Quantum Information & Computation
Volume 25, Issue 2
RESEARCH ARTICLE Open access

Networked Quantum Services†

Laszlo Gyongyosi, Sandor Imre

Author affiliations
  • Laszlo Gyongyosi1
  • Sandor Imre1
  1. Department of Networked Systems and Services, Faculty of Electrical Engineering and Informatics, Budapest University of Technology and Economics, 3 Muegyetem rkp., Budapest, Hungary

pp. 97-140 · 10.2478/qic-2025-0006

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.
Open accessCC BY-NC-ND 4.0

Keywords

  • quantum computing
  • quantum networking
  • quantum services
  • survey

Suggested citation

Laszlo Gyongyosi, Sandor Imre (2025). Networked Quantum Services†. Quantum Information & Computation, 25(2), 97-140. https://doi.org/10.2478/qic-2025-0006

References (434)

  1. C. H. Bennett, S. J. Wiesner (1992). “Communication via 1-and 2-particle operators on Einstein-Podolsky-Rosen states”. Physical Review Letters 69, 2881–2884. https://doi.org/10.1103/PhysRevLett.69.2881.DOI: 10.1103/PhysRevLett.69.2881Google Scholar
  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”. Physical Review Letters 70, 1895–1899. https://doi.org/10.1103/PhysRevLett.70.1895.DOI: 10.1103/PhysRevLett.70.1895Google Scholar
  3. S. Imre and M. Berces (2021). “Entanglement-based competition resolution in distributed systems”. IEEE Access 9, 10253–10262. https://doi.org/10.1109/ACCESS.2021.3050271.DOI: 10.1109/ACCESS.2021.3050271Google Scholar
  4. P. W. Shor (2002). “Introduction to quantum algorithms”. AMS PSAPM 58, 143–159. https://doi.org/10.48550/arXiv.quant-ph/0005003.DOI: 10.1090/psapm/058/1922896Google Scholar
  5. R. Jozsa (1998). “Quantum algorithms and the Fourier transform”. Proceedings of the Royal Society of London. Series A 454, 323–337. https://doi.org/10.1098/rspa.1998.0163DOI: 10.1098/rspa.1998.0163Google Scholar
  6. S. Imre (2007). “Quantum existence testing and its application for finding extreme values in unsorted databases”. IEEE Transactions on Computers 56: 5, 706–710. https://doi.org/10.1109/TC.2007.1032.DOI: 10.1109/TC.2007.1032Google Scholar
  7. L. Gyongyosi, S. Imre, H. V. Nguyen (2018). “A survey on quantum channel capacities”. IEEE Communications Surveys and Tutorials 20: 2. https://doi.org/10.1109/COMST.2017.2786748.DOI: 10.1109/COMST.2017.2786748Google Scholar
  8. Q. A. Memon, M. Al Ahmad and M. Pecht, M (2024). “Quantum computing: Navigating the future of computation, challenges, and technological breakthroughs”. Quantum Reports, 6, 627663. https://doi.org/10.3390/quantum6040039.DOI: 10.3390/quantum6040039Google Scholar
  9. Z. Yang, M. Zolanvari, and R. Jain (2023). “A survey of important issues in quantum computing and communications”. IEEE Communications and Surveys Tutorials 25: 2, 1059–1094. https://doi.org/10.1109/COMST.2023.3254481.DOI: 10.1109/COMST.2023.3254481Google Scholar
  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.Google Scholar
  11. P. Singh, R. Dasgupta, A. Singh et al. (2024). “A survey on available tools and technologies enabling quantum computing”. IEEE Access 57974–57991. https://doi.org/10.1109/ACCESS.2024.3388005.DOI: 10.1109/ACCESS.2024.3388005Google Scholar
  12. L. Gyongyosi and S. Imre (2019). “A survey on quantum computing technology”. Computer Science Review 31, 51–71. https://doi.org/10.1016/j.cosrev.2018.11.002.DOI: 10.1016/j.cosrev.2018.11.002Google Scholar
  13. S. S. Gill et al (2021). “Quantum computing: a taxonomy, systematic review and future directions”. Software: Practice and Experience https://doi.org/10.1002/spe.3039.DOI: 10.1002/spe.3039Google Scholar
  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.DOI: 10.1186/s40580-024-00418-5Google Scholar
  15. 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.Google Scholar
  16. Y. Li, M. Tian, G. Liu, C. Peng, and L. Jiao (2020). “Quantum optimization and quantum learning: A survey”. IEEE Access 8, 23 568–23 593. https://doi.org/10.1109/ACCESS.2020.2970105.DOI: 10.1109/ACCESS.2020.2970105Google Scholar
  17. J. Kusyk, S. M. Saeed, and M. U. Uyar (2021). “Survey on quantum circuit compilation for noisy intermediatescale quantum computers: Artificial intelligence to heuristics”. IEEE Transactions on Quantum Engineering 2, 1–16. https://doi.org/10.1109/TQE.2021.3068355.DOI: 10.1109/TQE.2021.3068355Google Scholar
  18. 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://doi.org/10.1109/COMPSAC54236.2022.00096.DOI: 10.1109/COMPSAC54236.2022.00096Google Scholar
  19. F. V. Massoli, L. Vadicamo, G. Amato, and F. Falchi (2022). “A leap among quantum computing and quantum neural networks: A survey”. ACM Computing Surveys 55, 5. https://doi.org/10.1145/3529756.DOI: 10.1145/3529756Google Scholar
  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) 1–8. https://doi.org/10.1109/IJCNN48605.2020.9207714.DOI: 10.1109/IJCNN48605.2020.9207714Google Scholar
  21. 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.DOI: 10.1016/j.cosrev.2024.100619Google Scholar
  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.DOI: 10.1109/ACCESS.2024.3519676Google Scholar
  23. T. Ayral, P. Besserve, D. Lacroix, E. A. R. Guzman (2023). “Quantum computing with and for many-body physics”. The European Physical Journal A 59, 227. https://doi.org/10.1140/epja/s10050–023-01141-1.DOI: 10.1140/epja/s10050-023-01141-1Google Scholar
  24. E. Moguel, J. R. and V. Garcia-Alonso (2022). “Quantum service-oriented computing: current landscape and challenges”. Software Quality Journal 30, 9831002. https://doi.org/10.1007/s11219-022-09589-y.DOI: 10.1007/s11219-022-09589-yGoogle Scholar
  25. M. A. Serrano, J. A. Cruz-Lemus, R.-P. Castillo and M. Piattini (2022). “Quantum software components and platforms: overview and quality assessment”. ACM Computing Surveys 55: 8 1–31. https://doi.org/10.1145/3548679.DOI: 10.1145/3548679Google Scholar
  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.DOI: 10.1016/j.jss.2023.111682Google Scholar
  27. 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.DOI: 10.26421/QIC24.7-8-4Google Scholar
  28. 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 Engineering, 28, 89–310. https://doi.org/10.1007/s11831-019-09372-6.DOI: 10.1007/s11831-019-09372-6Google Scholar
  29. K. Dwivedi, M. Haghparast, T. Mikkonen (2024). “Quantum software engineering and quantum software development lifecycle: a survey”. Cluster Computing 27, 7127–7145. https://doi.org/10.1007/s10586-024-04362-1.DOI: 10.1007/s10586-024-04362-1Google Scholar
  30. D. Cuomo, M. Caleffi (2020). “Towards a distributed quantum computing ecosystem”. IET Quantum Communication, 1: 1, 38. https://doi.org/10.1049/iet-qtc.2020.0002.DOI: 10.1049/iet-qtc.2020.0002Google Scholar
  31. 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.DOI: 10.1016/j.comnet.2024.110672Google Scholar
  32. D. Barrala, F. J. Cardamab, G. Diaz et al (2024). “Review of distributed quantum computing. From single QPU to high performance quantum computing”. arXiv:2404.01265v1 https://doi.org/10.48550/arXiv.2404.01265.Google Scholar
  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.DOI: 10.1007/978-3-031-92602-0_6Google Scholar
  34. G. M. Jones, H.-A. Jacobsen (2024). “Distributed quantum computing for chemical applications”. 2024 IEEE International Conference on Quantum Computing and Engineering (QCE) https://doi.org/10.1109/QCE60285.2024.10270.DOI: 10.1109/QCE60285.2024.10270Google Scholar
  35. 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.DOI: 10.1007/s42484-023-00114-3Google Scholar
  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.Google Scholar
  37. 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.DOI: 10.1007/978-3-031-64136-7_8Google Scholar
  38. F. Phillipson (2023). “Quantum computing in telecommunication-a survey”. Mathematics 11: 15, 3423. https://doi.org/10.3390/math11153423.DOI: 10.3390/math11153423Google Scholar
  39. 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.Google Scholar
  40. 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.Google Scholar
  41. Z. Li, K. Xue, J. Li, L. Chen, R. Li, Z. Wang, et al (2023). “Entanglement-assisted quantum networks: Mechanics, enabling technologies, challenges, and research directions”. IEEE Communications Surveys and Tutorials 25: 4, 2133–2189. https://doi.org/10.1109/COMST.2023.3294240.DOI: 10.1109/COMST.2023.3294240Google Scholar
  42. M. Mehic et al (2023). “Quantum cryptography in 5G networks: A comprehensive overview”. IEEE Communications Surveys and Tutorials 26: 1, https://doi.org/10.1109/COMST.2023.3309051.DOI: 10.1109/COMST.2023.3309051Google Scholar
  43. A. B. Popa, P. G. Popescu (2024). “The future of QKD networks”. arXiv:2407.00877 https://doi.org/10.48550/arXiv.2407.00877.Google Scholar
  44. A. Abane, M. Cubeddu, V. S. Mai, A. Battou (2025). “Entanglement routing in quantum networks: a comprehensive survey”. IEEE Transactions on Quantum Engineering 1–36. https://doi.org/10.1109/TQE.2025.3541123.DOI: 10.1109/TQE.2025.3541123Google Scholar
  45. L. Gyongyosi, S. Imre (2022). “Advances in the quantum internet”. Communications of the ACM 65: 8, 52–63. https://doi.org/10.1145/3524455.DOI: 10.1145/3524455Google Scholar
  46. 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.DOI: 10.1126/science.aam9288Google Scholar
  47. Y. Li. et al (2024). “A survey of quantum internet protocols from a layered perspective”. IEEE Communications Surveys and Tutorials 26: 3. https://doi.org/10.1109/COMST.2024.3361662.DOI: 10.1109/COMST.2024.3361662Google Scholar
  48. J. Ang, G. Carini, Y. Chen, I. Chuang et al (2024). “Architectures for multinode superconducting quantum computers”. ACM Transactions on Quantum Computing 5: 3, 1–59. https://doi.org/10.1145/3674151.DOI: 10.1145/3674151Google Scholar
  49. S. Barz et al (2012). “Demonstration of blind quantum computing”. Science 335: 6066, 303–308. https://doi.org/10.1126/science.1214707.DOI: 10.1126/science.1214707Google Scholar
  50. S. Ruiting et al (2021). “Verifiable multiparty universal blind quantum computing in distributed network”s. Chinese Journal of Electronics 30: 4, 712–718. https://dx.doi.org/10.1049/cje.2021.05.013.DOI: 10.1049/cje.2021.05.013Google Scholar
  51. A. Mantri, C. Perez-Delgado and J. Fitzsimons (2013). “Optimal blind quantum computation”. Physical Review Letters 111: 23, 230502. https://doi.org/10.1103/PhysRevLett.111.230502.DOI: 10.1103/PhysRevLett.111.230502Google Scholar
  52. J. I. Cirac, A. K. Ekert, S. F. Huelga, C. Macchiavello (1999). “Distributed quantum computation over noisy channels”. Physical Review A, 59, 4249–4254. https://doi.org/10.1103/PhysRevA.59.4249.DOI: 10.1103/PhysRevA.59.4249Google Scholar
  53. 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.DOI: 10.1103/PhysRevA.64.032302Google Scholar
  54. 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.DOI: 10.1103/PhysRevA.62.052317Google Scholar
  55. C. Gidney, M. Ekera (2021). “How to factor 2048 bit RSA integers in 8 hours using 20 million noisy qubits”. Quantum 5. https://doi.org/10.22331/q-2021-04-15-433.DOI: 10.22331/q-2021-04-15-433Google Scholar
  56. L. Gyongyosi, S. Imre (2018). “Multiple access multicarrier continuous-variable quantum key distribution”. Chaos, Solitons and Fractals 114, 491–505. https://doi.org/10.1016/j.chaos.2018.07.006.DOI: 10.1016/j.chaos.2018.07.006Google Scholar
  57. 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.DOI: 10.1038/s41598-020-78960-5Google Scholar
  58. L. Gyongyosi, S. Imre (2021). “Scalable distributed gate-model quantum computers”. Scientific Reports 11: 5172. https://doi.org/10.1038/s41598-020-76728-5.DOI: 10.1038/s41598-020-76728-5Google Scholar
  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.DOI: 10.2139/ssrn.4698889Google Scholar
  60. N. M. Neumann, R. van Houte, T. Attema (2020). “Imperfect distributed quantum phase estimation”. Computational Science-ICCS 2020: 12142 of LNCS, Springer, pp. 605–615. https://doi.org/10.1007/978-3-030-50433-5 46DOI: 10.1007/978-3-030-50433-5_46Google Scholar
  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 SC23 Workshops of The Int. Conf. on High Performance Computing Network, Storage, and Analysis, ACM, New York, pp. 1420–1425. https://doi.org/10.1145/3624062.3624212.DOI: 10.1145/3624062.3624212Google Scholar
  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.DOI: 10.1103/PhysRevA.106.032417Google Scholar
  63. R. Van Meter, W. J. Munro, K. Nemoto, K. M. Itoh (2008). “Arithmetic on a distributed-memory quantum multicomputer”. ACM Journal on Emerging Technologies in Computing Systems, 3: 4. https://doi.org/10.1145/1324177.1324179.DOI: 10.1145/1324177.1324179Google Scholar
  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.Google Scholar
  65. Z. Zhang and Q. Zhuang (2021). “Distributed quantum sensing”. Quantum Science and Technology 6: 4, 043001. https://doi.org/10.1088/2058-9565/abd4c3.DOI: 10.1088/2058-9565/abd4c3Google Scholar
  66. C. L. Degen, F. Reinhard, and P. Cappellaro (2017). “Quantum sensing”. Reviews of Modern Physics, 89: 3, 035002. https://doi.org/10.1103/RevModPhys.89.035002.DOI: 10.1103/RevModPhys.89.035002Google Scholar
  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.DOI: 10.1016/j.physa.2023.129209Google Scholar
  68. X. Zhou, D. Qiu, L. Luo (2023). “Distributed exact Grovers algorithm”. Frontiers of Physics, 18: 5, 1–25. https://doi.org/10.1007/s11467-023-1327-x.DOI: 10.1007/s11467-023-1327-xGoogle Scholar
  69. B. He, D. Zhang, S. W. Loke, S. Lin, L. Lu (2024). “Building a hierarchical architecture and communication model for the quantum internet”. IEEE Journal on Selected Areas in Communications 42, 7. https://doi.org/10.1109/JSAC.2024.3380103.DOI: 10.1109/JSAC.2024.3380103Google Scholar
  70. 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.DOI: 10.17487/RFC9340Google Scholar
  71. J. Roffe (2019). “Quantum error correction: an introductory guide”. Contemporary Physics 60, 3. https://doi.org/10.1080/00107514.2019.1667078.DOI: 10.1080/00107514.2019.1667078Google Scholar
  72. A. Paler, S. J. Devitt (2015). “An introduction to fault-tolerant quantum computing”. DAC’15 Proceedings of the 52nd Annual Design Automation Conference 60. https://doi.org/10.1145/2744769.2747911.DOI: 10.1145/2744769.2747911Google Scholar
  73. K. Heshami, D. G. England, P. C. Humphreys (2016). “Quantum memories: emerging applications and recent advances”. Journal of Modern Optics, 63, S3, S42–S65. https://doi.org/10.1080/09500340.2016.1148212.DOI: 10.1080/09500340.2016.1148212Google Scholar
  74. B. M. Terhal (2015). “Quantum error correction for quantum memories”. Reviews of Modern Physics, 87, 307. https://doi.org/10.1103/RevModPhys.87.307.DOI: 10.1103/RevModPhys.87.307Google Scholar
  75. S. Bravyi, D. Gosset, and R. Konig (2018). “Quantum advantage with shallow circuits”. Science, 362, 308. https://doi.org/10.1126/science.aar3106.DOI: 10.1126/science.aar3106Google Scholar
  76. J. D. Hidary (2021). Quantum Computing: an Applied Approach Springer, ISBN-10: 3030832732.DOI: 10.1007/978-3-030-83274-2Google Scholar
  77. T. D. Ladd, F. Jelezko, R. Laflamme, Y. Nakamura, C. Monroe, and J. L. O’Brien (2010). “Quantum computers”. Nature 464: 7285, 4553. https://doi.org/10.1038/nature08812.DOI: 10.1038/nature08812Google Scholar
  78. M. AbuGhanem (2024). “Photonic quantum computers”. arXiv:2409.08229 https://doi.org/10.48550/arXiv.2409.08229.Google Scholar
  79. 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 11, 369395. https://doi.org/10.1146/annurev-conmatphys-031119-050605.DOI: 10.1146/annurev-conmatphys-031119-050605Google Scholar
  80. F. Arute et al (2019). “Quantum supremacy using a programmable superconducting processor”. Nature 574. https://doi.org/10.1038/s41586-019-1666-5.DOI: 10.1038/s41586-019-1666-5Google Scholar
  81. 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 7: 1, 13575. https://doi.org/10.1038/ncomms13575.DOI: 10.1038/ncomms13575Google Scholar
  82. L. Henriet, L. Beguin, A. Signoles, T. Lahaye, A. Browaeys, G.-O. Reymond, and C. Jurczak (2020). “Quantum computing with neutral atoms”. Quantum 4: 327. https://doi.org/10.22331/q-2020-09-21-327.DOI: 10.22331/q-2020-09-21-327Google Scholar
  83. 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.Google Scholar
  84. C. D. Bruzewicz, J. Chiaverini, R. McConnell, and J. M. Sage (2019). “Trapped-ion quantum computing: Progress and challenges”. Applied Physics Reviews 6: 2, 021314. https://doi.org/10.1063/1.5088164.DOI: 10.1063/1.5088164Google Scholar
  85. C. Nayak, S. H. Simon, A. Stern, M. Freedman, and S. D. Sarma (2008). “Non-abelian anyons and topological quantum computation”. Reviews of Modern Physics 80: 3, 1083. https://doi.org/10.1103/RevModPhys.80.1083.DOI: 10.1103/RevModPhys.80.1083Google Scholar
  86. S. Pezzagna, J. Meijer (2021). “Quantum computer based on color centers in diamond”. Applied Physics Reviews, 8, 011308. https://doi.org/10.1063/5.0007444.DOI: 10.1063/5.0007444Google Scholar
  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.DOI: 10.1038/414883aGoogle Scholar
  88. L. M. K. Vandersypen, I. L. Chuang (2005). “NMR techniques for quantum control and computation”. Reviews of Modern Physics 76, 1037. https://doi.org/10.1103/RevModPhys.76.1037.DOI: 10.1103/RevModPhys.76.1037Google Scholar
  89. N. C. Jones, R. Van Meter, A. G. Fowler, P. L. McMahon, J. Kim, T. D. Ladd, Y. Yamamoto (2012). “Layered architecture for quantum computing”. Physical Review X 2, 031007. https://doi.org/10.1103/PhysRevX.2.031007.DOI: 10.1103/PhysRevX.2.031007Google Scholar
  90. S. Rodrigo, S. Abadal, E. Alarcon et al (2021). “On double full-stack communication-enabled architectures for multicore quantum computers”. IEEE Micro 41, 4856. https://doi.org/10.1109/MM.2021.3092706.DOI: 10.1109/MM.2021.3092706Google Scholar
  91. R. Van Meter (2014). Quantum Networking John Wiley and Sons Ltd.DOI: 10.1002/9781118648919Google Scholar
  92. J. Illiano, M. Caleffi, A. Manzalini, A. S. Cacciapuoti (2022). “Quantum Internet protocol stack: A comprehensive survey”. Computer Networks 213, 109092. https://doi.org/10.1016/j.comnet.2022.109092.DOI: 10.1016/j.comnet.2022.109092Google Scholar
  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, 1–14. https://doi.org/10.23919/JCC.2021.10.001.DOI: 10.23919/JCC.2021.10.001Google Scholar
  94. A. Dahlberg, M. Skrzypczyk, T. Coopmans, L. Wubben, F. Rozpundefineddek, M. Pompili et al (2019). “A link layer protocol for quantum networks”, in Proceedings of the ACM Special Interest Group on Data Communication ACM, New York, 159–173. https://doi.org/10.1145/3341302.3342070.DOI: 10.1145/3341302.3342070Google Scholar
  95. 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.DOI: 10.1088/1367-2630/ab05f7Google Scholar
  96. R. V. Meter, J. Touch (2013). “Designing quantum repeater networks. IEEE Communications Magazine, 51: 8, 64–71. https://doi.org/10.1109/MCOM.2013.6576340.DOI: 10.1109/MCOM.2013.6576340Google Scholar
  97. R. Van Meter, R. Satoh, N. Benchasattabuse, K. Teramoto, T. Matsuo, M. Hajdusek et al. (2022). “A quantum Internet architecture”. 2022 IEEE Int. Conf. on Quantum Computing and Engineering (QCE) 341–352. https://doi.org/10.1109/QCE53715.2022.00055.DOI: 10.1109/QCE53715.2022.00055Google Scholar
  98. J. Preskill (2018). “Quantum Computing in the NISQ era and beyond”. Quantum, 2, 79. https://doi.org/10.22331/q-2018-08-06-79.DOI: 10.22331/q-2018-08-06-79Google Scholar
  99. A. W. Harrow and A. Montanaro (2017). “Quantum computational supremacy”. Nature 549, 203–209. https://doi.org/10.1038/nature23458.DOI: 10.1038/nature23458Google Scholar
  100. S. Aaronson and L. Chen (2017). “Complexity-theoretic foundations of quantum supremacy experiments”, in Proceedings of the 32nd Computational Complexity Conference CCC ’17, pp. 22:1–22:67. https://doi.org/10.4230/LIPIcs.CCC.2017.22.Google Scholar
  101. 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.Google Scholar
  102. 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.DOI: 10.1007/s11082-024-06393-9Google Scholar
  103. Y. Alexeev et al (2019). “Quantum computer systems for scientific discovery”. PRX Quantum 2, 017001. https://doi.org/10.1103/PRXQuantum.2.017001.DOI: 10.1103/PRXQuantum.2.017001Google Scholar
  104. M. Loncar et al (2019). “Development of quantum interconnects for next-generation information technologies”. PRX Quantum 2, 017002. https://doi.org/10.1103/PRXQuantum.2.017002DOI: 10.1103/PRXQuantum.2.017002Google Scholar
  105. B. Foxen et al (2020). “Demonstrating a continuous set of two-qubit gates for near-term quantum algorithms”. Physical Review Letters 125, 120504. https://doi.org/10.1103/PhysRevLett.125.120504.DOI: 10.1103/PhysRevLett.125.120504Google Scholar
  106. A. Ajagekar, T. Humble, and F. You (2020). “Quantum computing based hybrid solution strategies for large-scale discrete-continuous optimization problems”. Computers and Chemical Engineering 132, 106630. https://doi.org/10.1016/j.compchemeng.2019.106630.DOI: 10.1016/j.compchemeng.2019.106630Google Scholar
  107. A. Ajagekar and F. You (2019). “Quantum computing for energy systems optimization: Challenges and opportunities”. Energy 179, 76–89. https://doi.org/10.1016/j.energy.2019.04.186.DOI: 10.1016/j.energy.2019.04.186Google Scholar
  108. M. Harrigan et al (2020). “Quantum approximate optimization of non-planar using eigen energies graph problems on a planar superconducting processor”. Nature Physics 17, 332–336. https://doi.org/10.1038/s41567-020-01105-y.DOI: 10.1038/s41567-020-01105-yGoogle Scholar
  109. 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.DOI: 10.1126/science.abb9811Google Scholar
  110. E. Farhi, J. Goldstone and S. Gutmann (2014). “A quantum approximate optimization algorithm”. arXiv:1411.4028v1 https://doi.org/10.48550/arXiv.1411.4028.Google Scholar
  111. E. Farhi, J. Goldstone, S. Gutmann and L. Zhou, L (2019). “The quantum approximate optimization algorithm and the Sherrington-Kirkpatrick model at infinite size”. Quantum 6, 759. https://doi.org/10.22331/q-2022-07-07-759.DOI: 10.22331/q-2022-07-07-759Google Scholar
  112. 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.Google Scholar
  113. I. Sax et al (2020). “Approximate approximation on a quantum annealer”. CF ‘20: Proceedings of the 17th ACM International Conference on Computing Frontiers pp. 108–117. https://doi.org/10.1145/3387902.3392635.DOI: 10.1145/3387902.3392635Google Scholar
  114. K. A. Brown and T. Roser (2020). “Towards storage rings as quantum computers”. Physical Review Accelerators and Beams 23, 054701. https://doi.org/10.1103/PhysRevAccelBeams.24.049901.DOI: 10.1103/PhysRevAccelBeams.23.054701Google Scholar
  115. J. Bae, P. M. Alsing, D. Ahn et al (2020). “Quantum circuit optimization using quantum Karnaugh map”. Scientific Reports, 10, 15651, https://doi.org/10.1038/s41598-020-72469-7.DOI: 10.1038/s41598-020-72469-7Google Scholar
  116. S. Li et al (2020). “Programmable unitary operations for orbital angular momentum encoded states”. National Science Open 1: 2, 20220019. https://doi.org/10.1360/nso/20220019.DOI: 10.1360/nso/20220019Google Scholar
  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”. Scientific Reports, DOI: https://doi.org/10.1038/s41598-020-79295-x.DOI: 10.1038/s41598-020-79295-xGoogle Scholar
  118. A. Teplukhin, B. Kendrick and D. Babikov (2020). “Solving complex eigenvalue problems on a quantum annealer with applications to quantum scattering resonances”. Physical Chemistry Chemical Physics. https://doi.org/10.1039/D0CP04272B.DOI: 10.1039/D0CP04272BGoogle Scholar
  119. S. Lloyd (2018). “Quantum approximate optimization is computationally universal”. arXiv:1812.11075 https://doi.org/10.48550/arXiv.1812.11075.Google Scholar
  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.DOI: 10.1016/j.scib.2021.10.017Google Scholar
  121. S. Aaronson, A. Arkhipov (2013). “The computational complexity of linear optics”. Theory of Computing 9: 4, 143–252. https://doi.org/10.1145/1993636.1993682.DOI: 10.1145/1993636.1993682Google Scholar
  122. H-S. Zhong et al (2020). “Quantum computational advantage using photons”. Science 370: 6523, 1460–1463. https://doi.org/10.1126/science.abe8770.DOI: 10.1126/science.abe8770Google Scholar
  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.DOI: 10.1038/s41586-022-04725-xGoogle Scholar
  124. M. Reiher, N. Wiebe, K. M. Svore et al (2017). “Elucidating reaction mechanisms on quantum computers”. Proceedings of the National Academy of Sciences, 114 7555–7560. https://doi.org/10.1073/pnas.1619152114.DOI: 10.1073/pnas.1619152114Google Scholar
  125. S. Mandra and H. G. Katzgraber (2018). “A deceptive step towards quantum speedup detection”. Quantum Science Technology 3 04LT. https://doi.org/10.1088/2058-9565/aac8b2.DOI: 10.1088/2058-9565/aac8b2Google Scholar
  126. V. Moret-Bonillo (2015). “Can artificial intelligence benefit from quantum computing?” Progress in Artificial Intelligence 3 89–105. https://doi.org/10.1007/s13748-014-0059-0.DOI: 10.1007/s13748-014-0059-0Google Scholar
  127. T. Yamakawa and M. Zhandry (2022). “Verifiable quantum advantage without structure”, in 2022 IEEE 63rd Annual Symposium on Foundations of Computer Science (FOCS) 69–74. https://doi.org/10.1145/3658665.DOI: 10.1109/FOCS54457.2022.00014Google Scholar
  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.DOI: 10.1126/science.1252319Google Scholar
  129. S. Aaronson (2015). “Quantum machine learning algorithms: Read the fine print”, Nature Physics, 11, 291–293. https://doi.org/10.1038/nphys3272.DOI: 10.1038/nphys3272Google Scholar
  130. 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”. Reviews of Modern Physics, 94, 015004. https://doi.org/10.1103/RevModPhys.94.015004.DOI: 10.1103/RevModPhys.94.015004Google Scholar
  131. P. W. Shor (1994). “Algorithms for quantum computation: discrete logarithms and factoring”, in Proceedings 35th Annual Symposium on Foundations of Computer Science, 124–134. https://doi.org/10.1109/SFCS.1994.365700.DOI: 10.1109/SFCS.1994.365700Google Scholar
  132. V. S. Denchev, S. Boixo, S. V. Isakov et al (2016). “What is the computational value of finite-range tunneling?” Physical Review X, 6, 1–17. https://doi.org/10.1103/PhysRevX.6.031015.DOI: 10.1103/PhysRevX.6.031015Google Scholar
  133. P. J. J. O’Malley et al (2016). “Scalable quantum simulation of molecular energies”. Physical Review X 6, 031007. https://doi.org/10.1103/PhysRevX.6.031007.DOI: 10.1103/PhysRevX.6.031007Google Scholar
  134. 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.Google Scholar
  135. 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.DOI: 10.1038/s41586-021-03576-2Google Scholar
  136. E. Farhi, D. Gamarnik and S. Gutmann (2020). “The quantum approximate optimization algorithm needs to see the whole graph: a typical case”. arXiv:2004.09002v1 https://doi.org/10.48550/arXiv.2004.09002.Google Scholar
  137. E. Farhi, D. Gamarnik and S. Gutmann (2020). “The quantum approximate optimization algorithm needs to see the whole graph: worst case examples”. arXiv:2005.08747 https://doi.org/10.48550/arXiv.2005.08747.Google Scholar
  138. A. Peruzzo et al (2014). “A variational eigenvalue solver on a photonic quantum processor”. Nature Communications, 5, 4213. https://doi.org/10.1038/ncomms5213.DOI: 10.1038/ncomms5213Google Scholar
  139. D. Wecker, M. B. Hastings, and M. Troyer (2015). “Progress towards practical quantum variational algorithms”. Physical Review A, 92, 042303. https://doi.org/10.1103/PhysRevA.92.042303.DOI: 10.1103/PhysRevA.92.042303Google Scholar
  140. J. R. McClean, J. Romero, R. Babbush, and A. Aspuru-Guzik (2016). “The theory of variational hybrid quantum-classical algorithms”. New Journal of Physics, 18. https://doi.org/10.1088/1367-2630/18/2/023023.DOI: 10.1088/1367-2630/18/2/023023Google Scholar
  141. X. Yuan et al (2019). “Theory of variational quantum simulation”. Quantum, 3, 191. https://doi.org/10.22331/q-2019-10-07-191.DOI: 10.22331/q-2019-10-07-191Google Scholar
  142. A. Kardashin et al (2021). “Benchmarking variational quantum simulation against an exact solution”, in 023 IEEE International Conference on Quantum Computing and Engineering (QCE) Bellevue, WA, USA, 518–523. https://doi.org/10.1109/QCE57702.2023.00065.DOI: 10.1109/QCE57702.2023.00065Google Scholar
  143. 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/abd7bcDOI: 10.1088/1367-2630/abd7bcGoogle Scholar
  144. T. Peng, A. W. Harrow, M. Ozols, and X. Wu (2020). “Simulating large quantum circuits on a small quantum computer”. Physical Review Letters 125, 150504. https://doi.org/10.1103/PhysRevLett.125.150504.DOI: 10.1103/PhysRevLett.125.150504Google Scholar
  145. L. Brenner, C. Piveteau, D. Sutter (2023). “Optimal wire cutting with classical communication”. arXiv.2302.03366 https://doi.org/10.48550/arXiv.2302.03366.Google Scholar
  146. 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.1907.13623Google Scholar
  147. 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, 1128. https://doi.org/10.1016/j.physrep.2022.08.003.DOI: 10.1016/j.physrep.2022.08.003Google Scholar
  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.DOI: 10.1088/1367-2630/acf9c3Google Scholar
  149. M. Schuld, V. Bergholm, C. Gogolin, J. Izaac, and N. Killoran (2019). “Evaluating analytic gradients on quantum hardware”. Physical Review A 99. https://doi.org/10.1103/PhysRevA.99.032331.DOI: 10.1103/PhysRevA.99.032331Google Scholar
  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 5: 2. https://doi.org/10.1088/2058-9565/ab6bf6DOI: 10.1088/2058-9565/ab6bf6Google Scholar
  151. A. J. McCaskey, T. Nguyen, A. Santana, D. Claudino, T. Kharazi, H. Finkel (2021). “Extending C++ for heterogeneous quantum-classical computing”. ACM Transactions on Quantum Computing, 2: 2, 136. https://doi.org/10.1145/3462670.DOI: 10.1145/3462670Google Scholar
  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.Google Scholar
  153. J. Gambetta (2022). Quantum-centric Supercomputing: The Next Wave of Computing https://www.ibm.com/quantum/blog/next-wave-quantum-centric-supercomputingGoogle Scholar
  154. J. Gambetta (2023). The Hardware and Software for the Era of Quantum Utility Is Here https://www.ibm.com/quantum/blog/quantum-roadmap-2033Google Scholar
  155. L. Liu, X. Dou (2021). “QuCloud: A new qubit mapping mechanism for multiprogramming quantum computing in cloud environment”, in IEEE Int. Symposium on High-performance Computer Architecture (HPCA) IEEE, pp. 167178. https://doi.org/10.1109/HPCA51647.2021.00024.DOI: 10.1109/HPCA51647.2021.00024Google Scholar
  156. L. Liu, X. Dou, QuCloud+ (2024). “A holistic qubit mapping scheme for single/multi-programming on 2D/3D NISQ quantum computers”. ACM Transactions on Architecture and Code Optimization 21: 1, 127. https://doi.org/10.1145/3631525.DOI: 10.1145/3631525Google Scholar
  157. 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, 130. https://doi.org/10.1007/s42484-023-00124-1.DOI: 10.1007/s42484-023-00124-1Google Scholar
  158. K. Li, D. Qiu, L. Li, S. Zheng, Z. Rong (2017). “Application of distributed semi-quantum computing model in phase estimation”. Information Processing Letters 120, 23–29. https://doi.org/10.1016/j.ipl.2016.12.002.DOI: 10.1016/j.ipl.2016.12.002Google Scholar
  159. T. Tanaka, Y. Suzuki, S. Uno, R. Raymond, T. Onodera, N. Yamamoto (2021). “Amplitude estimation via maximum likelihood on noisy quantum computer”. Quantum Information Processing 20, 1–29. https://doi.org/10.1007/s11128-021-03215-9.DOI: 10.1007/s11128-021-03215-9Google Scholar
  160. K. Zhang, P. Rao, K. Yu, H. Lim, V. Korepin (2021). “Implementation of efficient quantum search algorithms on NISQ computers”. Quantum Information Processing 20, 233. https://doi.org/10.1007/s11128-021-03165-2.DOI: 10.1007/s11128-021-03165-2Google Scholar
  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.DOI: 10.1007/s11128-022-03793-2Google Scholar
  162. P. Das, S. S. Tannu, P. J. Nair, M. Qureshi (2019). “A case for multiprogramming quantum computers”, in Proceedings of the 52nd Annual IEEE/ACM International Symposium on Microarchitecture pp. 291–303. https://doi.org/10.1145/3352460.3358287.DOI: 10.1145/3352460.3358287Google Scholar
  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.DOI: 10.22331/q-2023-02-16-925Google Scholar
  164. A. Ash-Saki, M. Alam, S. Ghosh (2020). “Analysis of crosstalk in NISQ devices and security implications in multi-programming regime”, in Proceedings of the ACM/IEEE International Symposium on Low Power Electronics and Design pp. 2530. https://doi.org/10.1145/3370748.3406570.DOI: 10.1145/3370748.3406570Google Scholar
  165. Y. Ohkura (2021). Crosstalk-aware NISQ Multi-programming Bachelor’s thesis, Faculty Policy Manage., Keio Univ., Tokyo, Japan (2021).Google Scholar
  166. R. Parekh, A. Ricciardi, A. Darwish, and S. DiAdamo (2021). “Quantum algorithms and simulation for parallel and distributed quantum computing”, in 2021 IEEE/ACM Second International Workshop on Quantum Computing Software (QCS) pp. 9–19. https://doi.ieeecomputersociety.org/10.1109/QCS54837.2021.00005.DOI: 10.1109/QCS54837.2021.00005Google Scholar
  167. P. Andres-Martinez, C. Heunen (2019). “Automated distribution of quantum circuits via hypergraph partitioning”. Physical Review A 100: 3, 032308. https://doi.org/10.1103/PhysRevA.100.032308.DOI: 10.1103/PhysRevA.100.032308Google Scholar
  168. A. Pastor, P. Escofet, S. B. Rached, E. Alarcon, P. Barlet-Ros, S. Abadal (2024). “Circuit partitioning for multi-core quantum architectures with deep reinforcement learning”. arXiv.2401.17976 https://doi.org/10.48550/arXiv.2401.17976.DOI: 10.1109/ISCAS58744.2024.10557956Google Scholar
  169. 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.DOI: 10.1137/1.9781611974768.3Google Scholar
  170. 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.DOI: 10.1145/3529090Google Scholar
  171. J.-Y. Wu, K. Matsui, T. Forrer, A. Soeda, P. Andres-Martinez, D. Mills et al (2023). “Entanglement-efficient bipartite-distributed quantum computing”. Quantum 7, 1196. https://doi.org/10.22331/q-2023-12-05-1196.DOI: 10.22331/q-2023-12-05-1196Google Scholar
  172. P. Andres-Martinez, T. Forrer, D. Mills, J.-Y. Wu, L. Henaut, K. Yamamoto et al (2023). “Distributing circuits over heterogeneous, modular quantum computing network architectures”. Quantum Science and Technology 9, 4. https://doi.org/10.1088/2058-9565/ad6734.DOI: 10.1088/2058-9565/ad6734Google Scholar
  173. R. G. Sundaram, H. Gupta, C. R. Ramakrishnan (2021). “Efficient distribution of quantum circuits”, in 35th Int. Symp. on Distributed Computing (DISC) 209 of Leibniz International Proceedings in Informatics (LIPIcs). https://doi.org/10.4230/LIPIcs.DISC.2021.41.Google Scholar
  174. R. G. Sundaram, H. Gupta, C. R. Ramakrishnan (2022). “Distribution of quantum circuits over general quantum networks”, in 2022 IEEE Int. Conf. on Quantum Computing and Engineering (QCE) pp. 415–425. https://doi.ieeecomputersociety.org/10.1109/QCE53715.2022.00063.DOI: 10.1109/QCE53715.2022.00063Google Scholar
  175. R. G. Sundaram, H. Gupta (2023). “Distributing quantum circuits using teleportations”, in 2023 IEEE Int. Conf. on Quantum Software (QSW) pp. 186–192. https://doi.ieeecomputersociety.org/10.1109/QSW59989.2023.00030.DOI: 10.1109/QSW59989.2023.00030Google Scholar
  176. Z. Davarzani, M. Zomorodi-Moghadam, M. Houshmand, M. Nouri-Baygi (2020). “A dynamic programming approach for distributing quantum circuits by bipartite graphs”. Quantum Information Processing 19, 9. https://doi.org/10.1007/s11128-020-02871-7.DOI: 10.1007/s11128-020-02871-7Google Scholar
  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.DOI: 10.1002/j.1538-7305.1970.tb01770.xGoogle Scholar
  178. 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.DOI: 10.1007/s10773-017-3618-xGoogle Scholar
  179. M. Houshmand, Z. Mohammadi, M. Zomorodi-Moghadam, M. Houshmand (2020). “An evolutionary 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.DOI: 10.1007/s10773-020-04409-0Google Scholar
  180. O. Daei, K. Navi, M. Zomorodi-Moghadam (2020). “Optimized quantum circuit partitioning”. International Journal of Theoretical Physics 59, 12, https://doi.org/3804-3820.DOI: 10.1007/s10773-020-04633-8Google Scholar
  181. 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/abd57cDOI: 10.1088/1402-4896/abd57cGoogle Scholar
  182. C. M. Fiduccia, R. M. Mattheyses (1982). “A linear-time heuristic for improving network partitions”. Papers on Twenty-five Years of Electronic Design Automation pp. 175–181. https://doi.org/10.1109/DAC.1982.1585498.DOI: 10.1109/DAC.1982.1585498Google Scholar
  183. W. Cambiucci, R. Silveira, W. Ruggiero (2023). “Hypergraphic partitioning of quantum circuits for distributed quantum computing”, in 2023 IEEE Int. Conf. on Quantum Computing and Engineering (QCE) IEEE Computer Society, Los Alamitos, CA, USA, pp. 268–269. https://doi.org/10.1109/QCE57702.2023.10237.DOI: 10.1109/QCE57702.2023.10237Google Scholar
  184. J. Clark, T. Humble, H. Thapliyal (2023). “TDAG: Tree-based directed acyclic graph partitioning for quantum circuits”, in Proceedings of the Great Lakes Symposium on VLSI 2023 GLSVLSI 23, ACM, New York, USA, p. 587–592. https://doi.org/10.1145/3583781.3590234.DOI: 10.1145/3583781.3590234Google Scholar
  185. T. Park, C. Y. Lee (1995). “Algorithms for partitioning a graph”. Computers and Industrial Engineering 28: 4, 899909. https://doi.org/10.1016/0360-8352(95)00003-J.DOI: 10.1016/0360-8352(95)00003-JGoogle Scholar
  186. J. M. Baker, C. Duckering, A. Hoover, F. T. Chong (2020). “Time-sliced quantum circuit partitioning for modular architectures”, in 17th ACM Int. Conf. on Computing Frontiers 2020 Proceedings ACM, pp. 98–107. https://doi.org/10.1145/3387902.3392617.DOI: 10.1145/3387902.3392617Google Scholar
  187. P. Escofet, A. Ovide, C. G. Almudever, E. Alarcon, S. Abadal (2023). “Hungarian qubit assignment for optimized mapping of quantum circuits on multi-core architectures”. IEEE Computer Architecture Letters https://doi.org/10.1109/LCA.2023.3318857.DOI: 10.1109/LCA.2023.3318857Google Scholar
  188. 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) 1, IEEE, pp. 790801. https://doi.org/10.1109/QCE57702.2023.00094.DOI: 10.1109/QCE57702.2023.00094Google Scholar
  189. A. Ovide, S. Rodrigo, M. Bandic, H. Van Someren, S. Feld, S. Abadal et al. (2023). “Mapping quantum algorithms to multi-core quantum computing architectures”. IEEE Int. Symposium on Circuits and Systems (ISCAS) IEEE, pp. 1–5. https://doi.org/10.1109/ISCAS46773.2023.10181589.DOI: 10.1109/ISCAS46773.2023.10181589Google Scholar
  190. L. K. Grover (1997). “Quantum telecomputation”. arXiv.quant-ph/9704012 https://doi.org/10. 48550/arXiv.quant-ph/9704012.Google Scholar
  191. M. Gupta, A. Pathak (2007). “A scheme for distributed quantum search through simultaneous state transfer mechanism”. Annalen der Physik 16: 12, 791797. https://doi.org/10.1002/andp.200710265.DOI: 10.1002/andp.20075191202Google Scholar
  192. A. Yimsiriwattana and S. J. Lomonaco (2004). “Distributed quantum computing: A distributed Shor algorithm”, in Quantum Information and Computation II 5436. International Society for Optics and Photonics, pp. 360372. DOI: https://doi.org/10.1117/12.546504.DOI: 10.1117/12.546504Google Scholar
  193. 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.DOI: 10.1007/978-3-319-59879-6_20Google Scholar
  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.DOI: 10.1016/j.scib.2018.06.007Google Scholar
  195. 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.DOI: 10.1103/PRXQuantum.3.010309Google Scholar
  196. M. A. Perlin, Z. H. Saleem, M. Suchara, and J. C. Osborn (2021). “Quantum circuit cutting with maximum likelihood tomography”. npj Quantum Information 7: 1, 64. https://doi.org/10.1038/s41534-021-00390-6.DOI: 10.1038/s41534-021-00390-6Google Scholar
  197. W. Tang, T. Tomesh, M. Suchara, J. Larson, and M. Martonosi (2021). “CutQC: using small Quantum computers for large Quantum circuit evaluations”, in Proceedings of the 26th ACM International Conference on Architectural Support for Programming Languages and Operating Systems (ASPLOS ’21) 473–486. https://doi.org/10.1145/3445814.3446758.DOI: 10.1145/3445814.3446758Google Scholar
  198. Z. H. Saleem, T. Tomesh, M. A. Perlin, P. Gokhale, and M. Suchara (2021). “Divide and conquer for combinatorial optimization and distributed quantum computation”. arXiv:2107.07532 https://doi.org/10.48550/arXiv.2107.07532.Google Scholar
  199. A. Lowe et al (2023). “Fast quantum circuit cutting with randomized measurements”. Quantum 7, 934. https://doi.org/10.22331/q-2023-03-02-934.DOI: 10.22331/q-2023-03-02-934Google Scholar
  200. S. C. Marshall, C. Gyurik, and V. Dunjko (2022). “High dimensional quantum machine learning with small quantum computers”. arXiv:2203.13739 https://doi.org/10.22331/q-2023-08-09-1078.DOI: 10.22331/q-2023-08-09-1078Google Scholar
  201. C. Piveteau and D. Sutter (2023). “Circuit knitting with classical communication”. IEEE Transactions on Information Theory DOI: 10.1109/TIT.2023.3310797. https://doi.org/10.1109/TIT.2023.3310797.DOI: 10.1109/TIT.2023.3310797Google Scholar
  202. C. Tuysuz et al (2021). “Classical splitting of parametrized quantum circuits”. Quantum Machine Intelligence 5, 34. https://doi.org/10.1007/s42484-023-00118-z.DOI: 10.1007/s42484-023-00118-zGoogle Scholar
  203. 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.DOI: 10.22331/q-2021-01-28-388Google Scholar
  204. 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.DOI: 10.1103/PhysRevX.6.021043Google Scholar
  205. A. W. Harrow, A. Lowe (2025). “Optimal quantum circuit cuts with application to clustered Hamiltonian simulation”. PRX Quantum 6, 010316. https://doi.org/10.1103/PRXQuantum.6.010316.DOI: 10.1103/PRXQuantum.6.010316Google Scholar
  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, 024027. https://doi.org/10.1103/PhysRevApplied. 19.024027.DOI: 10.1103/PhysRevApplied.19.024027Google Scholar
  207. 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.DOI: 10.1103/PRXQuantum.3.010346Google Scholar
  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.DOI: 10.22331/q-2023-08-09-1078Google Scholar
  209. D. Gottesman, I. L. Chuang (1999). “Demonstrating the viability of universal quantum computation using teleportation and single-qubit operations”. Nature 402, 6760, 390393. https://doi.org/10.1038/46503.DOI: 10.1038/46503Google Scholar
  210. Y. F. Huang, X. F. Ren, Y. S. Zhang, L. M. Duan, G. C. Guo (2004). “Experimental teleportation of a quantum controlled-NOT gate”. Physical Review Letters 93. https://doi.org/10.1103/PhysRevLett.93.240501.DOI: 10.1103/PhysRevLett.93.240501Google Scholar
  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, 368373. https://doi.org/10.1038/s41586-018-0470-y.DOI: 10.1038/s41586-018-0470-yGoogle Scholar
  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, 875878. https://doi.org/10.1126/science.aaw9415.DOI: 10.1126/science.aaw9415Google Scholar
  213. 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, 614617. https://doi.org/10.1126/science.abe3150.DOI: 10.1126/science.abe3150Google Scholar
  214. C. Qiao, Y. Zhao, G. Zhao, H. Xu (2022). “Quantum data networking for distributed quantum computing: opportunities and challenges”, in Proceedings of the IEEE Conference on Computer Communications Workshop New York, NY, pp. 16. https://doi.org/10.1109/INFOCOMWKSHPS54753.2022.9798138.DOI: 10.1109/INFOCOMWKSHPS54753.2022.9798138Google Scholar
  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.Google Scholar
  216. E. Alarcon, S. Abadal, F. Sebastiano et al (2023). “Scalable multi-chip quantum architectures enabled by cryogenic hybrid wireless/quantum-coherent network-in-package”, in Proceedings of the IEEE International Symposium on Circuits and Systems Monterey, CA, USA, pp. 15. https://doi.org/10.1109/ISCAS46773.2023.10181857.DOI: 10.1109/ISCAS46773.2023.10181857Google Scholar
  217. Y. Zheng, C. Zhai, D. Liu et al (2023). “Multichip multidimensional quantum networks with entanglement retrievability”. Science 381, 221226. https://doi.org/10.1126/science.adg9210.DOI: 10.1126/science.adg9210Google Scholar
  218. M. Field, A. Chen, B. Scharmann et al (2024). “Modular superconducting-qubit architecture with a multichip tunable coupler”. Physical Review Applied 21, 054063. https://doi.org/10.1103/PhysRevApplied.21.054063.DOI: 10.1103/PhysRevApplied.21.054063Google Scholar
  219. 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.DOI: 10.22331/q-2020-05-25-269Google Scholar
  220. M. S. Alvarez-Alvarado, F. E. Alban-Chacon, E. A. Lamilla-Rubio et al (2021). “Three novel quantum inspired swarm optimization algorithms using different bounded potential fields”. Scientific Reports 11: 1, 11655. https://doi.org/10.1038/s41598-021-90847-7.DOI: 10.1038/s41598-021-90847-7Google Scholar
  221. 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.DOI: 10.22331/q-2022-03-30-677Google Scholar
  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.DOI: 10.1038/s41467-022-35364-5Google Scholar
  223. 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/s41598-023-43 404-3.DOI: 10.1038/s41598-023-43404-3Google Scholar
  224. J. D. Viqueira, D. Failde, M. M. Juane, A. Gomez, D. Mera (2025). “Density matrix emulation of quantum recurrent neural networks for multivariate time series prediction”. Machine Learning: Science and Technology, 6, 015023. https://doi.org/10.1088/2632-2153/ad9431DOI: 10.1088/2632-2153/ad9431Google Scholar
  225. D. Ferrari, S. Carretta, M. Amoretti (2023). “A modular quantum compilation framework for distributed quantum computing”. IEEE Transactions on Quantum Engineering, 4, 2500213. https://doi.org/10.1109/TQE.2023.3303935.DOI: 10.1109/TQE.2023.3303935Google Scholar
  226. O. Mukhanov, B. L. T. Plourde, A. Opremcak et al (2019). “Scalable quantum computing infrastructure based on superconducting electronics”, in Proceedings of the IEEE International Electron Devices Meeting San Francisco, CA, USA, pp. 31.2.131.2.4. https://doi.org/10.1109/IEDM19573.2019.8993634.DOI: 10.1109/IEDM19573.2019.8993634Google Scholar
  227. B. Baheri, Q. Guan, S. Xu, V. Chaudhary (2022). “SQCC: Smart quantum circuit cutting”, in Proceedings of the IEEE International Parallel and Distributed Processing Symposium Workshops Lyon, France, pp. 614615. https://doi.org/10.1109/IPDPSW55747.2022.00104.DOI: 10.1109/IPDPSW55747.2022.00104Google Scholar
  228. K. Smith, M. Perlin, P. Gokhale et al (2023). “Clifford-based circuit cutting for quantum simulation”, in Proceedings of the 50th Annual International Symposium on Computer Architecture Orlando, FL, USA, pp. 113. https://doi.org/10.1145/3579371.3589352.DOI: 10.1145/3579371.3589352Google Scholar
  229. 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 Transactions on Computers, 72, 23502364. https://doi.org/10.1109/TC.2023.3248276.DOI: 10.1109/TC.2023.3248276Google Scholar
  230. E. Andres, M. P. Cuellar, G. Navarro (2023). “Efficient dimensionality reduction strategies for quantum reinforcement learning”. IEEE Access 11, 104534104553. https://doi.org/10.1109/ACCESS.2023.3318173.DOI: 10.1109/ACCESS.2023.3318173Google Scholar
  231. M. Benedetti, E. Lloyd, S. Sack, and M. Fiorentini (2019). “Parameterized quantum circuits as machine learning models”. Quantum Science and Technology, 4. https://doi.org/10.1088/2058-9565/ab4eb5.DOI: 10.1088/2058-9565/ab4eb5Google Scholar
  232. 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.DOI: 10.1007/s11128-014-0809-8Google Scholar
  233. K. Beer, D. Bondarenko, T. Farrelly, T. Osborne, R. Salzmann, D. Scheiermann, and R. Wolf. (2020). “Training deep quantum neural networks”. Nature Communications, 11, 808. https://doi.org/10.1038/s41467-020-14 454-2.DOI: 10.1038/s41467-020-14454-2Google Scholar
  234. M. Cerezo, A. Arrasmith, R. Babbush, S. C. Benjamin, S. Endo, K. Fujii, J. R. McClean, K. Mitarai, X. Yuan, L. Cincio, et al (2021). “Variational quantum algorithms”. Nature Reviews Physics, 3, 625. https://doi.org/10.1038/s42254-021-00348-9.DOI: 10.1038/s42254-021-00348-9Google Scholar
  235. S. Mangini, F. Tacchino, D. Gerace, D. Bajoni, and C. Macchiavello (2021). “Quantum computing models for artificial neural networks”. Europhysics Letters, 134, 10002. https://doi.org/10.1209/0295-5075/134/10002.DOI: 10.1209/0295-5075/134/10002Google Scholar
  236. 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 magnets”. Nature, 549, 242. https://doi.org/10.1038/nature23879.DOI: 10.1038/nature23879Google Scholar
  237. 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.DOI: 10.22331/q-2020-08-31-314Google Scholar
  238. J. Biamonte et al (2017). “Quantum machine learning”. Nature 549, 195–202. https://doi.org/10.1038/nature23474.DOI: 10.1038/nature23474Google Scholar
  239. Z.-C. Yang et al (2017). “Optimizing variational quantum algorithms using Pontryagin’s minimum principle”. Physical Review X, 7, 021027. https://doi.org/10.1103/PhysRevX.7.021027.DOI: 10.1103/PhysRevX.7.021027Google Scholar
  240. 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.Google Scholar
  241. J. Biamonte (2021). “Universal variational quantum computation”. Physical Review A 103: 3, L030401. https://doi.org/10.1103/PhysRevA.103.L030401.DOI: 10.1103/PhysRevA.103.L030401Google Scholar
  242. 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.DOI: 10.1038/s41586-019-0980-2Google Scholar
  243. A. Manzano et al (2023). “Parametrized quantum circuits and their approximation capacities in the context of quantum machine learning”. arXiv:2307.14792 https://doi.org/10.48550/arXiv.2307.14792.Google Scholar
  244. 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.DOI: 10.1103/PhysRevLett.117.130501Google Scholar
  245. L. Pira (2024). The Fundamentals of Quantum Neural Networks. PhD Dissertation. University of Technology Sydney.DOI: 10.1007/s42484-024-00191-yGoogle Scholar
  246. E. Tang (2019). “A quantum-inspired classical algorithm for recommendation systems”, in Proceedings of the 51st Annual ACM SIGACT Symposium on Theory of Computing https://doi.org/10.1145/3313276.3316310.DOI: 10.1145/3313276.3316310Google Scholar
  247. S. Lloyd, M. Mohseni, and P. Rebentrost (2013). “Quantum algorithms for supervised and unsupervised machine learning”. arXiv:1307.0411 https://doi.org/10.48550/arXiv.1307.0411.Google Scholar
  248. 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.DOI: 10.1103/PhysRevA.78.052310Google Scholar
  249. V. Giovannetti, S. Lloyd, and L. Maccone (2008). “Quantum random access memory”. Physical Review Letters, 100. https://doi.org/10.1103/PhysRevLett.100.160501.DOI: 10.1103/PhysRevLett.100.160501Google Scholar
  250. 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.DOI: 10.1088/1367-2630/17/12/123010Google Scholar
  251. L. Gyongyosi and S. Imre (2019). “Training optimization for gate-model quantum neural networks”. Scientific Reports DOI: 10.1038/s41598-019-48892-w. https://doi.org/10.1038/s41598-019-48892-w.DOI: 10.1038/s41598-019-48892-wGoogle Scholar
  252. 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.DOI: 10.1103/RevModPhys.91.045002Google Scholar
  253. 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.Google Scholar
  254. 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.DOI: 10.1103/PhysRevX.8.031086Google Scholar
  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.DOI: 10.1038/s41534-019-0141-3Google Scholar
  256. H. P. Nautrup, N. Delfosse, V. Dunjko, H. J. Briegel, and N. Friis (2019). “Optimizing quantum error correction codes with reinforcement learning”. Quantum, 3, 215. https://doi.org/10.22331/q-2019-12-16-215.DOI: 10.22331/q-2019-12-16-215Google Scholar
  257. 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.DOI: 10.1103/PhysRevLett.119.030501Google Scholar
  258. 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.DOI: 10.1038/s41567-018-0048-5Google Scholar
  259. 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.DOI: 10.1103/PhysRevA.106.012409Google Scholar
  260. 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.DOI: 10.1103/PhysRevX.9.041029Google Scholar
  261. 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.DOI: 10.1103/PhysRevA.97.042315Google Scholar
  262. 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.DOI: 10.1038/s41467-021-27045-6Google Scholar
  263. J. R. McClean, S. Boixo, V. N. Smelyanskiy, R. Babbush, and H. Neven (2018). “Barren plateaus in quantum neural network training landscapes”. Nature Communications, 9. https://doi.org/10.1038/s41467-018-07090-4.DOI: 10.1038/s41467-018-07090-4Google Scholar
  264. 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.DOI: 10.1038/s41467-021-21728-wGoogle Scholar
  265. A. Arrasmith et al (2022). “Equivalence of quantum barren plateaus to cost concentration and narrow gorges”. Quantum Science and Technology 7: 4, 045015. https://doi.org/10.1088/2058-9565/ac7d06.DOI: 10.1088/2058-9565/ac7d06Google Scholar
  266. M. Cerezo et al (2022). “Challenges and opportunities in quantum machine learning”. Nature Computational Science 2: 9, 567–576. https://doi.org/10.1038/s43588-022-00311-3.DOI: 10.1038/s43588-022-00311-3Google Scholar
  267. S. Herbst (2024). “Beyond 0s and 1s: Exploring the impact of noise, data encoding, and hyperparameter optimization in quantum machine learning”. Diploma Thesis Technische Universitat Wien.Google Scholar
  268. D. Suchan (2024). “Hyperparameter tuning for quantum machine learning”. Diploma Thesis Technische Universitat Wien.Google Scholar
  269. L. Alchieri et al (2021). “An introduction to quantum machine learning: from quantum logic to quantum deep learning”. Quantum Machine Intelligence 3: 2, 28. https://doi.org/10.1007/s42484-021-00056-8.DOI: 10.1007/s42484-021-00056-8Google Scholar
  270. 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/abac39DOI: 10.1088/1367-2630/abac39Google Scholar
  271. D. Ventura and T. Martinez (2000). “Quantum associative memory”. Information Sciences, 126, 273. https://doi.org/10.1016/S0020-0255(99)00101-2.DOI: 10.1016/S0020-0255(99)00101-2Google Scholar
  272. R. LaRose and B. Coyle (2020). “Robust data encodings for quantum classifiers”. Physical Review A, 102. https://doi.org/10.1103/PhysRevA.102.032420.DOI: 10.1103/PhysRevA.102.032420Google Scholar
  273. M. Schuld and F. Petruccione (2018). Supervised Learning with Quantum Computers Springer, DOI: 10.1007/978-3-319-96424-9.DOI: 10.1007/978-3-319-96424-9Google Scholar
  274. 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/s41467-021-22 539-9.DOI: 10.1038/s41467-021-22539-9Google Scholar
  275. M. Schuld and N. Killoran (2019). “Quantum machine learning in feature Hilbert spaces”. Physical Review Letters, 122, 040504. https://doi.org/10.1103/PhysRevLett.122.040504.DOI: 10.1103/PhysRevLett.122.040504Google Scholar
  276. 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.DOI: 10.1007/s42484-020-00036-4Google Scholar
  277. T. Haug, C. N. Self, and M. S. Kim (2023). “Quantum machine learning of large datasets using randomized measurements”. Machine Learning: Science and Technology, 4 015005. https://doi.org/10.1088/2632-2153/acb0b4.DOI: 10.1088/2632-2153/acb0b4Google Scholar
  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.Google Scholar
  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.DOI: 10.1103/PhysRevB.102.235122Google Scholar
  280. R. Wiersema, C. Zhou, Y. de Sereville, J. F. Carrasquilla, Y. B. Kim, and H. Yuen (2020). “Exploring entanglement and optimization within the Hamiltonian Variational Ansatz”. PRX Quantum, 1. https://doi.org/10.1103/PRXQuantum.1.020319.DOI: 10.1103/PRXQuantum.1.020319Google Scholar
  281. M. Weigold, J. Barzen, F. Leymann, and M. Salm (2020). “Data encoding patterns for quantum computing” in Proceedings of the 27th Conference on Pattern Languages of Programs https://doi.org/10.5555/3511065.3511068.Google Scholar
  282. M. Weigold, J. Barzen, F. Leymann, and M. Salm (2021). “Expanding data encoding patterns for quantum algorithms”, in 2021 IEEE 18th International Conference on Software Architecture Companion (ICSA-C) pp. 95–101. https://doi.org/10.1109/ICSA-C52384.2021.00025.DOI: 10.1109/ICSA-C52384.2021.00025Google Scholar
  283. 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/10.1209/0295-5075/119/60002DOI: 10.1209/0295-5075/119/60002Google Scholar
  284. J. Romero, J.P. Olson, and A. Aspuru-Guzik (2017). “Quantum autoencoders for efficient compression of quantum data”. Quantum Science and Technology, 2, 045001. https://doi.org/10.1088/2058-9565/aa8072.DOI: 10.1088/2058-9565/aa8072Google Scholar
  285. M. H. Amin, E. Andriyash, J. Rolfe, B. Kulchytskyy, and R. Melko (2018). “Quantum Boltzmann Machine”. Physical Review X, 8, 021050. https://doi.org/10.1103/PhysRevX.8.021050.DOI: 10.1103/PhysRevX.8.021050Google Scholar
  286. R. Moretti, A. Giachero, V. Radescu, M. Grossi (2024). “Enhanced feature encoding and classification on distributed quantum hardware”. arXiv:2412.01664 https://doi.org/10.48550/arXiv.2412.01664.DOI: 10.1088/2632-2153/adb4bcGoogle Scholar
  287. 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.DOI: 10.3390/electronics10141690Google Scholar
  288. A. W. Harrow (2020). “Small quantum computers and large classical data sets”. arXiv:2004.00026 https://doi.org/10.48550/arXiv.2004.00026.Google Scholar
  289. 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.DOI: 10.1038/s41534-021-00452-9Google Scholar
  290. Y. Du, Y. Qian, X. Wu, D. Tao (2022). “A distributed learning scheme for variational quantum algorithms”. IEEE Transactions on Quantum Engineering, 3, 116. https://doi.org/10.1109/TQE.2022.3175267.DOI: 10.1109/TQE.2022.3175267Google Scholar
  291. J. F. Fitzsimons (2017). “Private quantum computation: an introduction to blind quantum computing and related protocols”. npj Quantum Information 3, 23. https://doi.org/10.1038/s41534-017-0025-3DOI: 10.1038/s41534-017-0025-3Google Scholar
  292. 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.DOI: 10.1109/NOMS56928.2023.10154430Google Scholar
  293. M. A. Serrano, L. E. Sanchez, A. Santos-Olmo et al (2023). “Minimizing incident response time in realworld scenarios using quantum computing”. Software Quality Journal 32, 163192. https://doi.org/10.1007/s11219-023-09632-6.DOI: 10.1007/s11219-023-09632-6Google Scholar
  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.DOI: 10.1088/2058-9565/ab7559Google Scholar
  295. Y. Ding and A. Javadi-Abhari. (2022). “Quantum and post-Moore’s law computing”. IEEE Internet Computing 26: 1, 56. https://doi.org/10.1109/MIC.2021.3133675.DOI: 10.1109/MIC.2021.3133675Google Scholar
  296. D. Subhi and L. Bacsardi (2023). “Using quantum nodes connected via the quantum cloud to perform IOT quantum network”. Condensed Matter 8: 1, p. 24. https://doi.org/10.3390/condmat8010024.DOI: 10.3390/condmat8010024Google Scholar
  297. IBM Quantum Computing Services, IBM (2023). https://quantum-computing.ibm.com/Google Scholar
  298. IBM Cloud, IBM (2024). https://www.ibm.com/cloudGoogle Scholar
  299. Google Cloud, Google (2024). Google Quantum AI. https://quantumai.google/Google Scholar
  300. IonQ (2022). IonQ Cloud Service. https://ionq.com/Google Scholar
  301. Quantinuum Cloud Service, Quantinuum (2022). https://www.quantinuum.com/.Google Scholar
  302. Pasqal: Programmable Atomic Arrays (2024). https://www.pasqal.com/.Google Scholar
  303. Azure Quantum, Microsoft (2023). https://azure.microsoft.com/en-us/services/quantumGoogle Scholar
  304. QuEra, Quantum Computing with Neutral Atoms (2024). https://www.quera.com/Google Scholar
  305. C. Gonzalez (2021). “Cloud based QC with Amazon Braket”. Digitale Welt 5: 2, 14–17. https://doi.org/10.1007/s42354-021-0330-z.DOI: 10.1007/s42354-021-0330-zGoogle Scholar
  306. Amazon Braket, Amazon (2024). https://aws.amazon.com/braket/Google Scholar
  307. PlanQK (2020). https://www.planqk.de/Google Scholar
  308. C. Linnhoff-Popien (2020). “PlanQK: Quantum computing meets artificial intelligence: How to make an ambitious idea reality”. Digitale Welt 4: 2, 28–35. https://doi.org/10.1007/s42354-020-0257-9.DOI: 10.1007/s42354-020-0257-9Google Scholar
  309. Quantum Inspire, De Voorhoede (2024). https://www.quantum-inspire.com/Google Scholar
  310. QuantumPath. https://www.quantumpath.es/Google Scholar
  311. J. L. Hevia, G. Peterssen, M. Piattini (2021). “QuantumPath: A quantum software development platform”. Software: Practice and Experience 1–14. https://doi.org/10.1002/spe.3064.DOI: 10.1007/978-3-031-05324-5_13Google Scholar
  312. Strangeworks Quantum Computing Platform, Strangeworks (2022). https://strangeworks.com/Google Scholar
  313. QFaaS, Github (2022). https://github.com/Cloudslab/qfaasGoogle Scholar
  314. H. T. Nguyen, M. Usman, and R. Buyya (2024). “QFaaS: A serverless function-as-a-service framework for quantum computing”. Future Generation Computer Systems 154, 281–300. https://doi.org/10.1016/j.future.2024.01.018.DOI: 10.1016/j.future.2024.01.018Google Scholar
  315. 1Qloud Optimization Platform, 1QBit (2024). https://1qbit.com/1qloud/Google Scholar
  316. Qemist Cloud, Good Chemistry Co (2024). https://goodchemistry.com/qemist-cloud/Google Scholar
  317. N. Aslam, H. Zhou, E. K. Urbach, M. J. Turner, R. L. Walsworth, M. D. Lukin, and H. Park (2023). “Quantum sensors for biomedical applications. Nature Reviews Physics 5: 3, 157–169. https://doi.org/10.1038/s42254-023-00558-3.DOI: 10.1038/s42254-023-00558-3Google Scholar
  318. L. Thiel, D. Rohner, M. Ganzhorn, P. Appel, E. Neu, B. Muller, R. Kleiner, D. Koelle, and P. Maletinsky (2016). “Quantitative nanoscale vortex imaging using a cryogenic quantum magnetometer”. Nature Nanotechnology, 11: 8, 677–681. https://doi.org/10.1038/nnano.2016.63.DOI: 10.1038/nnano.2016.63Google Scholar
  319. H. M. J. Boffin, G. Hussain, J.-P. Berger, and L. Schmidtobreick (2016). “Astronomy at high angular resolution”. Astrophysics and Space Science Library 439. https://doi.org/10.1007/978-3-319-39739-9.DOI: 10.1007/978-3-319-39739-9Google Scholar
  320. Y. Zhang et al (2021). “QED driven QAOA for networkflow optimization”. Quantum 5: 510. https://doi.org/10.22331/q-2021-07-27-510.DOI: 10.22331/q-2021-07-27-510Google Scholar
  321. B. Chevalier, W. Roga, M. Takeoka (2024). “Compressed sensing enhanced by a quantum approximate optimization algorithm”. Physical Review A 110, 062410. https://doi.org/10.1103/PhysRevA.110.062410.DOI: 10.1103/PhysRevA.110.062410Google Scholar
  322. J. Li, M. Alam, and S. Ghosh (2023). “Large-scale quantum approximate optimization via divide-and-conquer”. IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems 42: 6, 18521860. https://doi.org/10.1109/TCAD.2022.3212196.DOI: 10.1109/TCAD.2022.3212196Google Scholar
  323. G. D. Kahanamoku-Meyer et al (2022). “Classically verifiable quantum advantage from a computational Bell test”. Nature Physics 18: 8, 918–924. https://doi.org/10.1038/s41567-022-01643-7.DOI: 10.1038/s41567-022-01643-7Google Scholar
  324. Z. Brakerski et al (2021). “A cryptographic test of quantumness and certifiable randomness from a single quantum device”. Journal of the ACM (JACM) 68: 5, 1–47. https://doi.org/10.1145/3441309.DOI: 10.1145/3441309Google Scholar
  325. H. R. Grimsley et al (2019). “An adaptive variational algorithm for exact molecular simulations on a quantum computer”. Nature Communications 10: 1, 3007. https://doi.org/10.1038/s41467-019-10988-2.DOI: 10.1038/s41467-019-10988-2Google Scholar
  326. Y.-F. Niu, S. Zhang, C. Ding, W.-S. Bao, and H.-L. Huang (2023). “Parameter-parallel distributed variational quantum algorithm”. SciPost Physics 14, 5. https://doi.org/10.21468/SciPostPhys.14.5.132.DOI: 10.21468/SciPostPhys.14.5.132Google Scholar
  327. D. Bluvstein et al (2024). “Logical quantum processor based on reconfigurable atom arrays”. Nature 626: 7997, 58–65. https://doi.org/10.1038/s41586-023-06927-3.DOI: 10.1038/s41586-023-06927-3Google Scholar
  328. J. Bartusek et al (2023). “Obfuscation of pseudo-deterministic quantum circuits”, in Proceedings of the 55th Annual ACM Symposium on Theory of Computing 1567–1578. https://doi.org/10.1145/3564246.3585179DOI: 10.1145/3564246.3585179Google Scholar
  329. J. Rajakumar et al (2024). “Polynomial-time classical simulation of noisy IQP circuits with constant depth”. arXiv:2403.14607 https://doi.org/10.48550/arXiv.2403.14607.DOI: 10.1137/1.9781611978322.30Google Scholar
  330. S. Chen, J. Cotler, H.-Y. Huang, and J. Li (2023). “The complexity of NISQ”. Nature Communications 14, 6001. https://doi.org/10.1038/s41467-023-41217-6.DOI: 10.1038/s41467-023-41217-6Google Scholar
  331. V. Dunjko and H. J. Briegel (2018). “Machine learning and artificial intelligence in the quantum domain”. Reports on Progress in Physics 81, 074001. https://doi.org/10.1088/1361-6633/aab406DOI: 10.1088/1361-6633/aab406Google Scholar
  332. J. A. Cortese, Timothy M. Braje (2018). “Loading classical data into a quantum computer”. arXiv:1803.01958 https://doi.org/10.48550/arXiv.1803.01958.Google Scholar
  333. Y. Cao, G. G. Guerreschi, and A. Aspuru-Guzik (2017). “Quantum neuron: An elementary building block for machine learning on quantum computers”. arXiv:1711.11240 https://doi.org/10.48550/arXiv.1711.11240.Google Scholar
  334. K. Mitarai, M. Negoro, M. Kitagawa, and K. Fujii (2018). “Quantum circuit learning”. Physical Review A 98. https://doi.org/10.1103/PhysRevA.98.032309.DOI: 10.1103/PhysRevA.98.032309Google Scholar
  335. J. Allcock, C.-Y. Hsieh, I. Kerenidis, and S. Zhang (2020). “Quantum algorithms for feedforward neural networks”. ACM Transactions on Quantum Computing, 1. https://doi.org/10.1145/3411466.DOI: 10.1145/3411466Google Scholar
  336. M. Schuld, A. Bocharov, K. M. Svore, and N. Wiebe (2020). “Circuit-centric quantum classifiers”. Physical Review A, 101. https://doi.org/10.1103/PhysRevA.101.032308.DOI: 10.1103/PhysRevA.101.032308Google Scholar
  337. Q.-X. Xiea, Y. Zhaobc (2024). “A novel quantum-classical hybrid algorithm for determining eigenstate energies in quantum chemistry”. arXiv:2406.00296 https://doi.org/10.48550/arXiv.2406.00296.Google Scholar
  338. C. C. Hian (2024). Resource-Efficient Quantum Algorithms for Quantum Chemistry. PhD Dissertation, National University of Singapore.Google Scholar
  339. J. Bausch (2018). “Classifying data using near-term quantum devices”. International Journal of Quantum Information, 16, 8. https://doi.org/10.1142/S0219749918400014.DOI: 10.1142/S0219749918400014Google Scholar
  340. M. L. Wall et al (2021). “Generative machine learning with tensor networks: Benchmarks on near-term quantum computers”. Physical Review Research, 3: 2. https://doi.org/10.1103/PhysRevResearch.3.023010.DOI: 10.1103/PhysRevResearch.3.023010Google Scholar
  341. B. Coecke et al (2020). “Foundations for near-term quantum natural language processing”. arXiv:2012.03755 https://doi.org/10.48550/arXiv.2012.03755.Google Scholar
  342. M. Alam et al (2022). “QNet: A scalable and noise-resilient quantum neural network architecture for noisy intermediate-scale quantum computers”. Frontiers in Physics 9. https://doi.org/10.3389/fphy.2021.755139.DOI: 10.3389/fphy.2021.755139Google Scholar
  343. S. Lloyd and C. Weedbrook (2018). “Quantum generative adversarial learning”. Physical Review Letters, 121. https://doi.org/10.1103/PhysRevLett.121.040502.DOI: 10.1103/PhysRevLett.121.040502Google Scholar
  344. P.-L. Dallaire-Demers and N. Killoran (2018). “Quantum generative adversarial networks”. Physical Review A, 98, 012324. https://doi.org/10.1103/PhysRevA.98.012324.DOI: 10.1103/PhysRevA.98.012324Google Scholar
  345. C. Zoufal, A. Lucchi, and S. Woerner (2019). “Quantum generative adversarial networks for learning and loading random distributions”. npj Quantum Information, 5. https://doi.org/10.1038/s41534-019-0223-2.DOI: 10.1038/s41534-019-0223-2Google Scholar
  346. M. Henderson, S. Shakya, S. Pradhan, and T. Cook (2019). “Quanvolutional neural networks: powering image recognition with quantum circuits”. arXiv:1904.04767 https://doi.org/10.48550/arXiv.1904.04767.DOI: 10.1007/s42484-020-00012-yGoogle Scholar
  347. J. Bausch (2020). “Recurrent quantum neural networks”, in H. Larochelle, M. Ranzato, R. Hadsell, M. Balcan, and H. Lin (eds), Advances in Neural Information Processing Systems Curran Associates, Inc., 33, pp. 1368–1379. https://doi.org/10.48550/arXiv.2006.14619.Google Scholar
  348. I. Kerenidis, J. Landman, and A. Prakash (2020). “Quantum algorithms for deep convolutional neural networks”. arXiv:1911.01117 https://doi.org/10.48550/arXiv.1911.01117.Google Scholar
  349. I. Cong, S. Choi, and M. D. Lukin (2019). “Quantum convolutional neural networks”. Nature Physics, 15, 1273. https://doi.org/10.1038/s41567-019-0648-8.DOI: 10.1038/s41567-019-0648-8Google Scholar
  350. E. Grant, L. Wossnig, M. Ostaszewski, and M. Benedetti (2019). “An initialization strategy for addressing barren plateaus in parametrized quantum circuits”. Quantum 3. https://doi.org/10.22331/q-2019-12-09-214.DOI: 10.22331/q-2019-12-09-214Google Scholar
  351. A. Pesah, M. Cerezo, S. Wang, T. Volko, A. T. Sornborger, and P. J. Coles (2021). “Absence of barren plateaus in quantum convolutional neural networks”. Physical Review X 11, 041011. https://doi.org/10.1103/PhysRevX.11.041011.DOI: 10.1103/PhysRevX.11.041011Google Scholar
  352. Y. Ding, L. Lamata, M. Sanz, X. Chen, and E. Solano (2019). “Experimental implementation of a quantum autoencoder via quantum adders”. Advanced Quantum Technologies 2, 1800065. https://doi.org/10.1002/qute.201800065.DOI: 10.1002/qute.201800065Google Scholar
  353. A. Rocchetto, S. Aaronson, S. Severini, G. Carvacho, D. Poderini, I. Agresti, M. Bentivegna, and F. Sciarrino (2019). “Experimental learning of quantum states”. Science Advances 5, eaau1946. https://doi.org/10.1126/sciadv.aau1946.DOI: 10.1126/sciadv.aau1946Google Scholar
  354. B. Coyle, D. Mills, V. Danos, and E. Kashe (2020). “The born supremacy: Quantum advantage and training of an Ising Born Machine”. npj Quantum Information 6, 1. https://doi.org/10.1038/s41534-020-00 288-9.DOI: 10.1038/s41534-020-00288-9Google Scholar
  355. M. Benedetti, D. Garcia-Pintos, O. Perdomo, V. Leyton-Ortega, Y. Nam, and A. Perdomo-Ortiz (2019). “A generative modeling approach for benchmarking and training shallow quantum circuits”. npj Quantum Information 5, 1. https://doi.org/10.1038/s41534-019-0157-8.DOI: 10.1038/s41534-019-0157-8Google Scholar
  356. F. Tacchino, C. Macchiavello, D. Gerace, and D. Bajoni (2019). “An artificial neuron implemented on an actual quantum processor”. npj Quantum Information 5, 1. https://doi.org/10.1038/s41534-019-0140-4.DOI: 10.1038/s41534-019-0140-4Google Scholar
  357. E. Grant, M. Benedetti, S. Cao, A. Hallam, J. Lockhart, V. Stojevic, A. G. Green, and S. Severini (2018). “Hierarchical quantum classifiers”. npj Quantum Information 4, 1. https://doi.org/10.1038/s41534-018-0116-9.DOI: 10.1038/s41534-018-0116-9Google Scholar
  358. D. Riste, M. P. Da Silva, C. A. Ryan, A. W. Cross, A. D. Corcoles, J. A. Smolin, J. M. Gambetta, J. M. Chow, and B. R. Johnson (2017). “Demonstration of quantum advantage in machine learning”. npj Quantum Information 3, 1. https://doi.org/10.1038/s41534-017-0017-3.DOI: 10.1038/s41534-017-0017-3Google Scholar
  359. J. S. Otterbach, R. Manenti, N. Alidoust, A. Bestwick, M. Block, B. Bloom, S. Caldwell, N. Didier, E. S. Fried, S. Hong, et al (2017). “Unsupervised machine learning on a hybrid quantum computer”. arXiv:1712.05771 https://doi.org/10.48550/arXiv.1712.05771.Google Scholar
  360. B. Heim, M. Soeken, S. Marshall, C. Granade, M. Roetteler, A. Geller, M. Troyer, and K. Svore (2020). “Quantum programming languages”. Nature Reviews Physics 2: 12, 709–722. https://doi.org/10.1038/s42254-020-00245-7.DOI: 10.1038/s42254-020-00245-7Google Scholar
  361. A. Tavakoli, A. Pozas-Kerstjens, P. Brown, M. Araujo (2024). “Semidefinite programming relaxations for quantum correlations”. Reviews of Modern Physics, 96, 045006. https://doi.org/10.1103/RevModPhys.96.045006.DOI: 10.1103/RevModPhys.96.045006Google Scholar
  362. R. LaRose (2019). “Overview and comparison of gate level quantum software platforms”. Quantum 3, 130. https://doi.org/10.22331/q-2019-03-25-130.DOI: 10.22331/q-2019-03-25-130Google Scholar
  363. M. Fingerhuth, T. Babej, and P. Wittek (2018). “Open source software in quantum computing”. PloS One 13: 12, e0208561. https://doi.org/10.1371/journal.pone.0208561.DOI: 10.1371/journal.pone.0208561Google Scholar
  364. J. Zhao (2020). “Quantum software engineering: landscapes and horizons”. arXiv:2007.07047 https://doi.org/10.48550/arXiv.2007.07047.Google Scholar
  365. J. M. Murillo et al. (2024). “Quantum software engineering: roadmap and challenges ahead”. ACM Transactions on Software Engineering and Methodology https://doi.org/10.1145/3712002.DOI: 10.1145/3712002Google Scholar
  366. J. Ray. (2022). “China at the nexus of AI and quantum computing”. Chinese Power and Artificial Intelligence: Perspectives and Challenges 155–172.DOI: 10.4324/9781003212980-12Google Scholar
  367. M. Ying, Y. Feng, R. Duan et al (2012). “Quantum programming: From theories to implementations”. Chinese Science Bulletin 57, 1903–1909. https://doi.org/10.1007/s11434-012-5147-6.DOI: 10.1007/s11434-012-5147-6Google Scholar
  368. I. Kumara, W. J. Van Den Heuvel, D. A. Tamburri (2021). “Qsoc: Quantum service-oriented computing”, in Symposium and Summer School on Service-Oriented Computing 5263. https://doi.org/10.1007/978-3-030-87568-8 3.DOI: 10.1007/978-3-030-87568-8_3Google Scholar
  369. J. Romero-Alvarez, J. Alvarado-Valiente, E. Moguel, J. Garcia-Alonso (2023). “Quantum web services: Development and deployment”, in Web Engineering Springer, Alicante, Spain, pp. 421–423. https://doi.org/10.1007/978-3-031-34444-239.DOI: 10.1007/978-3-031-34444-2_39Google Scholar
  370. V. Bergholm, J. Izaac, M. Schuld, C. Gogolin, S. Ahmed, V. Ajith, M. S. Alam, G. Alonso-Linaje, B. Akash Narayanan, A. Asadi, et al (2018). “PennyLane: Automatic differentiation of hybrid quantum-classical computations”. arXiv:1811.04968 https://doi.org/10.48550/arXiv.1811.04968.Google Scholar
  371. G. Aleksandrowicz, T. Alexander, P. Barkoutsos, L. Bello, Y. Ben-Haim, D. Bucher, F. J. Cabrera-Hernandez, J. Carballo-Franquis, A. Chen, C.-F. Chen, et al (2019). “Qiskit: An open-source framework for quantum computing”. https://doi.org/10.5281/zenodo.2562111.Google Scholar
  372. H. Nagarajan, O. Lockwood and C. Coffrin (2021). “QuantumCircuitOpt: An open-source framework for provably optimal quantum circuit design”. arXiv:2111.11674 https://doi.org/10.48550/arXiv.2111.11674.DOI: 10.1109/QCS54837.2021.00010Google Scholar
  373. QuPanda: an open source quantum computing framework (2018). “Origin quantum”, https://github.com/OriginQ/QPanda-2Google Scholar
  374. S. Diadamo, J. Notzel, B. Zanger, and M. M. Bese (2021). “Distributed quantum computing and network control for accelerated VQE”. IEEE Transactions on Quantum Engineering, 2, 1. https://doi.org/10.1109/TQE.2021.3057908.DOI: 10.1109/TQE.2021.3057908Google Scholar
  375. T. Chatterjee, A. Das, S. I. Mohtashim, A. Saha, A. Chakrabarti (2022). “Qurzon: A prototype for a divide and conquer-based quantum compiler for distributed quantum systems”. SN Computer Science, 3, 4. https://doi.org/10.1007/s42979-022-01207-9.DOI: 10.1007/s42979-022-01207-9Google Scholar
  376. W. Tang, M. Martonosi, ScaleQC (2022). “A scalable framework for hybrid computation on quantum and classical processors”. arXiv.2207.00933. https://doi.org/10.48550/arXiv.2207.00933.Google Scholar
  377. K. N. Smith, M. A. Perlin, P. Gokhale, P. Frederick, D. Owusu-Antwi, R. Rines et al. (2023). “Clifford-based circuit cutting for quantum simulation”. Proc. of the 50th Annual Int. Symp. on Computer Architecture (ISCA’23) ACM, New York, pp. 113. https://doi.org/10.1145/3579371.3589352.DOI: 10.1145/3579371.3589352Google Scholar
  378. “TorchQuantum: Fast library for quantum computing in PyTorch”. (2022). https://hanruiwanghw.wixsite. com/torchquantumGoogle Scholar
  379. M. Broughton, G. Verdon, T. McCourt, A. J. Martinez, J. H. Yoo, S. V. Isakov, P. Massey, R. Halavati, M. Y. Niu, A. Zlokapa, et al (2020). “TensorFlow quantum: A software framework for quantum machine learning”. arXiv:2003.02989 https://doi.org/10.48550/arXiv.2003.02989.Google Scholar
  380. C. Xing and M. Broughton (2021). “Training with multiple workers using tensor flow quantum”. https://blog.tensorflow.org.Google Scholar
  381. N. N. Hegade, N. L. Kortikar, B. Das, B. K. Behera, and P. K. Panigrahi (2017). “Experimental demonstration of quantum tunneling in IBM quantum computer”. arXiv:1712.07326 https://doi.org/10.48550/arXiv.1712.07326.Google Scholar
  382. H. Norlen (2020). Quantum Computing in Practice with Qiskit and IBM Quantum Experience: Practical Recipes for Quantum Computer Coding at the Gate and Algorithm Level with Python. Packt Publishing Ltd.Google Scholar
  383. D. Fortunato, J. Campos, and R. Abreu (2022). “Mutation testing of quantum programs: A case study with qiskit”. IEEE Transactions on Quantum Engineering 3, 1–17. https://doi.org/10.1109/TQE.2022.3195061.DOI: 10.1109/TQE.2022.3195061Google Scholar
  384. Pyquil, Rigetti Computing (2017). https://www.rigetti.com/applications/pyquilGoogle Scholar
  385. K. Singhal, K. Hietala, S. Marshall, and R. Rand (2022). “Q# as a quantum algorithmic language”. arXiv:2206.03532. https://doi.org/10.4204/EPTCS.394.10.DOI: 10.4204/EPTCS.394.10Google Scholar
  386. The Quipper Language (2013). https://www.mathstat.dal.ca/ selinger/quipper/Google Scholar
  387. J. M. Smith, N. J. Ross, P. Selinger, and B. Valiron (2014). “Quipper: Concrete resource estimation in quantum algorithms”. arXiv:1412.0625. https://doi.org/10.48550/arXiv.1412.0625.Google Scholar
  388. Dwave Ocean (2018). https://docs.ocean.dwavesys.com/en/stable/Google Scholar
  389. D. Willsch, M. Willsch, C. D. Gonzalez Calaza, F. Jin, H. De Raedt, M. Svensson, and K. Michielsen (2022). “Benchmarking advantage and Dwave 2000q quantum annealers with exact cover problems”. Quantum Information Processing 21: 4, 141. https://doi.org/10.1007/s11128-022-03476-y.DOI: 10.1007/s11128-022-03476-yGoogle Scholar
  390. R. Forest (2020). https://qcs.rigetti.com/sdk-downloadsGoogle Scholar
  391. J. Olivares-Sanchez, J. Casanova, E. Solano, and L. Lamata (2020). “Measurement-based adaptation protocol with quantum reinforcement learning in a Rigetti quantum computer”. Quantum Reports 2: 2, 293–304. https://doi.org/10.3390/quantum2020019.DOI: 10.3390/quantum2020019Google Scholar
  392. Microsoft Quantum SDK, Microsoft (2022). https://learn.microsoft.com/en-us/azure/quantum/qsharp-overviewGoogle Scholar
  393. J. Hooyberghs (2022). Introducing Microsoft Quantum Computing for Developers: Using the Quantum Development Kit and Q# Apress, ISBN-10: 1484272455.DOI: 10.1007/978-1-4842-7246-6Google Scholar
  394. Strawberry Fields, Xanadu (2018). https://strawberryfields.ai/Google Scholar
  395. ProjectQ: An open source software framework for quantum computing (2022). https://github.com/ProjectQ-Framework/ProjectQGoogle Scholar
  396. Cirq: An open source framework for programming quantum computers. https://quantumai.google/cirqGoogle Scholar
  397. J. R. McClean, N. C. Rubin, K. J. Sung, I. D. Kivlichan, X. Bonet-Monroig, Y. Cao, C. Dai, E. S. Fried, C. Gidney, B. Gimby et al (2020). “Openfermion: the electronic structure package for quantum computers”. Quantum Science and Technology 5: 3, 034014. https://doi.org/10.1088/2058-9565/ab8ebc.DOI: 10.1088/2058-9565/ab8ebcGoogle Scholar
  398. J. R. Johansson, P. D. Nation, and F. Nori (2012). “Qutip: An open-source Python framework for the dynamics of open quantum systems”. Computer Physics Communications 183: 8, 1760–1772. https://doi.org/10.1016/j.cpc.2012.02.021.DOI: 10.1016/j.cpc.2012.02.021Google Scholar
  399. J. Garcia-Alonso, J. Rojo, D. Valencia, E. Moguel, J. Berrocal, and J. M. Murillo (2021). “Quantum software as a service through a quantum API gateway”. IEEE Internet Computing 26: 1, 34–41. https://doi.org/10.1109/MIC.2021.3132688.DOI: 10.1109/MIC.2021.3132688Google Scholar
  400. T. L. Patti, J. Kossaifi, S. F. Yelin, and A. Anandkumar (2021). “Tensorly-quantum: Quantum machine learning with tensor methods”. arXiv:2112.10239. https://doi.org/10.48550/arXiv.2112.10239.Google Scholar
  401. C. F. Negre, H. Ushijima-Mwesigwa, and S. M. Mniszewski (2020). “Detecting multiple communities using quantum annealing on the D-wave system”. Plos One 15: 2, e0227538. https://doi.org/10.1371/journal.pone.0227538.DOI: 10.1371/journal.pone.0227538Google Scholar
  402. J. Romero-Alvarez, J. Alvarado-Valiente, E. Moguel et al (2023). “Leveraging API specifications for scaffolding quantum applications”, in International Workshop on Quantum Software Engineering and Technology(QCE23) IEEE Quantum Week 2023. https://doi.org/10.1109/QCE57702.2023.10208.DOI: 10.1109/QCE57702.2023.10208Google Scholar
  403. I. Kumara, W.-J. Van Den Heuvel, D. A. Tamburri (2021). “Qsoc: Quantum service-oriented computing”, in Symposium and Summer School on Service-Oriented Computing Springer, pp. 52–63. https://doi.org/10.1007/978-3-030-87568-8 3.DOI: 10.1007/978-3-030-87568-8_3Google Scholar
  404. J. Alvarado-Valiente, J. Romero-Alvarez, E. Moguel, J. Garcia-Alonso, J. M. Murillo (2023). “Technological diversity of quantum computing providers: a comparative study and a proposal for API Gateway integration”. Software Quality Journal 32, 5373. https://doi.org/10.1007/s11219-023-09633-5.DOI: 10.1007/s11219-023-09633-5Google Scholar
  405. S. Schwichtenberg, C. Gerth, G. Engels (2017). “From Open API to semantic specifications and code adapters” in 2017 IEEE International Conference on Web Services (ICWS) pp. 484-491. https://doi.org/10.1109/ICWS.2017.56.DOI: 10.1109/ICWS.2017.56Google Scholar
  406. J. Romero-Alvarez, J. Alvarado-Valiente, J. Casco-Seco et al. (2023). ”Developing high-level abstractions for creating quantum services: Open API and Async API”, in Symposium and Summer School On Service-Oriented Computing (SummerSOC 2023) Crete, Greece. https://doi.org/10.1007/978-3-031-64136-7 8.DOI: 10.1007/978-3-031-64136-7Google Scholar
  407. B. Heim (2021). “Universal quantum intermediate representation”. APS March Meeting Abstracts 2021, 34-009.Google Scholar
  408. Y. Ohkura, T. Satoh, R. Van Meter (2022). “Simultaneous execution of quantum circuits on current and near-future NISQ systems”. IEEE Transactions on Quantum Engineering 3. https://doi.org/10.1109/TQE.2022.3164716.DOI: 10.1109/TQE.2022.3164716Google Scholar
  409. M. Kaliyanandi, J. Murugan, S. K. Subburaj et al (2023). “Design and development of novel security approach designed for cloud computing with load balancing”, in Advances in Intelligent Applications and Innovative Approach 2760, 050005. https://doi.org/10.1063/5.0126814.DOI: 10.1063/5.0126814Google Scholar
  410. E. Karacan, A. Karakaya, S. Akleylek (2022). “ Quantum secure communication between service provider and SIM”. IEEE Access 10, 69135-69146. https://doi.org/10.1109/ACCESS.2022.3186306.DOI: 10.1109/ACCESS.2022.3186306Google Scholar
  411. M. Salm, J. Barzen, F. Leymann, B. Weder (2022). “Prioritization of compiled quantum circuits for different quantum computers”, in 2022 IEEE International Conference on Software Analysis, Evolution and Reengineering (SANER) pp. 1258-1265. https://doi.org/10.1109/SANER53432.2022.00150.DOI: 10.1109/SANER53432.2022.00150Google Scholar
  412. J. Alvarado-Valiente, J. Romero-Alvarez, D. Arias et al (2023). ”Improving the quality of quantum services generation process: Controlling errors and noise”, in Hybrid Artificial Intelligent Systems Springer, Salamanca, Spain, pp. 180–191. https://doi.org/10.1007/978-3-031-40725-3 16.DOI: 10.1007/978-3-031-40725-3_16Google Scholar
  413. J. Alvarado-Valiente, J. Romero-Alvarez, A. Diaz et al (2023). ”Quantum services generation and deployment process: A quality-oriented approach”, in Quality of Information and Communications Technology Springer, Aveiro, Portugal, pp. 200–214. https://doi.org/10.1007/978-3-031-43703-8 15.DOI: 10.1007/978-3-031-43703-8_15Google Scholar
  414. V. Silva (2018). Practical Quantum Computing for Developers Programming Quantum Rigs in the Cloud Using Python, Quantum Assembly Language and IBM QExperience. Apress, USA.DOI: 10.1007/978-1-4842-4218-6Google Scholar
  415. B. Weder, J. Barzen, F. Leymann et al (2021). “Qprov: A provenance system for quantum computing”. IET Quantum Communication, 2: 4, 171–181. https://doi.org/10.1049/qtc2.12012.DOI: 10.1049/qtc2.12012Google Scholar
  416. B. Weder, J. Barzen, J. F. Leymann, M. Zimmermann (2021). “Hybrid quantum applications need two orchestrations in superposition: A software architecture perspective”, in 2021 IEEE International Conference on Web Services (ICWS) pp. 1–13. https://doi.org/10.1109/ICWS53863.2021.00015.DOI: 10.1109/ICWS53863.2021.00015Google Scholar
  417. S. Imre, L. Gyongyosi (2013). Advanced Quantum Communications: An Engineering Approach. Wiley-IEEE Press, 488 pp. ISBN: 978-1-118-00236-0.Google Scholar
  418. W. Cai, X. Mu, W. Wang et al. (2024). “Protecting entanglement between logical qubits via quantum error correction”. Nature Physics, 20, 1022–1026. https://doi.org/10.1038/s41567-024-02446-8.DOI: 10.1038/s41567-024-02446-8Google Scholar
  419. N. Benchasattabuse, M. Hajdusek and R. Van Meter (2024). “Engineering challenges in all-photonic quantum repeaters”. IEEE Network https://doi.org/10.1109/MNET.2024.3411802.DOI: 10.1109/QCE57702.2023.10259Google Scholar
  420. A. K. Nayak, E. Chitambar, L. R. Varshney (2024). “Reliable quantum memories with unreliable components”. Physical Review A, 110, 032423. https://doi.org/10.1103/PhysRevA.110.032423.DOI: 10.1103/PhysRevA.110.032423Google Scholar
  421. W. Dur, H.J. Briegel (2007). “Entanglement purification and quantum error correction”. Reports on Progress in Physics 70: 8, 1381–1424. DOI: 10.1088/0034-4885/70/8/R03.DOI: 10.1088/0034-4885/70/8/R03Google Scholar
  422. C. Wang, A. Rahman, R. Li, M. Aelmans, K. Chakraborty (2024). “Application Scenarios for the Quantum Internet”. RFC 9583 Internet-Draft https://datatracker.ietf.org/doc/rfc9583/.DOI: 10.17487/RFC9583Google Scholar
  423. D. J. Reilly (2019). “Challenges in scaling-up the control interface of a quantum computer”. Proc. IEEE Int. Electron Devices Meeting (IEDM) pp. 31.7.1–31.7.6. https://doi.org/10.1109/IEDM19573.2019.8993497.DOI: 10.1109/IEDM19573.2019.8993497Google Scholar
  424. A. G. Fowler, M. Mariantoni, J. M. Martinis, and A. N. Cleland (2012). “Surface codes: Towards practical large-scale quantum computation”. Physical Review A 86, 32324. https://doi.org/10.1103/PhysRevA.86.032324.DOI: 10.1103/PhysRevA.86.032324Google Scholar
  425. T. S. Metodi, D. D. Thaker, A. W. Cross et al. “A quantum logic array microarchitecture: scalable quantum data movement and computation” in Proc. 38th Annu. IEEE/ACM Int. Symp. Microarchit. (MICRO) p. 12. https://doi.org/10.1109/MICRO.2005.9DOI: 10.1109/MICRO.2005.9Google Scholar
  426. D. Aharonov, M. Ben-Or (1999). “Fault-tolerant quantum computation with constant error rate”. arXiv:quant-ph/9906129 https://doi.org/10.48550/arXiv.quant-ph/9906129.Google Scholar
  427. Z. Cai, R. Babbush, S. C. Benjamin, S. Endo, W. J. Huggins, Y. Li, J. R. McClean, and T. E. O’Brien (2023). “Quantum error mitigation”. Reviews of Modern Physics 95, 045005. https://link.aps.org/doi/10.1103/RevModPhys.95.045005.DOI: 10.1103/RevModPhys.95.045005Google Scholar
  428. S. M. Attya, S. Q. G. Haddad, H. K. R. Al-Zaidi et al (2024). “Quantum computing impact on traditional computer architecture models”. Radioelectronics. Nanosystems. Information Technologies 16: 5, 691704. http://dx.doi.org/10.17725/j.rensit.2024.16.691.DOI: 10.17725/j.rensit.2024.16.691Google Scholar
  429. S. Muralidharan, L. Li, J. Kim et al (2016). “Optimal architectures for long distance quantum communication”. Scientific Reports, 6, 20463. https://doi.org/10.1038/srep20463.DOI: 10.1038/srep20463Google Scholar
  430. P. Wang, C. Y. Luan, M. Qiao et al. et al (2021). “Single ion qubit with estimated coherence time exceeding one hour”. Nature Communications 12, 233. https://doi.org/10.1038/s41467-020-20330-w.DOI: 10.1038/s41467-020-20330-wGoogle Scholar
  431. Y. Wang, M. Um, J. Zhang et al (2017). “Single-qubit quantum memory exceeding ten-minute coherence time”. Nature Photon 11, 646–650. https://doi.org/10.1038/s41566-017-0007-1.DOI: 10.1038/s41566-017-0007-1Google Scholar
  432. C.E. Bradley, J. Randall, M.H. Abobeih et al (2019). “A ten-qubit solid-state spin register with quantum memory up to one minute”. Physical Review X 9, 031045. https://doi.org/10.1103/PhysRevX.9.031045.DOI: 10.1103/PhysRevX.9.031045Google Scholar
  433. M. H. Abobeih, J. Cramer, M. A. Bakker et al (2018). “One-second coherence for a single electron spin coupled to a multi-qubit nuclear-spin environment”. Nature Communications 9, 2552. https://doi.org/10.1038/s41467-018-04916-z.DOI: 10.1038/s41467-018-04916-zGoogle Scholar
  434. O. Milul, B. Guttel, U. Goldblatt, S. Hazanov et al (2023). “Superconducting cavity qubit with tens of milliseconds single-photon coherence time”. PRX Quantum 4, 030336. https://doi.org/10.1103/PRXQuantum.4.030336.DOI: 10.1103/PRXQuantum.4.030336Google Scholar