{"title":"Correction to “From Quantum Algorithm Primitives to Design Patterns: A Unified Framework for NISQ and Fault-Tolerant Regimes”","authors":"","doi":"10.1002/qute.70388","DOIUrl":null,"url":null,"abstract":"<p>S. Miriyala and V. R. Chirra, “ From Quantum Algorithm Primitives to Design Patterns: A Unified Framework for NISQ and Fault-Tolerant Regimes.” Advanced Quantum Technologies 9, no. 6 (2026): e70310. https://doi.org/10.1002/qute.70310</p><p>Some inadvertent errors were identified in the reference list, affecting certain author names, article titles, and publication details. The corrected reference entries are provided below. These corrections are bibliographic in nature and do not affect the scientific content, interpretation, or conclusions of the article.</p><p>12. A. Gilyén, Y. Su, G. H. Low, and N. Wiebe, “Quantum Singular Value Transformation and Beyond: Exponential Improvements for Quantum Matrix Arithmetics,” <i>arXiv preprint arXiv:1806.01838</i> (2018), https://doi.org/10.48550/arXiv.1806.01838.</p><p>13. S. Chakraborty, A. Gilyén, and S. Jeffery, “The Power of Block-Encoded Matrix Powers: Improved Regression Techniques via Faster Hamiltonian Simulation,” <i>arXiv preprint arXiv:1804.01973</i> (2018), https://doi.org/10.48550/arXiv.1804.01973.</p><p>24. R. Chao, D. Ding, A. Gilyén, C. Huang, and M. Szegedy, “Finding Angles for Quantum Signal Processing with Machine Precision,” <i>arXiv preprint arXiv:2003.02831</i> (2020), https://doi.org/10.48550/arXiv.2003.02831.</p><p>29. S. Kumar, S. Chilkoti, and M. G. Majumdar, “A Symmetry-Based Taxonomy of Quantum Algorithms,” <i>arXiv preprint arXiv:2508.09236</i> (2025), https://doi.org/10.48550/arXiv.2508.09236.</p><p>32. R. Babbush, C. Gidney, D. W. Berry, N. Wiebe, J. McClean, A. Paler, A. Fowler, and H. Neven, “Encoding Electronic Spectra in Quantum Circuits with Linear T Complexity,” <i>Physical Review X</i> 8, no. 4 (2018): 041015, https://doi.org/10.1103/PhysRevX.8.041015.</p><p>35. S. Aaronson, “Shadow Tomography of Quantum States,” in <i>Proceedings of the 50th Annual ACM SIGACT Symposium on Theory of Computing (STOC ’18)</i> (Association for Computing Machinery, New York, NY, USA, 2018), 325–338, https://doi.org/10.1145/3188745.3188802.</p><p>40. L. Lin and Y. Tong, “Heisenberg-Limited Ground-State Energy Estimation for Early Fault-Tolerant Quantum Computers,” <i>PRX Quantum</i> 3, no. 1 (2022): 010318, https://doi.org/10.1103/PRXQuantum.3.010318.</p><p>41. G. H. Low and Y. Su, “Quantum Eigenvalue Processing,” <i>SIAM Journal on Computing</i> 55 (2026): 135–215, https://doi.org/10.1137/24M1689363.</p><p>44. D. E. Koh and S. Grewal, “Classical Shadows with Noise,” <i>Quantum</i> 6 (2022): 776, https://doi.org/10.22331/q-2022-08-16-776.</p><p>45. S. Chen, W. Yu, P. Zeng, and S. T. Flammia, “Robust Shadow Estimation,” <i>PRX Quantum</i> 2, no. 3 (2021): 030348, https://doi.org/10.1103/PRXQuantum.2.030348.</p><p>47. H.-Y. Huang, M. Broughton, J. Cotler, S. Chen, J. Li, M. Mohseni, H. Neven, R. Babbush, R. Kueng, J. Preskill, and J. R. McClean, “Quantum Advantage in Learning from Experiments,” <i>Science</i> 376, no. 6598 (2022): 1182–1186, https://doi.org/10.1126/science.abn7293.</p><p>52. M. Ostaszewski, E. Grant, and M. Benedetti, “Structure Optimization for Parameterized Quantum Circuits,” <i>Quantum</i> 5 (2021): 391, https://doi.org/10.22331/q-2021-01-28-391.</p><p>58. M. Ragone, B. N. Bakalov, F. Sauvage, A. F. Kemper, C. O. Marrero, M. Larocca, and M. Cerezo, “A Lie Algebraic Theory of Barren Plateaus for Deep Parameterized Quantum Circuits,” <i>Nature Communications</i> 15 (2024): 7172, https://doi.org/10.1038/s41467-024-49909-3.</p><p>60. M. Cerezo, M. Larocca, D. García-Martín, et al., “Does Provable Absence of Barren Plateaus Imply Classical Simulability?,” <i>Nature Communications</i> 16 (2025): 7907, https://doi.org/10.1038/s41467-025-63099-6.</p><p>61. Y. Yan, Z. Du, J. Chen, and X. Ma, “Limitations of Noisy Quantum Devices in Computing and Entangling Power,” <i>npj Quantum Information</i> 11 (2025): 188, https://doi.org/10.1038/s41534-025-01136-4.</p><p>66. A. Gilyén, Y. Su, G. H. Low, and N. Wiebe, “Quantum Singular Value Transformation and Beyond: Exponential Improvements for Quantum Matrix Arithmetics,” in <i>Proceedings of the 51st Annual ACM SIGACT Symposium on Theory of Computing (STOC ’19)</i> (Association for Computing Machinery, New York, NY, USA, 2019), 193–204, https://doi.org/10.1145/3313276.3316366.</p><p>67. G. H. Low and I. L. Chuang, “Hamiltonian Simulation by Uniform Spectral Amplification,” <i>arXiv preprint arXiv:1707.05391</i> (2017), https://doi.org/10.48550/arXiv.1707.05391.</p><p>69. M. Reiher, N. Wiebe, K. M. Svore, D. Wecker, and M. Troyer, “Elucidating Reaction Mechanisms on Quantum Computers,” <i>Proceedings of the National Academy of Sciences of the United States of America</i> 114, no. 29 (2017): 7555–7560, https://doi.org/10.1073/pnas.1619152114.</p><p>70. G. E. Crooks, “Performance of the Quantum Approximate Optimization Algorithm on the Maximum Cut Problem,” <i>arXiv preprint arXiv:1811.08419</i> (2018), https://doi.org/10.48550/arXiv.1811.08419.</p><p>71. L. Zhou, S.-T. Wang, S. Choi, H. Pichler, and M. D. Lukin, “Quantum Approximate Optimization Algorithm: Performance, Mechanism, and Implementation on Near-Term Devices,” <i>Physical Review X</i> 10, no. 2 (2020): 021067, https://doi.org/10.1103/PhysRevX.10.021067.</p><p>72. D. J. Egger, J. Mareček, and S. Woerner, “Warm-Starting Quantum Optimization,” <i>Quantum</i> 5 (2021): 479, https://doi.org/10.22331/q-2021-06-17-479.</p><p>73. T. Shirai and N. Togawa, “Compressed Space Quantum Approximate Optimization Algorithm for Constrained Combinatorial Optimization,” <i>arXiv preprint arXiv:2410.05703</i> (2024), https://doi.org/10.48550/arXiv.2410.05703.</p><p>77. J. Liu, A. Zang, M. Suchara, T. Zhong, and P. D. Hovland, “Hardware-Software Co-Design for Distributed Quantum Computing,” <i>arXiv preprint arXiv:2503.18329</i> (2025), https://doi.org/10.48550/arXiv.2503.18329.</p><p>78. J. Ang, G. Carini, Y. Chen, I. Chuang, M. Demarco, S. Economou, A. Eickbusch, A. Faraon, K.-M. Fu, S. Girvin, M. Hatridge, A. Houck, P. Hilaire, K. Krsulich, A. Li, C. Liu, Y. Liu, M. Martonosi, D. McKay, J. Misewich, M. Ritter, R. Schoelkopf, S. Stein, S. Sussman, H. Tang, W. Tang, T. Tomesh, N. M. Tubman, C. Wang, N. Wiebe, Y. Yao, D. Yost, and Y. Zhou, “ARQUIN: Architectures for Multinode Superconducting Quantum Computers,” <i>ACM Transactions on Quantum Computing</i> 5, no. 3 (2024): Article 19, https://doi.org/10.1145/3674151.</p><p>84. Google Quantum AI and Collaborators, “Quantum Error Correction Below the Surface Code Threshold,” <i>Nature</i> 638, no. 8052 (2025): 920–926, https://doi.org/10.1038/s41586-024-08449-y.</p><p>86. E. Rosenberg, T. I. Andersen, R. Samajdar, A. Petukhov, J. C. Hoke, D. Abanin, A. Bengtsson, I. K. Drozdov, C. Erickson, P. V. Klimov, et al., “Dynamics of Magnetization at Infinite Temperature in a Heisenberg Spin Chain,” <i>Science</i> 384, no. 6691 (2024): 48–53, https://doi.org/10.1126/science.adi7877.</p><p>87. G. R. Dahale, “Quantum Simulations for Carbon Capture on Metal-Organic Frameworks,” in <i>2023 IEEE International Conference on Quantum Computing and Engineering (QCE)</i> (IEEE, Bellevue, WA, USA, 2023), 89–93, https://doi.org/10.1109/QCE57702.2023.10189.</p><p>88. R. Babbush, C. Gidney, D. W. Berry, et al., “Encoding Electronic Spectra in Quantum Circuits with Linear T Complexity,” <i>Physical Review X</i> 8, no. 4 (2018): 041015, https://doi.org/10.1103/PhysRevX.8.041015.</p><p>89. A. Caesura, C. L. Cortes, W. Pol, et al., “Faster Quantum Chemistry Simulations on a Quantum Computer with Improved Tensor Factorization and Active Volume Compilation,” <i>arXiv preprint arXiv:2501.06165</i> (2025), https://doi.org/10.48550/arXiv.2501.06165.</p><p>94. P. A. Viana and F. M. de Paula Neto, “A Quantum Genetic Algorithm Framework for the MaxCut Problem,” <i>arXiv preprint arXiv:2501.01058</i> (2025), https://doi.org/10.48550/arXiv.2501.01058.</p><p>97. S. Jin and N. Liu, “Quantum Algorithms for Nonlinear Partial Differential Equations,” <i>Bulletin des Sciences Mathématiques</i> 194 (2024): 103457, https://doi.org/10.1016/j.bulsci.2024.103457.</p><p>100. A. M. Alkadri, T. D. Kharazi, K. B. Whaley, and K. K. Mandadapu, “A Quantum Algorithm for the Finite Element Method,” <i>arXiv preprint arXiv:2510.18150</i> (2025), https://doi.org/10.48550/arXiv.2510.18150.</p><p>106. Google Quantum AI and Collaborators, “Quantum Error Correction Below the Surface Code Threshold,” <i>Nature</i> 638, no. 8052 (2025): 920–926, https://doi.org/10.1038/s41586-024-08449-y.</p><p>111. F. Alam and B. K. Clark, “Learning Dynamic Quantum Circuits for Efficient State Preparation,” <i>arXiv preprint arXiv:2410.09030</i> (2024), https://doi.org/10.48550/arXiv.2410.09030.</p><p>112. K. C. Smith, A. Khan, B. K. Clark, S. M. Girvin, and T.-C. Wei, “Constant-Depth Preparation of Matrix Product States with Adaptive Quantum Circuits,” <i>PRX Quantum</i> 5, no. 3 (2024): 030344, https://doi.org/10.1103/PRXQuantum.5.030344.</p><p>116. T. Hao, J. Sullivan, S. Omanakuttan, M. A. Perlin, and R. Shaydulin, “Compilation Pipeline for Predicting Algorithmic Break-Even in an Early-Fault-Tolerant Surface Code Architecture,” <i>arXiv preprint arXiv:2511.20947</i> (2025), https://doi.org/10.48550/arXiv.2511.20947.</p><p>117. S. Zhu, A. Sundaram, and G. H. Low, “Unified Architecture for Quantum Lookup Tables,” <i>Physical Review Research</i> 7, no. 4 (2025): 043230, https://doi.org/10.1103/d896-mktn.</p><p>136. S. Sivarajah, S. Dilkes, A. Cowtan, W. Simmons, A. Edgington, and R. Duncan, “t|ket⟩: A Retargetable Compiler for NISQ Devices,” <i>Quantum Science and Technology</i> 6, no. 1 (2021): 014003, https://doi.org/10.1088/2058-9565/ab8e92.</p><p>139. F. Hosseinynejad, P. Iyer, G. Dauphinais, and D. Feder, “Realistic Gottesman-Kitaev-Preskill Stabilizer States Enable Universal Quantum Computation,” <i>arXiv preprint arXiv:2511.03874</i> (2025), https://doi.org/10.48550/arXiv.2511.03874.</p><p>142. Y. Li and S. C. Benjamin, “Efficient Variational Quantum Simulator Incorporating Active Error Minimization,” <i>Physical Review X</i> 7, no. 2 (2017): 021050, https://doi.org/10.1103/PhysRevX.7.021050.</p><p>148. S. Abdul Sater and H. Ollivier, “Composable Verification in the Circuit-Model via Magic-Blindness,” <i>arXiv preprint arXiv:2601.07111</i> (2026), https://doi.org/10.48550/arXiv.2601.07111.</p><p>151. S. Lloyd, M. Schuld, A. Ijaz, J. Izaac, and N. Killoran, “Quantum Embeddings for Machine Learning,” <i>arXiv preprint arXiv:2001.03622</i> (2020), https://doi.org/10.48550/arXiv.2001.03622.</p><p>152. M. Schuld, “Supervised Quantum Machine Learning Models Are Kernel Methods,” <i>arXiv preprint arXiv:2101.11020</i> (2021), https://doi.org/10.48550/arXiv.2101.11020.</p><p>154. P.-L. Dallaire-Demers and N. Killoran, “Quantum Generative Adversarial Networks,” <i>Physical Review A</i> 98, no. 1 (2018): 012324, https://doi.org/10.1103/PhysRevA.98.012324.</p><p>157. J. Biamonte, P. Wittek, N. Pancotti, P. Rebentrost, N. Wiebe, and S. Lloyd, “Quantum Machine Learning,” <i>Nature</i> 549, no. 7671 (2017): 195–202, https://doi.org/10.1038/nature23474.</p><p>158. M. Schuld and N. Killoran, “Quantum Machine Learning in Feature Hilbert Spaces,” <i>Physical Review Letters</i> 122, no. 4 (2019): 040504, https://doi.org/10.1103/PhysRevLett.122.040504.</p><p>159. S. Herbst, I. Brandić, and A. Pérez-Salinas, “Limits of Quantum Generative Models with Classical Sampling Hardness,” <i>arXiv preprint arXiv:2512.24801</i> (2025), https://doi.org/10.48550/arXiv.2512.24801.</p><p>162. S. Y.-C. Chen and S. Yoo, “Federated Quantum Machine Learning,” <i>Entropy</i> 23, no. 4 (2021): 460, https://doi.org/10.3390/e23040460.</p><p>167. A. Morvan, B. Villalonga, X. Mi, S. Mandrà, A. Bengtsson, P. V. Klimov, Z. Chen, S. Hong, C. Erickson, I. K. Drozdov, et al., “Phase Transitions in Random Circuit Sampling,” <i>Nature</i> 634, no. 8033 (2024): 328–333, https://doi.org/10.1038/s41586-024-07998-6.</p><p>169. E. Armengol and J. Bowles, “IQPopt: Fast Optimization of Instantaneous Quantum Polynomial Circuits in JAX,” <i>arXiv preprint arXiv:2501.04776</i> (2025), https://doi.org/10.48550/arXiv.2501.04776.</p><p>179. F. F. Flöther, J. Mikolon, and M. Longobardi, “Accelerating the Drive Towards Energy-Efficient Generative AI with Quantum Computing Algorithms,” <i>arXiv preprint arXiv:2508.20720</i> (2025), https://doi.org/10.48550/arXiv.2508.20720.</p><p>181. M. Bertl, A. Mott, S. Sinno, and B. Bhalgamiya, “Quantum Machine Learning in Precision Medicine and Drug Discovery—A Game Changer for Tailored Treatments?,” <i>arXiv preprint arXiv:2502.18639</i> (2025), https://doi.org/10.48550/arXiv.2502.18639.</p><p>185. A. Lerose, T. Parolini, R. Fazio, D. A. Abanin, and S. Pappalardi, “Theory of Robust Quantum Many-Body Scars in Long-Range Interacting Systems,” <i>Physical Review X</i> 15, no. 1 (2025): 011020, https://doi.org/10.1103/PhysRevX.15.011020.</p><p>187. M. J. Cervia, H. Lamm, D. Liu, E. M. Murairi, and S. Zhu, “Magic State Distillation Using Asymptotically Good Codes on Qudits,” <i>arXiv preprint arXiv:2512.21874</i> (2025), https://doi.org/10.48550/arXiv.2512.21874.</p><p>The corresponding in-text citations in which the cited author names required correction are provided below.\n\n </p><p>We apologize for these inadvertent errors.</p>","PeriodicalId":72073,"journal":{"name":"Advanced quantum technologies","volume":"9 8","pages":""},"PeriodicalIF":4.3000,"publicationDate":"2026-08-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/qute.70388","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Advanced quantum technologies","FirstCategoryId":"1085","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1002/qute.70388","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"OPTICS","Score":null,"Total":0}
引用次数: 0
Abstract
S. Miriyala and V. R. Chirra, “ From Quantum Algorithm Primitives to Design Patterns: A Unified Framework for NISQ and Fault-Tolerant Regimes.” Advanced Quantum Technologies 9, no. 6 (2026): e70310. https://doi.org/10.1002/qute.70310
Some inadvertent errors were identified in the reference list, affecting certain author names, article titles, and publication details. The corrected reference entries are provided below. These corrections are bibliographic in nature and do not affect the scientific content, interpretation, or conclusions of the article.
12. A. Gilyén, Y. Su, G. H. Low, and N. Wiebe, “Quantum Singular Value Transformation and Beyond: Exponential Improvements for Quantum Matrix Arithmetics,” arXiv preprint arXiv:1806.01838 (2018), https://doi.org/10.48550/arXiv.1806.01838.
13. S. Chakraborty, A. Gilyén, and S. Jeffery, “The Power of Block-Encoded Matrix Powers: Improved Regression Techniques via Faster Hamiltonian Simulation,” arXiv preprint arXiv:1804.01973 (2018), https://doi.org/10.48550/arXiv.1804.01973.
24. R. Chao, D. Ding, A. Gilyén, C. Huang, and M. Szegedy, “Finding Angles for Quantum Signal Processing with Machine Precision,” arXiv preprint arXiv:2003.02831 (2020), https://doi.org/10.48550/arXiv.2003.02831.
29. S. Kumar, S. Chilkoti, and M. G. Majumdar, “A Symmetry-Based Taxonomy of Quantum Algorithms,” arXiv preprint arXiv:2508.09236 (2025), https://doi.org/10.48550/arXiv.2508.09236.
32. R. Babbush, C. Gidney, D. W. Berry, N. Wiebe, J. McClean, A. Paler, A. Fowler, and H. Neven, “Encoding Electronic Spectra in Quantum Circuits with Linear T Complexity,” Physical Review X 8, no. 4 (2018): 041015, https://doi.org/10.1103/PhysRevX.8.041015.
35. S. Aaronson, “Shadow Tomography of Quantum States,” in Proceedings of the 50th Annual ACM SIGACT Symposium on Theory of Computing (STOC ’18) (Association for Computing Machinery, New York, NY, USA, 2018), 325–338, https://doi.org/10.1145/3188745.3188802.
40. L. Lin and Y. Tong, “Heisenberg-Limited Ground-State Energy Estimation for Early Fault-Tolerant Quantum Computers,” PRX Quantum 3, no. 1 (2022): 010318, https://doi.org/10.1103/PRXQuantum.3.010318.
41. G. H. Low and Y. Su, “Quantum Eigenvalue Processing,” SIAM Journal on Computing 55 (2026): 135–215, https://doi.org/10.1137/24M1689363.
44. D. E. Koh and S. Grewal, “Classical Shadows with Noise,” Quantum 6 (2022): 776, https://doi.org/10.22331/q-2022-08-16-776.
45. S. Chen, W. Yu, P. Zeng, and S. T. Flammia, “Robust Shadow Estimation,” PRX Quantum 2, no. 3 (2021): 030348, https://doi.org/10.1103/PRXQuantum.2.030348.
47. H.-Y. Huang, M. Broughton, J. Cotler, S. Chen, J. Li, M. Mohseni, H. Neven, R. Babbush, R. Kueng, J. Preskill, and J. R. McClean, “Quantum Advantage in Learning from Experiments,” Science 376, no. 6598 (2022): 1182–1186, https://doi.org/10.1126/science.abn7293.
52. M. Ostaszewski, E. Grant, and M. Benedetti, “Structure Optimization for Parameterized Quantum Circuits,” Quantum 5 (2021): 391, https://doi.org/10.22331/q-2021-01-28-391.
58. M. Ragone, B. N. Bakalov, F. Sauvage, A. F. Kemper, C. O. Marrero, M. Larocca, and M. Cerezo, “A Lie Algebraic Theory of Barren Plateaus for Deep Parameterized Quantum Circuits,” Nature Communications 15 (2024): 7172, https://doi.org/10.1038/s41467-024-49909-3.
60. M. Cerezo, M. Larocca, D. García-Martín, et al., “Does Provable Absence of Barren Plateaus Imply Classical Simulability?,” Nature Communications 16 (2025): 7907, https://doi.org/10.1038/s41467-025-63099-6.
61. Y. Yan, Z. Du, J. Chen, and X. Ma, “Limitations of Noisy Quantum Devices in Computing and Entangling Power,” npj Quantum Information 11 (2025): 188, https://doi.org/10.1038/s41534-025-01136-4.
66. A. Gilyén, Y. Su, G. H. Low, and N. Wiebe, “Quantum Singular Value Transformation and Beyond: Exponential Improvements for Quantum Matrix Arithmetics,” in Proceedings of the 51st Annual ACM SIGACT Symposium on Theory of Computing (STOC ’19) (Association for Computing Machinery, New York, NY, USA, 2019), 193–204, https://doi.org/10.1145/3313276.3316366.
67. G. H. Low and I. L. Chuang, “Hamiltonian Simulation by Uniform Spectral Amplification,” arXiv preprint arXiv:1707.05391 (2017), https://doi.org/10.48550/arXiv.1707.05391.
69. M. Reiher, N. Wiebe, K. M. Svore, D. Wecker, and M. Troyer, “Elucidating Reaction Mechanisms on Quantum Computers,” Proceedings of the National Academy of Sciences of the United States of America 114, no. 29 (2017): 7555–7560, https://doi.org/10.1073/pnas.1619152114.
70. G. E. Crooks, “Performance of the Quantum Approximate Optimization Algorithm on the Maximum Cut Problem,” arXiv preprint arXiv:1811.08419 (2018), https://doi.org/10.48550/arXiv.1811.08419.
71. L. Zhou, S.-T. Wang, S. Choi, H. Pichler, and M. D. Lukin, “Quantum Approximate Optimization Algorithm: Performance, Mechanism, and Implementation on Near-Term Devices,” Physical Review X 10, no. 2 (2020): 021067, https://doi.org/10.1103/PhysRevX.10.021067.
72. D. J. Egger, J. Mareček, and S. Woerner, “Warm-Starting Quantum Optimization,” Quantum 5 (2021): 479, https://doi.org/10.22331/q-2021-06-17-479.
73. T. Shirai and N. Togawa, “Compressed Space Quantum Approximate Optimization Algorithm for Constrained Combinatorial Optimization,” arXiv preprint arXiv:2410.05703 (2024), https://doi.org/10.48550/arXiv.2410.05703.
77. J. Liu, A. Zang, M. Suchara, T. Zhong, and P. D. Hovland, “Hardware-Software Co-Design for Distributed Quantum Computing,” arXiv preprint arXiv:2503.18329 (2025), https://doi.org/10.48550/arXiv.2503.18329.
78. J. Ang, G. Carini, Y. Chen, I. Chuang, M. Demarco, S. Economou, A. Eickbusch, A. Faraon, K.-M. Fu, S. Girvin, M. Hatridge, A. Houck, P. Hilaire, K. Krsulich, A. Li, C. Liu, Y. Liu, M. Martonosi, D. McKay, J. Misewich, M. Ritter, R. Schoelkopf, S. Stein, S. Sussman, H. Tang, W. Tang, T. Tomesh, N. M. Tubman, C. Wang, N. Wiebe, Y. Yao, D. Yost, and Y. Zhou, “ARQUIN: Architectures for Multinode Superconducting Quantum Computers,” ACM Transactions on Quantum Computing 5, no. 3 (2024): Article 19, https://doi.org/10.1145/3674151.
84. Google Quantum AI and Collaborators, “Quantum Error Correction Below the Surface Code Threshold,” Nature 638, no. 8052 (2025): 920–926, https://doi.org/10.1038/s41586-024-08449-y.
86. E. Rosenberg, T. I. Andersen, R. Samajdar, A. Petukhov, J. C. Hoke, D. Abanin, A. Bengtsson, I. K. Drozdov, C. Erickson, P. V. Klimov, et al., “Dynamics of Magnetization at Infinite Temperature in a Heisenberg Spin Chain,” Science 384, no. 6691 (2024): 48–53, https://doi.org/10.1126/science.adi7877.
87. G. R. Dahale, “Quantum Simulations for Carbon Capture on Metal-Organic Frameworks,” in 2023 IEEE International Conference on Quantum Computing and Engineering (QCE) (IEEE, Bellevue, WA, USA, 2023), 89–93, https://doi.org/10.1109/QCE57702.2023.10189.
88. R. Babbush, C. Gidney, D. W. Berry, et al., “Encoding Electronic Spectra in Quantum Circuits with Linear T Complexity,” Physical Review X 8, no. 4 (2018): 041015, https://doi.org/10.1103/PhysRevX.8.041015.
89. A. Caesura, C. L. Cortes, W. Pol, et al., “Faster Quantum Chemistry Simulations on a Quantum Computer with Improved Tensor Factorization and Active Volume Compilation,” arXiv preprint arXiv:2501.06165 (2025), https://doi.org/10.48550/arXiv.2501.06165.
94. P. A. Viana and F. M. de Paula Neto, “A Quantum Genetic Algorithm Framework for the MaxCut Problem,” arXiv preprint arXiv:2501.01058 (2025), https://doi.org/10.48550/arXiv.2501.01058.
97. S. Jin and N. Liu, “Quantum Algorithms for Nonlinear Partial Differential Equations,” Bulletin des Sciences Mathématiques 194 (2024): 103457, https://doi.org/10.1016/j.bulsci.2024.103457.
100. A. M. Alkadri, T. D. Kharazi, K. B. Whaley, and K. K. Mandadapu, “A Quantum Algorithm for the Finite Element Method,” arXiv preprint arXiv:2510.18150 (2025), https://doi.org/10.48550/arXiv.2510.18150.
106. Google Quantum AI and Collaborators, “Quantum Error Correction Below the Surface Code Threshold,” Nature 638, no. 8052 (2025): 920–926, https://doi.org/10.1038/s41586-024-08449-y.
111. F. Alam and B. K. Clark, “Learning Dynamic Quantum Circuits for Efficient State Preparation,” arXiv preprint arXiv:2410.09030 (2024), https://doi.org/10.48550/arXiv.2410.09030.
112. K. C. Smith, A. Khan, B. K. Clark, S. M. Girvin, and T.-C. Wei, “Constant-Depth Preparation of Matrix Product States with Adaptive Quantum Circuits,” PRX Quantum 5, no. 3 (2024): 030344, https://doi.org/10.1103/PRXQuantum.5.030344.
116. T. Hao, J. Sullivan, S. Omanakuttan, M. A. Perlin, and R. Shaydulin, “Compilation Pipeline for Predicting Algorithmic Break-Even in an Early-Fault-Tolerant Surface Code Architecture,” arXiv preprint arXiv:2511.20947 (2025), https://doi.org/10.48550/arXiv.2511.20947.
117. S. Zhu, A. Sundaram, and G. H. Low, “Unified Architecture for Quantum Lookup Tables,” Physical Review Research 7, no. 4 (2025): 043230, https://doi.org/10.1103/d896-mktn.
136. S. Sivarajah, S. Dilkes, A. Cowtan, W. Simmons, A. Edgington, and R. Duncan, “t|ket⟩: A Retargetable Compiler for NISQ Devices,” Quantum Science and Technology 6, no. 1 (2021): 014003, https://doi.org/10.1088/2058-9565/ab8e92.
139. F. Hosseinynejad, P. Iyer, G. Dauphinais, and D. Feder, “Realistic Gottesman-Kitaev-Preskill Stabilizer States Enable Universal Quantum Computation,” arXiv preprint arXiv:2511.03874 (2025), https://doi.org/10.48550/arXiv.2511.03874.
142. Y. Li and S. C. Benjamin, “Efficient Variational Quantum Simulator Incorporating Active Error Minimization,” Physical Review X 7, no. 2 (2017): 021050, https://doi.org/10.1103/PhysRevX.7.021050.
148. S. Abdul Sater and H. Ollivier, “Composable Verification in the Circuit-Model via Magic-Blindness,” arXiv preprint arXiv:2601.07111 (2026), https://doi.org/10.48550/arXiv.2601.07111.
151. S. Lloyd, M. Schuld, A. Ijaz, J. Izaac, and N. Killoran, “Quantum Embeddings for Machine Learning,” arXiv preprint arXiv:2001.03622 (2020), https://doi.org/10.48550/arXiv.2001.03622.
152. M. Schuld, “Supervised Quantum Machine Learning Models Are Kernel Methods,” arXiv preprint arXiv:2101.11020 (2021), https://doi.org/10.48550/arXiv.2101.11020.
154. P.-L. Dallaire-Demers and N. Killoran, “Quantum Generative Adversarial Networks,” Physical Review A 98, no. 1 (2018): 012324, https://doi.org/10.1103/PhysRevA.98.012324.
157. J. Biamonte, P. Wittek, N. Pancotti, P. Rebentrost, N. Wiebe, and S. Lloyd, “Quantum Machine Learning,” Nature 549, no. 7671 (2017): 195–202, https://doi.org/10.1038/nature23474.
158. M. Schuld and N. Killoran, “Quantum Machine Learning in Feature Hilbert Spaces,” Physical Review Letters 122, no. 4 (2019): 040504, https://doi.org/10.1103/PhysRevLett.122.040504.
159. S. Herbst, I. Brandić, and A. Pérez-Salinas, “Limits of Quantum Generative Models with Classical Sampling Hardness,” arXiv preprint arXiv:2512.24801 (2025), https://doi.org/10.48550/arXiv.2512.24801.
162. S. Y.-C. Chen and S. Yoo, “Federated Quantum Machine Learning,” Entropy 23, no. 4 (2021): 460, https://doi.org/10.3390/e23040460.
167. A. Morvan, B. Villalonga, X. Mi, S. Mandrà, A. Bengtsson, P. V. Klimov, Z. Chen, S. Hong, C. Erickson, I. K. Drozdov, et al., “Phase Transitions in Random Circuit Sampling,” Nature 634, no. 8033 (2024): 328–333, https://doi.org/10.1038/s41586-024-07998-6.
169. E. Armengol and J. Bowles, “IQPopt: Fast Optimization of Instantaneous Quantum Polynomial Circuits in JAX,” arXiv preprint arXiv:2501.04776 (2025), https://doi.org/10.48550/arXiv.2501.04776.
179. F. F. Flöther, J. Mikolon, and M. Longobardi, “Accelerating the Drive Towards Energy-Efficient Generative AI with Quantum Computing Algorithms,” arXiv preprint arXiv:2508.20720 (2025), https://doi.org/10.48550/arXiv.2508.20720.
181. M. Bertl, A. Mott, S. Sinno, and B. Bhalgamiya, “Quantum Machine Learning in Precision Medicine and Drug Discovery—A Game Changer for Tailored Treatments?,” arXiv preprint arXiv:2502.18639 (2025), https://doi.org/10.48550/arXiv.2502.18639.
185. A. Lerose, T. Parolini, R. Fazio, D. A. Abanin, and S. Pappalardi, “Theory of Robust Quantum Many-Body Scars in Long-Range Interacting Systems,” Physical Review X 15, no. 1 (2025): 011020, https://doi.org/10.1103/PhysRevX.15.011020.
187. M. J. Cervia, H. Lamm, D. Liu, E. M. Murairi, and S. Zhu, “Magic State Distillation Using Asymptotically Good Codes on Qudits,” arXiv preprint arXiv:2512.21874 (2025), https://doi.org/10.48550/arXiv.2512.21874.
The corresponding in-text citations in which the cited author names required correction are provided below.
S. Miriyala和V. R. Chirra，“从量子算法原语到设计模式：NISQ和容错机制的统一框架”。《先进量子技术》第9期。6 (2026): e70310。https://doi.org/10.1002/qute.70310Some在参考文献列表中发现了无意的错误，影响了某些作者姓名、文章标题和出版细节。更正后的参考分录如下。这些更正是书目性质的，不影响第12条的科学内容、解释或结论。A. gily<s:1>， Y. Su， G. H. Low， N. Wiebe，“量子奇异值变换及其超越：量子矩阵算法的指数改进”，《量子学报》，预印版，2018,https://doi.org/10.48550/arXiv.1806.01838.13。S. Chakraborty， A. gily<s:1>，和S. Jeffery，“块编码矩阵功率的力量：通过更快的哈密顿模拟改进的回归技术，”arXiv预印本arXiv:1804.01973 (2018), https://doi.org/10.48550/arXiv.1804.01973.24。赵R.，丁D.， A. gily<s:1>，黄C.， M. Szegedy，“基于机器精度的量子信号处理角度研究”，中国机械工程学报，2003.02831 (2020),https://doi.org/10.48550/arXiv.2003.02831.29。S. Kumar， S. Chilkoti， M. G. Majumdar，“一种基于对称的量子算法分类”，《量子算法学报》，预印本，第2期：2508.09236 (2025),https://doi.org/10.48550/arXiv.2508.09236.32。R. Babbush， C. Gidney， D. W. Berry， N. Wiebe， J. McClean， A. Paler， A. Fowler，和H. Neven，“在线性T复杂度的量子电路中编码电子光谱”，《物理评论》第8期。4 (2018): 041015, https://doi.org/10.1103/PhysRevX.8.041015.35。S. Aaronson，“量子态的阴影层析成像”，第50届ACM SIGACT计算理论研讨会论文集（美国计算机协会，纽约，纽约，美国，2018），325-338,https://doi.org/10.1145/3188745.3188802.40。林林和佟勇，“早期容错量子计算机的海森堡有限基态能量估计”，量子力学，第3期。1 (2022): 010318, https://doi.org/10.1103/PRXQuantum.3.010318.41。Low g.h.和Su Y.，“量子特征值处理”，计算学报55 (2026):135-215,https://doi.org/10.1137/24M1689363.44。D. E. Koh和S. Grewal，“带噪声的经典阴影”，量子6 (2022):776,https://doi.org/10.22331/q-2022-08-16-776.45。陈士林，余文伟，曾培平，“鲁棒阴影估计”，电子学报，第2期。3 (2021): 030348, https://doi.org/10.1103/PRXQuantum.2.030348.47。H.-Y。黄，M. Broughton， J. Cotler， S. Chen， J. Li， M. Mohseni， H. Neven， R. Babbush， R. Kueng， J. Preskill， J. R. McClean，“从实验中学习的量子优势”，《科学》第376期。6598 (2022): 1182-1186, https://doi.org/10.1126/science.abn7293.52。M. Ostaszewski， E. Grant和M. Benedetti，“参数化量子电路的结构优化”，量子5 (2021):391,https://doi.org/10.22331/q-2021-01-28-391.58。M. Ragone， B. N. Bakalov， F. Sauvage， A. F. Kemper， C. O. Marrero， M. Larocca， M. Cerezo，“贫瘠高原深度参数化量子电路的李代数理论”，自然通信15 (2024):7172,https://doi.org/10.1038/s41467-024-49909-3.60。M. Cerezo， M. Larocca， D. García-Martín等，“可证明的无荒芜高原是否意味着经典的可模拟性？”，《自然通讯》16 (2025):7907,https://doi.org/10.1038/s41467-025-63099-6.61。闫勇，杜正杰，陈建军，马晓霞，“噪声量子器件在计算和纠缠功率中的局限性”，量子信息学报，2025，第11期：188，https://doi.org/10.1038/s41534-025-01136-4.66。A. gily<s:1>， Y. Su， G. H. Low， N. Wiebe，“量子奇异值变换及其超越：量子矩阵算法的指数改进”，第51届ACM SIGACT计算理论研讨会论文集（STOC ' 19）（计算机械协会，纽约，美国，2019），193-204,https://doi.org/10.1145/3313276.3316366.67。Low . H.和chui . L.，“均匀光谱放大的哈密顿模拟”，中国科学院学报（自然科学版），1707.05391 (2017),https://doi.org/10.48550/arXiv.1707.05391.69。M. Reiher， N. Wiebe， K. M. Svore， D. Wecker和M. Troyer，“阐明量子计算机上的反应机制”，《美国国家科学院院刊》114，第114期。29 (2017): 7555-7560, https://doi.org/10.1073/pnas.1619152114.70。G. E. Crooks，“量子近似优化算法在最大割问题上的性能”，中国机械工程学报，1811.08419 (2018),https://doi.org/10.48550/arXiv.1811.08419.71。周磊，s.t。Wang， S. Choi， H. Pichler， M. D. Lukin，“量子近似优化算法：性能、机制和在近期设备上的实现”，物理评论，第10期。2 (2020): 021067, https://doi.org/10.1103/PhysRevX.10.021067.72。D. J. Egger， J. mare<e:1> ek和S。 Woerner，“暖启动量子优化”，量子5 (2021):479,https://doi.org/10.22331/q-2021-06-17-479.73。T. Shirai和N. Togawa，“约束组合优化的压缩空间量子近似优化算法，”arXiv预印本arXiv:2410.05703 (2024), https://doi.org/10.48550/arXiv.2410.05703.77。刘杰，张安，M. Suchara，钟涛，P. D. Hovland，“分布式量子计算的软硬件协同设计”，中国计算机学报，第25卷第1期：253.18329 (2025),https://doi.org/10.48550/arXiv.2503.18329.78。J. Ang， G. Carini， Y. Chen， I. Chuang， M. Demarco， S. Economou， A. Eickbusch， A. Faraon, k - m。Fu， S. Girvin， M. Hatridge， A. Houck， P. Hilaire， K. Krsulich， A. Li， C. Liu， Y. Liu， M. Martonosi， D. McKay， J. Misewich， M. Ritter， R. Schoelkopf， S. Stein， S. Sussman， H. Tang， W. Tang， T. Tomesh， N. M. Tubman， C. Wang， N. Wiebe， Y. Yao， D. Yost，和Y. Zhou，“ARQUIN：多节点超导量子计算机的架构”，ACM量子计算学报，第5期，no。3(2024)：第19条https://doi.org/10.1145/3674151.84。谷歌量子人工智能和合作者，“表面代码阈值以下的量子纠错”，《自然》638，第6期。8052 (2025): 920-926, https://doi.org/10.1038/s41586-024-08449-y.86。E. Rosenberg， T. I. Andersen， R. Samajdar, a . Petukhov， J. C. Hoke， D. Abanin, a . Bengtsson， I. K. Drozdov， C. Erickson， P. V. Klimov等，“海森堡自旋链在无限温度下的磁化动力学”，《科学》第384期。6691 (2024): 48-53, https://doi.org/10.1126/science.adi7877.87。G. R. Dahale，“金属有机框架上碳捕获的量子模拟”，2023年IEEE量子计算与工程国际会议（QCE） （IEEE, Bellevue， WA， USA, 2023）， 89-93, https://doi.org/10.1109/QCE57702.2023.10189.88。R. Babbush， C. Gidney， D. W. Berry等，“在线性T复杂度的量子电路中编码电子光谱”，《物理评论》第8期。4 (2018): 041015, https://doi.org/10.1103/PhysRevX.8.041015.89。a . Caesura， C. L. Cortes， W. Pol，等，“基于改进张量分解和主动卷编译的量子计算机上更快的量子化学模拟”，arXiv预印本arXiv:2501.06165 (2025), https://doi.org/10.48550/arXiv.2501.06165.94。P. A. Viana和F. M. de Paula Neto，“MaxCut问题的量子遗传算法框架”，arXiv预印arXiv:2501.01058 (2025), https://doi.org/10.48550/arXiv.2501.01058.97。金生、刘宁，“非线性偏微分方程的量子算法”，数学学报，1994 (4):103457,https://doi.org/10.1016/j.bulsci.2024.103457.100。A. M. Alkadri， T. D. Kharazi， K. B. Whaley， K. K. Mandadapu，“有限元方法的量子算法”，中国机械工程学报，预印版，第2卷第1期：2510.18150 (2025),https://doi.org/10.48550/arXiv.2510.18150.106。谷歌量子人工智能和合作者，“表面代码阈值以下的量子纠错”，《自然》638，第6期。8052 (2025): 920-926, https://doi.org/10.1038/s41586-024-08449-y.111。F. Alam和B. K. Clark，“学习动态量子电路的高效状态制备”，arXiv预印arXiv:2410.09030 (2024), https://doi.org/10.48550/arXiv.2410.09030.112。k·c·史密斯，a·汗，b·k·克拉克，s·m·吉文，t·c·c。魏，“基于自适应量子电路的矩阵积态的恒深度制备”，《量子学报》，第5期。3 (2024): 030344, https://doi.org/10.1103/PRXQuantum.5.030344.116。郝T.， J. Sullivan， S. Omanakuttan， M. A. Perlin， R. Shaydulin，“早期容错表面代码体系结构中预测算法保本的编译管道”，《计算机工程学报》，第25卷第1期，2047 (2025),https://doi.org/10.48550/arXiv.2511.20947.117。S. Zhu， A. Sundaram和G. H. Low，“量子查找表的统一架构”，物理评论研究，第7期。4 (2025): 043230, https://doi.org/10.1103/d896-mktn.136。S. Sivarajah， S. Dilkes， A. Cowtan， W. Simmons， A. Edgington，和R. Duncan，“t|ket⟩：NISQ设备的可重目标编译器”，量子科学与技术6，第6期。1 (2021): 014003, https://doi.org/10.1088/2058-9565/ab8e92.139。F. Hosseinynejad， P. Iyer， G. Dauphinais和D. Feder，“现实的Gottesman-Kitaev-Preskill稳定状态使通用量子计算成为可能，”arXiv预印版arXiv:2511.03874 (2025), https://doi.org/10.48550/arXiv.2511.03874.142。李阳和S. C. Benjamin，“基于主动误差最小化的高效变分量子模拟器”，《物理评论》，第7期。2 (2017): 021050, https://doi.org/10.1103/PhysRevX.7.021050.148。S. Abdul Sater和H. Ollivier，“基于Magic-Blindness的电路模型的可组合验证”，arXiv预印版arXiv:2601.07111 (2026), https://doi.org/10.48550/arXiv.2601.07111.151。S. Lloyd， M. Schuld， A. Ijaz， J. Izaac， N. Killoran，“机器学习中的量子嵌入”，arXiv预印本arXiv:2001.03622 (2020), https://doi.org/10.48550/arXiv.2001.03622.152。M。 Schuld，“监督量子机器学习模型是核心方法”，arXiv预印本arXiv:2101.11020 (2021), https://doi.org/10.48550/arXiv.2101.11020.154。p.l.。Dallaire-Demers和N. Killoran，“量子生成对抗网络”，《物理评论》第98期。1 (2018): 012324, https://doi.org/10.1103/PhysRevA.98.012324.157。J. Biamonte， P. Wittek， N. Pancotti， P. Rebentrost， N. Wiebe和S. Lloyd，“量子机器学习”，《自然》549，第5期。7671 (2017): 195-202, https://doi.org/10.1038/nature23474.158。M. Schuld和N. Killoran，“特征希尔伯特空间中的量子机器学习”，《物理评论快报》，第122期。4 (2019): 040504, https://doi.org/10.1103/PhysRevLett.122.040504.159。S. Herbst， I. brandiki， A. psamrez - salinas，“具有经典采样硬度的量子生成模型的极限”，arXiv预印arXiv:2512.24801 (2025), https://doi.org/10.48550/arXiv.2512.24801.162。美国研究。Chen和S. Yoo，“联合量子机器学习”，《熵》23期，no。4 (2021): 460, https://doi.org/10.3390/e23040460.167。A. Morvan， B. Villalonga， X. Mi， S. mandr<e:1>， A. Bengtsson， P. V. Klimov，陈正忠，S. Hong， C. Erickson， I. K. Drozdov，等，“随机电路采样中的相变”，《自然》，第634期。8033 (2024): 328-333, https://doi.org/10.1038/s41586-024-07998-6.169。E. Armengol， J. Bowles，“IQPopt：基于JAX的瞬时量子多项式电路的快速优化”，电子学报，第1卷第2期，https://doi.org/10.48550/arXiv.2501.04776.179。F. F. Flöther， J. Mikolon， M. Longobardi，“利用量子计算算法加速推动节能生成人工智能，”arXiv预印arXiv:2508.20720 (2025), https://doi.org/10.48550/arXiv.2508.20720.181。M. Bertl， A. Mott， S. Sinno和B. Bhalgamiya，“精准医学和药物发现中的量子机器学习-量身定制治疗的游戏规则改变者？”， [j] . arXiv预印本arXiv:2502.18639 (2025), https://doi.org/10.48550/arXiv.2502.18639.185。A. Lerose， T. Parolini， R. Fazio， D. A. Abanin， S. Pappalardi，“远程相互作用系统中鲁棒量子多体伤痕理论”，《物理评论》，第15期。1 (2025): 011020, https://doi.org/10.1103/PhysRevX.15.011020.187。M. J. Cervia， H. Lamm， D. Liu， E. M. Murairi， S. Zhu，“在Qudits上使用渐近好码的神奇状态蒸馏”，arXiv预印本arXiv:2512.21874 (2025), https://doi.org/10.48550/arXiv.2512.21874.The我们为这些无心的错误道歉。
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