi.org/10.1038/s41534-021-00452-9

  276. [294]

    P. J. Karalekas, T. Ryan, R. S. Smith (2020). A quantum-classical cloud platform optimized for variational hybrid algorithms. Quantum Science and Technology 5, 2. https://doi.org/10.1088/2058-9565/ab7559

  277. [295]

    Ding and A

    Y. Ding and A. Javadi-Abhari. Quantum and post-Moore’s law computing (2022). IEEE Internet Computing, vol. 26, no. 1, pp. 5–6. https://doi.org/10.1109/MIC.2021.3133675

  278. [296]

    Subhi and L

    D. Subhi and L. Bacsardi (2023). Using quantum nodes connected via the quantum cloud to perform IOT quantum network. Condensed Matter , vol. 8, no. 1, p. 24. https://doi.org/10.3390/condmat8010024

  279. [297]

    M. A. Serrano, L. E. Sanchez, A. Santos-Olmo et al (2023). Minimizing incident response time in real-world scenarios using quantum computing. Software Quality Journal, Volume 32, pp. 163–192. https://doi.org/10.1007/s11219-023-09632-6

  280. [307]

    https://doi.org/10.1103/RevModPhys.87.307

  281. [934]

    https://doi.org/10.22331/q-2023-03-02-934

  282. [5172]

    https://doi.org/10.1038/s41598-020-76728-5

Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.