Modeling Short-Range Microwave Networks to Scale Superconducting Quantum Computation

Nicholas LaRacuente1, Kaitlin N. Smith2, Poolad Imany3, Kevin L. Silverman4, and Frederic T. Chong5

1Indiana University Bloomington, Bloomington, IN 47404, USA
2Northwestern University, Evanston, IL 60208, USA
3Icarus Quantum Inc., Boulder, CO 80302, USA
4National Institute of Standards and Technology, Boulder, CO 80305, USA
5University of Chicago, Chicago, IL 60642, USA

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Abstract

A core challenge for superconducting quantum computers is to scale up the number of qubits in each processor without increasing noise or cross-talk. Distributed quantum computing across small qubit arrays, known as chiplets, can address these challenges in a scalable manner. We propose a chiplet architecture over microwave links with potential to exceed monolithic performance on near-term hardware. Our methods of modeling and evaluating the chiplet architecture bridge the physical and network layers in these processors. We find evidence that distributing computation across chiplets may reduce the overall error rates associated with moving data across the device, despite higher error figures for transfers across links. Preliminary analyses suggest that latency is not substantially impacted, and that at least some applications and architectures may avoid bottlenecks around chiplet boundaries. In the long-term, short-range networks may underlie quantum computers just as local area networks underlie classical datacenters and supercomputers today.

For quantum computers to reach their full potential, a primary challenge is to scale up the number of qubits without also increasing noise and unwanted crosstalk. In this work, we explore and evaluate the possibility to split a superconducting quantum processor into smaller chiplets, connected by high-fidelity, low-latency microwave links. Both conventional multicore processors and high-performance distributed systems use analogous architectures. Our methods bridge from modeling the physical hardware to evaluating architectures at the more abstracted network layer. Results show a tradeoff between higher errors to transmit data over cross-chiplet links and lower on-chip errors from smaller chips. Chiplet architectures enable larger quantum computers to maintain low error rates per operation as they scale, paving the way for large-scale yet low-noise quantum processors.

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► References

[1] Peter W Shor. ``Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer''. SIAM review 41, 303–332 (1999).
https:/​/​doi.org/​10.1137/​s0097539795293172

[2] Edward Farhi, Jeffrey Goldstone, and Sam Gutmann. ``A Quantum Approximate Optimization Algorithm'' (2014). arXiv:1411.4028. DOI: 10.48550/​arXiv.1411.4028.
https:/​/​doi.org/​10.48550/​arXiv.1411.4028
arXiv:1411.4028

[3] Abhinav Kandala, Antonio Mezzacapo, Kristan Temme, Maika Takita, Markus Brink, Jerry M Chow, and Jay M Gambetta. ``Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets''. Nature 549, 242–246 (2017).
https:/​/​doi.org/​10.1038/​nature23879

[4] Michael A. Nielsen and Isaac L. Chuang. ``Quantum Computation and Quantum Information: 10th Anniversary Edition''. Cambridge University Press. (2010). 1 edition.
https:/​/​doi.org/​10.1017/​CBO9780511976667

[5] M. H. Devoret, A. Wallraff, and J. M. Martinis. ``Superconducting Qubits: A Short Review'' (2004). arXiv:cond-mat/​0411174. DOI: 10.48550/​ARXIV.COND-MAT/​0411174.
https:/​/​doi.org/​10.48550/​arXiv.cond-mat/​0411174
arXiv:cond-mat/0411174

[6] G Wendin. ``Quantum information processing with superconducting circuits: a review''. Reports on Progress in Physics 80, 106001 (2017).
https:/​/​doi.org/​10.1088/​1361-6633/​aa7e1a

[7] Morten Kjaergaard, Mollie E. Schwartz, Jochen Braumüller, Philip Krantz, Joel I.-J. Wang, Simon Gustavsson, and William D. Oliver. ``Superconducting Qubits: Current State of Play''. Annual Review of Condensed Matter Physics 11, 369–395 (2020).
https:/​/​doi.org/​10.1146/​annurev-conmatphys-031119-050605

[8] Frank Arute, Kunal Arya, Ryan Babbush, Dave Bacon, Joseph C Bardin, Rami Barends, Rupak Biswas, Sergio Boixo, Fernando GSL Brandão, David A Buell, et al. ``Quantum supremacy using a programmable superconducting processor''. Nature 574, 505–510 (2019).
https:/​/​doi.org/​10.1038/​s41586-019-1666-5

[9] Yulin Wu, Wan-Su Bao, Sirui Cao, Fusheng Chen, Ming-Cheng Chen, Xiawei Chen, Tung-Hsun Chung, Hui Deng, Yajie Du, Daojin Fan, et al. ``Strong quantum computational advantage using a superconducting quantum processor''. Physical review letters 127, 180501 (2021).
https:/​/​doi.org/​10.1103/​PhysRevLett.127.180501

[10] Han-Sen Zhong, Hui Wang, Yu-Hao Deng, Ming-Cheng Chen, Li-Chao Peng, Yi-Han Luo, Jian Qin, Dian Wu, Xing Ding, Yi Hu, et al. ``Quantum computational advantage using photons''. Science 370, 1460–1463 (2020).
https:/​/​doi.org/​10.1126/​science.abe8770

[11] Google Quantum AI. ``Suppressing quantum errors by scaling a surface code logical qubit''. Nature 614, 676–681 (2023).
https:/​/​doi.org/​10.1038/​s41586-022-05434-1

[12] Rajeev Acharya, Dmitry A. Abanin, Laleh Aghababaie-Beni, Igor Aleiner, Trond I. Andersen, Markus Ansmann, Frank Arute, Kunal Arya, Abraham Asfaw, Nikita Astrakhantsev, Juan Atalaya, Ryan Babbush, Dave Bacon, Brian Ballard, Joseph C. Bardin, Johannes Bausch, Andreas Bengtsson, Alexander Bilmes, Sam Blackwell, Sergio Boixo, Gina Bortoli, Alexandre Bourassa, Jenna Bovaird, Leon Brill, Michael Broughton, David A. Browne, Brett Buchea, Bob B. Buckley, David A. Buell, Tim Burger, Brian Burkett, Nicholas Bushnell, Anthony Cabrera, Juan Campero, Hung-Shen Chang, Yu Chen, Zijun Chen, Ben Chiaro, Desmond Chik, Charina Chou, Jahan Claes, Agnetta Y. Cleland, Josh Cogan, Roberto Collins, Paul Conner, William Courtney, Alexander L. Crook, Ben Curtin, Sayan Das, Alex Davies, Laura De Lorenzo, Dripto M. Debroy, Sean Demura, Michel Devoret, Agustin Di Paolo, Paul Donohoe, Ilya Drozdov, Andrew Dunsworth, Clint Earle, Thomas Edlich, Alec Eickbusch, Aviv Moshe Elbag, Mahmoud Elzouka, Catherine Erickson, Lara Faoro, Edward Farhi, Vinicius S. Ferreira, Leslie Flores Burgos, Ebrahim Forati, Austin G. Fowler, Brooks Foxen, Suhas Ganjam, Gonzalo Garcia, Robert Gasca, Élie Genois, William Giang, Craig Gidney, Dar Gilboa, Raja Gosula, Alejandro Grajales Dau, Dietrich Graumann, Alex Greene, Jonathan A. Gross, Steve Habegger, John Hall, Michael C. Hamilton, Monica Hansen, Matthew P. Harrigan, Sean D. Harrington, Francisco J. H. Heras, Stephen Heslin, Paula Heu, Oscar Higgott, Gordon Hill, Jeremy Hilton, George Holland, Sabrina Hong, Hsin-Yuan Huang, Ashley Huff, William J. Huggins, Lev B. Ioffe, Sergei V. Isakov, Justin Iveland, Evan Jeffrey, Zhang Jiang, Cody Jones, Stephen Jordan, Chaitali Joshi, Pavol Juhas, Dvir Kafri, Hui Kang, Amir H. Karamlou, Kostyantyn Kechedzhi, Julian Kelly, Trupti Khaire, Tanuj Khattar, Mostafa Khezri, Seon Kim, Paul V. Klimov, Andrey R. Klots, Bryce Kobrin, Pushmeet Kohli, Alexander N. Korotkov, Fedor Kostritsa, Robin Kothari, Borislav Kozlovskii, John Mark Kreikebaum, Vladislav D. Kurilovich, Nathan Lacroix, David Landhuis, Tiano Lange-Dei, Brandon W. Langley, Pavel Laptev, Kim-Ming Lau, Loïck Le Guevel, Justin Ledford, Joonho Lee, Kenny Lee, Yuri D. Lensky, Shannon Leon, Brian J. Lester, Wing Yan Li, Yin Li, Alexander T. Lill, Wayne Liu, William P. Livingston, Aditya Locharla, Erik Lucero, Daniel Lundahl, Aaron Lunt, Sid Madhuk, Fionn D. Malone, Ashley Maloney, Salvatore Mandrà, James Manyika, Leigh S. Martin, Orion Martin, Steven Martin, Cameron Maxfield, Jarrod R. McClean, Matt McEwen, Seneca Meeks, Anthony Megrant, Xiao Mi, Kevin C. Miao, Amanda Mieszala, Reza Molavi, Sebastian Molina, Shirin Montazeri, Alexis Morvan, Ramis Movassagh, Wojciech Mruczkiewicz, Ofer Naaman, Matthew Neeley, Charles Neill, Ani Nersisyan, Hartmut Neven, Michael Newman, Jiun How Ng, Anthony Nguyen, Murray Nguyen, Chia-Hung Ni, Murphy Yuezhen Niu, Thomas E. O’Brien, William D. Oliver, Alex Opremcak, Kristoffer Ottosson, Andre Petukhov, Alex Pizzuto, John Platt, Rebecca Potter, Orion Pritchard, Leonid P. Pryadko, Chris Quintana, Ganesh Ramachandran, Matthew J. Reagor, John Redding, David M. Rhodes, Gabrielle Roberts, Eliott Rosenberg, Emma Rosenfeld, Pedram Roushan, Nicholas C. Rubin, Negar Saei, Daniel Sank, Kannan Sankaragomathi, Kevin J. Satzinger, Henry F. Schurkus, Christopher Schuster, Andrew W. Senior, Michael J. Shearn, Aaron Shorter, Noah Shutty, Vladimir Shvarts, Shraddha Singh, Volodymyr Sivak, Jindra Skruzny, Spencer Small, Vadim Smelyanskiy, W. Clarke Smith, Rolando D. Somma, Sofia Springer, George Sterling, Doug Strain, Jordan Suchard, Aaron Szasz, Alex Sztein, Douglas Thor, Alfredo Torres, M. Mert Torunbalci, Abeer Vaishnav, Justin Vargas, Sergey Vdovichev, Guifre Vidal, Benjamin Villalonga, Catherine Vollgraff Heidweiller, Steven Waltman, Shannon X. Wang, Brayden Ware, Kate Weber, Travis Weidel, Theodore White, Kristi Wong, Bryan W. K. Woo, Cheng Xing, Z. Jamie Yao, Ping Yeh, Bicheng Ying, Juhwan Yoo, Noureldin Yosri, Grayson Young, Adam Zalcman, Yaxing Zhang, Ningfeng Zhu, Nicholas Zobrist, and Google Quantum AI and Collaborators. ``Quantum error correction below the surface code threshold''. NaturePages 1–3 (2024).
https:/​/​doi.org/​10.1038/​s41586-024-08449-y

[13] John Preskill. ``Quantum computing in the nisq era and beyond''. Quantum 2, 79 (2018).
https:/​/​doi.org/​10.22331/​q-2018-08-06-79

[14] Kaitlin N Smith and Mitchell A Thornton. ``A quantum computational compiler and design tool for technology-specific targets''. In Proceedings of the 46th International Symposium on Computer Architecture. Pages 579–588. (2019).
https:/​/​doi.org/​10.1145/​3307650.3322262

[15] Jaime Sevilla and C. Jess Riedel. ``Forecasting timelines of quantum computing'' (2020). arXiv:2009.05045. DOI: 10.48550/​arXiv.2009.05045.
https:/​/​doi.org/​10.48550/​arXiv.2009.05045
arXiv:2009.05045

[16] Sergey Bravyi, David Gosset, Robert König, and Marco Tomamichel. ``Quantum advantage with noisy shallow circuits''. Nature Physics 16, 1040–1045 (2020).
https:/​/​doi.org/​10.1038/​s41567-020-0948-z

[17] Dmitri Maslov, Jin-Sung Kim, Sergey Bravyi, Theodore J. Yoder, and Sarah Sheldon. ``Quantum advantage for computations with limited space''. Nature Physics 17, 894–897 (2021).
https:/​/​doi.org/​10.1038/​s41567-021-01271-7

[18] Jerry M. Chow. ``Quantum intranet''. https:/​/​doi.org/​10.1049/​qtc2.12002. Accessed: 2021-10-10.
https:/​/​doi.org/​10.1049/​qtc2.12002

[19] Florent Lecocq, Franklyn Quinlan, Katarina Cicak, Jose Aumentado, SA Diddams, and JD Teufel. ``Control and readout of a superconducting qubit using a photonic link''. Nature 591, 575–579 (2021).
https:/​/​doi.org/​10.1038/​s41586-021-03268-x

[20] Christopher Chamberland, Guanyu Zhu, Theodore J Yoder, Jared B Hertzberg, and Andrew W Cross. ``Topological and subsystem codes on low-degree graphs with flag qubits''. Physical Review X 10, 011022 (2020).
https:/​/​doi.org/​10.1103/​PhysRevX.10.011022

[21] Kaitlin N Smith, Gokul Subramanian Ravi, Jonathan M Baker, and Frederic T Chong. ``Scaling superconducting quantum computers with chiplet architectures''. In 2022 55th IEEE/​ACM International Symposium on Microarchitecture (MICRO). Pages 1092–1109. IEEE (2022).
https:/​/​doi.org/​10.1109/​MICRO56248.2022.00078

[22] Jerry M Chow, Jay M Gambetta, Easwar Magesan, David W Abraham, Andrew W Cross, Blake R Johnson, Nicholas A Masluk, Colm A Ryan, John A Smolin, Srikanth J Srinivasan, et al. ``Implementing a strand of a scalable fault-tolerant quantum computing fabric''. Nature communications 5, 4015 (2014).
https:/​/​doi.org/​10.1038/​ncomms5015

[23] Sihao Huang, Benjamin Lienhard, Greg Calusine, Antti Vepsäläinen, Jochen Braumüller, David K Kim, Alexander J Melville, Bethany M Niedzielski, Jonilyn L Yoder, Bharath Kannan, et al. ``Microwave package design for superconducting quantum processors''. PRX Quantum 2, 020306 (2021).
https:/​/​doi.org/​10.1103/​PRXQuantum.2.020306

[24] Teresa Brecht, Wolfgang Pfaff, Chen Wang, Yiwen Chu, Luigi Frunzio, Michel H Devoret, and Robert J Schoelkopf. ``Multilayer microwave integrated quantum circuits for scalable quantum computing''. npj Quantum Information 2, 1–4 (2016).
https:/​/​doi.org/​10.1038/​npjqi.2016.2

[25] David Awschalom, Karl K Berggren, Hannes Bernien, Sunil Bhave, Lincoln D Carr, Paul Davids, Sophia E Economou, Dirk Englund, Andrei Faraon, Martin Fejer, et al. ``Development of quantum interconnects (quics) for next-generation information technologies''. PRX Quantum 2, 017002 (2021).
https:/​/​doi.org/​10.1103/​PRXQuantum.2.017002

[26] Jerry Chow, Oliver Dial, and Jay Gambetta. ``IBM quantum breaks the 100‑qubit processor barrier''. https:/​/​research.ibm.com/​blog/​127-qubit-quantum-processor-eagle. Accessed: 2021-16-11.
https:/​/​research.ibm.com/​blog/​127-qubit-quantum-processor-eagle

[27] Yigit Demir, Yan Pan, Seukwoo Song, Nikos Hardavellas, John Kim, and Gokhan Memik. ``Galaxy: A high-performance energy-efficient multi-chip architecture using photonic interconnects''. In Proceedings of the 28th ACM international conference on Supercomputing. Pages 303–312. (2014).
https:/​/​doi.org/​10.1145/​2597652.2597664

[28] C. Neil Berglund. ``Trends in systematic nonparticle yield loss mechanisms and the implications for IC design''. In Anthony Yen, editor, Proc. SPIE 5040, Optical Microlithography XVI. Page 457. Santa Clara, CA (2003).
https:/​/​doi.org/​10.1117/​12.497494

[29] Natalie E. Jerger. ``Chiplet-based systems''. https:/​/​www.sigarch.org/​chiplet-based-systems/​. Accessed: 2021-10-10.
https:/​/​www.sigarch.org/​chiplet-based-systems/​

[30] C Monroe, R Raussendorf, A Ruthven, KR Brown, P Maunz, L-M Duan, and J Kim. ``Large-scale modular quantum-computer architecture with atomic memory and photonic interconnects''. Physical Review A 89, 022317 (2014).
https:/​/​doi.org/​10.1103/​PhysRevA.89.022317

[31] Daniele Cuomo, Marcello Caleffi, and Angela Sara Cacciapuoti. ``Towards a distributed quantum computing ecosystem''. IET Quantum Communication 1, 3–8 (2020).
https:/​/​doi.org/​10.1049/​iet-qtc.2020.0002

[32] Santiago Rodrigo, Sergi Abadal, Eduard Alarcón, and Carmen G Almudever. ``Will quantum computers scale without inter-chip comms? a structured design exploration to the monolithic vs distributed architectures quest''. In 2020 XXXV Conference on Design of Circuits and Integrated Systems (DCIS). Pages 1–6. IEEE (2020).
https:/​/​doi.org/​10.1109/​DCIS51330.2020.9268630

[33] Jonathan M Baker, Casey Duckering, Alexander Hoover, and Frederic T Chong. ``Time-sliced quantum circuit partitioning for modular architectures''. In Proceedings of the 17th ACM International Conference on Computing Frontiers. Pages 98–107. (2020).
https:/​/​doi.org/​10.1145/​3387902.3392617

[34] Davide Ferrari, Angela Sara Cacciapuoti, Michele Amoretti, and Marcello Caleffi. ``Compiler design for distributed quantum computing''. IEEE Transactions on Quantum Engineering 2, 1–20 (2021).
https:/​/​doi.org/​10.1109/​TQE.2021.3053921

[35] Peter Chapman. ``Quantum computing’s next trick? The power of networked clusters''. Wired (2021). url: https:/​/​www.wired.com/​story/​quantum-computers-networked-clusters/​.
https:/​/​www.wired.com/​story/​quantum-computers-networked-clusters/​

[36] Stefano Pirandola and Samuel L Braunstein. ``Physics: Unite to build a quantum internet''. Nature News 532, 169 (2016).
https:/​/​doi.org/​10.1038/​532169a

[37] Stephanie Wehner, David Elkouss, and Ronald Hanson. ``Quantum internet: A vision for the road ahead''. Science 362 (2018).
https:/​/​doi.org/​10.1126/​science.aam9288

[38] Angela Sara Cacciapuoti, Marcello Caleffi, Francesco Tafuri, Francesco Saverio Cataliotti, Stefano Gherardini, and Giuseppe Bianchi. ``Quantum internet: networking challenges in distributed quantum computing''. IEEE Network 34, 137–143 (2019).
https:/​/​doi.org/​10.1109/​MNET.001.1900092

[39] Takaaki Matsuo, Clément Durand, and Rodney Van Meter. ``Quantum link bootstrapping using a RuleSet-based communication protocol''. Physical Review A 100, 052320 (2019).
https:/​/​doi.org/​10.1103/​PhysRevA.100.052320

[40] Tim Coopmans, Robert Knegjens, Axel Dahlberg, David Maier, Loek Nijsten, Julio de Oliveira Filho, Martijn Papendrecht, Julian Rabbie, Filip Rozpedek, Matthew Skrzypczyk, Leon Wubben, Walter de Jong, Damian Podareanu, Ariana Torres-Knoop, David Elkouss, and Stephanie Wehner. ``NetSquid, a NETwork Simulator for QUantum Information using Discrete events''. Communications Physics 4, 1–15 (2021).
https:/​/​doi.org/​10.1038/​s42005-021-00647-8

[41] Hudson Leone, Nathaniel R. Miller, Deepesh Singh, Nathan K. Langford, and Peter P. Rohde. ``Cost vector analysis & multi-path entanglement routing in quantum networks'' (2024). arXiv:2105.00418. DOI: 10.48550/​arXiv.2105.00418.
https:/​/​doi.org/​10.48550/​arXiv.2105.00418
arXiv:2105.00418

[42] Xiaoliang Wu, Alexander Kolar, Joaquin Chung, Dong Jin, Tian Zhong, Rajkumar Kettimuthu, and Martin Suchara. ``Sequence: a customizable discrete-event simulator of quantum networks''. Quantum Science and Technology 6, 045027 (2021).
https:/​/​doi.org/​10.1088/​2058-9565/​ac22f6

[43] Koji Azuma, Stefan Bäuml, Tim Coopmans, David Elkouss, and Boxi Li. ``Tools for quantum network design''. AVS Quantum Science 3, 014101 (2021).
https:/​/​doi.org/​10.1116/​5.0024062

[44] Mohammad Mirhosseini, Alp Sipahigil, Mahmoud Kalaee, and Oskar Painter. ``Superconducting qubit to optical photon transduction''. Nature 588, 599–603 (2020).
https:/​/​doi.org/​10.1038/​s41586-020-3038-6

[45] Nikolai Lauk, Neil Sinclair, Shabir Barzanjeh, Jacob P Covey, Mark Saffman, Maria Spiropulu, and Christoph Simon. ``Perspectives on quantum transduction''. Quantum Science and Technology 5, 020501 (2020).
https:/​/​doi.org/​10.1088/​2058-9565/​ab788a

[46] Joaquin Chung, Gregory Kanter, Nikolai Lauk, Raju Valivarthi, Wenji Wu, Russell R. Ceballos, Cristián Peña, Neil Sinclair, Jordan Thomas, Si Xie, Rajkumar Kettimuthu, Prem Kumar, Panagiotis Spentzouris, and Maria Spiropulu. ``Illinois Express Quantum Network (IEQNET): metropolitan-scale experimental quantum networking over deployed optical fiber''. In Michael Hayduk and Eric Donkor, editors, Quantum Information Science, Sensing, and Computation XIII. Page 1. Online Only, United States (2021). SPIE.
https:/​/​doi.org/​10.1117/​12.2588007

[47] Wenji Wu, Joaquin Chung, Gregory Kanter, Nikolai Lauk, Raju Valivarthi, Russell R Ceballos, Cristián Pena, Neil Sinclair, Jordan M Thomas, Ely M Eastman, et al. ``Illinois express quantum network for distributing and controlling entanglement on metro-scale''. In 2021 IEEE/​ACM Second International Workshop on Quantum Computing Software (QCS). Pages 35–42. IEEE (2021).
https:/​/​doi.org/​10.1109/​QCS54837.2021.00008

[48] Tim van Leent, Matthias Bock, Robert Garthoff, Kai Redeker, Wei Zhang, Tobias Bauer, Wenjamin Rosenfeld, Christoph Becher, and Harald Weinfurter. ``Long-distance distribution of atom-photon entanglement at telecom wavelength''. Physical review letters 124, 010510 (2020).
https:/​/​doi.org/​10.1103/​PhysRevLett.124.010510

[49] Dounan Du, Leonardo Castillo-Veneros, Guodong Cui, Dillion Cottrill, Julián Martínez-Rincón, Paul Stankus, Dimitrios Katramatos, and Eden Figueroa. ``A quantum-capable internet testbed connecting room temperature quantum memories''. In Quantum 2.0 Conference and Exhibition. Page QM2B.3. Optica Publishing Group (2022).
https:/​/​doi.org/​10.1364/​QUANTUM.2022.QM2B.3

[50] NQCO. ``A Coordinated Approach to Quantum Networking Research''. quantum.gov (2021). Accessed 2024-12-12.
https:/​/​www.quantum.gov/​a-coordinated-approach-to-quantum-networking-research/​

[51] Philipp Kurpiers, Paul Magnard, Theo Walter, Baptiste Royer, Marek Pechal, Johannes Heinsoo, Yves Salathé, Abdulkadir Akin, Simon Storz, J-C Besse, et al. ``Deterministic quantum state transfer and remote entanglement using microwave photons''. Nature 558, 264–267 (2018).
https:/​/​doi.org/​10.1038/​s41586-018-0195-y

[52] Youpeng Zhong, Hung-Shen Chang, Audrey Bienfait, Étienne Dumur, Ming-Han Chou, Christopher R Conner, Joel Grebel, Rhys G Povey, Haoxiong Yan, David I Schuster, et al. ``Deterministic multi-qubit entanglement in a quantum network''. Nature 590, 571–575 (2021).
https:/​/​doi.org/​10.1038/​s41586-021-03288-7

[53] Paul Magnard, Simon Storz, Philipp Kurpiers, Josua Schär, Fabian Marxer, Janis Lütolf, T Walter, J-C Besse, M Gabureac, K Reuer, et al. ``Microwave quantum link between superconducting circuits housed in spatially separated cryogenic systems''. Physical Review Letters 125, 260502 (2020).
https:/​/​doi.org/​10.1103/​PhysRevLett.125.260502

[54] Chao Zhou, Pinlei Lu, Matthieu Praquin, Tzu-Chiao Chien, Ryan Kaufman, Xi Cao, Mingkang Xia, Roger S. K. Mong, Wolfgang Pfaff, David Pekker, and Michael Hatridge. ``Realizing all-to-all couplings among detachable quantum modules using a microwave quantum state router''. npj Quantum Information 9, 54 (2023).
https:/​/​doi.org/​10.1038/​s41534-023-00723-7

[55] Jingjing Niu, Libo Zhang, Yang Liu, Jiawei Qiu, Wenhui Huang, Jiaxiang Huang, Hao Jia, Jiawei Liu, Ziyu Tao, Weiwei Wei, et al. ``Low-loss interconnects for modular superconducting quantum processors''. Nature Electronics 6, 235–241 (2023).
https:/​/​doi.org/​10.1038/​s41928-023-00925-z

[56] Aniruddha Bapat, Zachary Eldredge, James R Garrison, Abhinav Deshpande, Frederic T Chong, and Alexey V Gorshkov. ``Unitary entanglement construction in hierarchical networks''. Physical Review A 98, 062328 (2018).
https:/​/​doi.org/​10.1103/​PhysRevA.98.062328

[57] Zachary Eldredge, Leo Zhou, Aniruddha Bapat, James R Garrison, Abhinav Deshpande, Frederic T Chong, and Alexey V Gorshkov. ``Entanglement bounds on the performance of quantum computing architectures''. Physical review research 2, 033316 (2020).
https:/​/​doi.org/​10.1103/​PhysRevResearch.2.033316

[58] Rodney Van Meter, WJ Munro, Kae Nemoto, and Kohei M Itoh. ``Arithmetic on a distributed-memory quantum multicomputer''. ACM Journal on Emerging Technologies in Computing Systems (JETC) 3, 1–23 (2008).
https:/​/​doi.org/​10.1145/​1324177.1324179

[59] Ismail Ghodsollahee, Zohreh Davarzani, Mariam Zomorodi, Paweł Pławiak, Monireh Houshmand, and Mahboobeh Houshmand. ``Connectivity matrix model of quantum circuits and its application to distributed quantum circuit optimization''. Quantum Information Processing 20, 1–21 (2021).
https:/​/​doi.org/​10.1007/​s11128-021-03170-5

[60] Thomas Häner, Damian S Steiger, Torsten Hoefler, and Matthias Troyer. ``Distributed quantum computing with qmpi''. In Proceedings of the International Conference for High Performance Computing, Networking, Storage and Analysis. Pages 1–13. (2021).
https:/​/​doi.org/​10.1145/​3458817.3476172

[61] Andrew Eddins, Mario Motta, Tanvi P Gujarati, Sergey Bravyi, Antonio Mezzacapo, Charles Hadfield, and Sarah Sheldon. ``Doubling the size of quantum simulators by entanglement forging''. PRX Quantum 3, 010309 (2022).
https:/​/​doi.org/​10.1103/​PRXQuantum.3.010309

[62] Wei Tang, Teague Tomesh, Martin Suchara, Jeffrey Larson, and Margaret Martonosi. ``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. Pages 473–486. (2021).
https:/​/​doi.org/​10.1145/​3445814.3446758

[63] Fergus Barratt, James Dborin, Matthias Bal, Vid Stojevic, Frank Pollmann, and Andrew G Green. ``Parallel quantum simulation of large systems on small nisq computers''. npj Quantum Information 7, 79 (2021).
https:/​/​doi.org/​10.1038/​s41534-021-00420-3

[64] Teague Tomesh, Zain H. Saleem, Michael A. Perlin, Pranav Gokhale, Martin Suchara, and Margaret Martonosi. `` Divide and Conquer for Combinatorial Optimization and Distributed Quantum Computation ''. In 2023 IEEE International Conference on Quantum Computing and Engineering (QCE). Pages 1–12. Los Alamitos, CA, USA (2023). IEEE Computer Society.
https:/​/​doi.org/​10.1109/​QCE57702.2023.00009

[65] Stephen DiAdamo, Marco Ghibaudi, and James Cruise. ``Distributed quantum computing and network control for accelerated vqe''. IEEE Transactions on Quantum Engineering 2, 1–21 (2021).
https:/​/​doi.org/​10.1109/​TQE.2021.3057908

[66] Petar Jurcevic, Ali Javadi-Abhari, Lev S Bishop, Isaac Lauer, Daniela F Bogorin, Markus Brink, Lauren Capelluto, Oktay Günlük, Toshinari Itoko, Naoki Kanazawa, et al. ``Demonstration of quantum volume 64 on a superconducting quantum computing system''. Quantum Science and Technology 6, 025020 (2021).
https:/​/​doi.org/​10.1088/​2058-9565/​abe519

[67] ``Quantum roadmap''. https:/​/​www.ibm.com/​roadmaps/​quantum/​ . Accessed: 2024-09-14.
https:/​/​www.ibm.com/​roadmaps/​quantum/​

[68] ``The IBM quantum heavy hex lattice''. https:/​/​www.research.ibm.com/​blog/​heavy-hex-lattice. Accessed: 2021-09-11.
https:/​/​www.research.ibm.com/​blog/​heavy-hex-lattice

[69] Andrew W Cross, Lev S Bishop, Sarah Sheldon, Paul D Nation, and Jay M Gambetta. ``Validating quantum computers using randomized model circuits''. Physical Review A 100, 032328 (2019).
https:/​/​doi.org/​10.1103/​PhysRevA.100.032328

[70] ``IBM quantum systems''. https:/​/​quantum-computing.ibm.com/​services?systems=all. Accessed: 2021-11-18.
https:/​/​quantum-computing.ibm.com/​services?systems=all

[71] ``Randomized benchmarking''. https:/​/​qiskit.org/​textbook/​ch-quantum-hardware/​randomized-benchmarking.html##protocol. Accessed: 2021-09-13.
https:/​/​qiskit.org/​textbook/​ch-quantum-hardware/​randomized-benchmarking.html##protocol

[72] Easwar Magesan, Jay M Gambetta, and Joseph Emerson. ``Scalable and robust randomized benchmarking of quantum processes''. Physical review letters 106, 180504 (2011).
https:/​/​doi.org/​10.1103/​PhysRevLett.106.180504

[73] Easwar Magesan, Jay M Gambetta, and Joseph Emerson. ``Characterizing quantum gates via randomized benchmarking''. Physical Review A 85, 042311 (2012).
https:/​/​doi.org/​10.1103/​PhysRevA.85.042311

[74] Andrew Wack, Hanhee Paik, Ali Javadi-Abhari, Petar Jurcevic, Ismael Faro, Jay M. Gambetta, and Blake R. Johnson. ``Quality, Speed, and Scale: three key attributes to measure the performance of near-term quantum computers'' (2021). arXiv:2110.14108. DOI: 10.48550/​ARXIV.2110.14108.
https:/​/​doi.org/​10.48550/​arXiv.2110.14108
arXiv:2110.14108

[75] Sheng-Kai Liao, Wen-Qi Cai, Wei-Yue Liu, Liang Zhang, Yang Li, Ji-Gang Ren, Juan Yin, Qi Shen, Yuan Cao, Zheng-Ping Li, et al. ``Satellite-to-ground quantum key distribution''. Nature 549, 43–47 (2017).
https:/​/​doi.org/​10.1038/​nature23655

[76] Linran Fan, Chang-Ling Zou, Risheng Cheng, Xiang Guo, Xu Han, Zheng Gong, Sihao Wang, and Hong X Tang. ``Superconducting cavity electro-optics: a platform for coherent photon conversion between superconducting and photonic circuits''. Science Advances 4 (2018).
https:/​/​doi.org/​10.1126/​sciadv.aar4994

[77] Linbo Shao, Mengjie Yu, Smarak Maity, Neil Sinclair, Lu Zheng, Cleaven Chia, Amirhassan Shams-Ansari, Cheng Wang, Mian Zhang, Keji Lai, et al. ``Microwave-to-optical conversion using lithium niobate thin-film acoustic resonators''. Optica 6, 1498–1505 (2019).
https:/​/​doi.org/​10.1364/​OPTICA.6.001498

[78] Andrew P Higginbotham, PS Burns, MD Urmey, RW Peterson, NS Kampel, BM Brubaker, G Smith, KW Lehnert, and CA Regal. ``Harnessing electro-optic correlations in an efficient mechanical converter''. Nature Physics 14, 1038–1042 (2018).
https:/​/​doi.org/​10.1038/​s41567-018-0210-0

[79] Moritz Forsch, Robert Stockill, Andreas Wallucks, Igor Marinković, Claus Gärtner, Richard A Norte, Frank van Otten, Andrea Fiore, Kartik Srinivasan, and Simon Gröblacher. ``Microwave-to-optics conversion using a mechanical oscillator in its quantum ground state''. Nature Physics 16, 69–74 (2020).
https:/​/​doi.org/​10.1038/​s41567-019-0673-7

[80] John G Bartholomew, Jake Rochman, Tian Xie, Jonathan M Kindem, Andrei Ruskuc, Ioana Craiciu, Mi Lei, and Andrei Faraon. ``On-chip coherent microwave-to-optical transduction mediated by ytterbium in yvo4''. Nature communications 11, 1–6 (2020).
https:/​/​doi.org/​10.1038/​s41467-020-16996-x

[81] Poolad Imany, Zixuan Wang, Ryan A DeCrescent, Robert C Boutelle, Corey A McDonald, Travis Autry, Samuel Berweger, Pavel Kabos, Sae Woo Nam, Richard P Mirin, et al. ``Quantum phase modulation with acoustic cavities and quantum dots''. Optica 9, 501–504 (2022).
https:/​/​doi.org/​10.1364/​OPTICA.451418

[82] Alysson Gold, JP Paquette, Anna Stockklauser, Matthew J Reagor, M Sohaib Alam, Andrew Bestwick, Nicolas Didier, Ani Nersisyan, Feyza Oruc, Armin Razavi, et al. ``Entanglement across separate silicon dies in a modular superconducting qubit device''. npj Quantum Information 7, 1–10 (2021).
https:/​/​doi.org/​10.1038/​s41534-021-00484-1

[83] N. Leung, Y. Lu, S. Chakram, R. K. Naik, N. Earnest, R. Ma, K. Jacobs, A. N. Cleland, and D. I. Schuster. ``Deterministic bidirectional communication and remote entanglement generation between superconducting qubits''. npj Quantum Information 5, 1–5 (2019).
https:/​/​doi.org/​10.1038/​s41534-019-0128-0

[84] Paul Nation, Hanhee Paik, Andrew W. Cross, and Zaira Nazario. ``The IBM Quantum heavy hex lattice''. https:/​/​research.ibm.com/​blog/​heavy-hex-lattice (2021). Accessed 2024-12-12.
https:/​/​research.ibm.com/​blog/​heavy-hex-lattice

[85] Doron Puder. ``Expansion of random graphs: New proofs, new results''. Inventiones mathematicae 201, 845–908 (2015).
https:/​/​doi.org/​10.1007/​s00222-014-0560-x

[86] ``Rigetti QCS''. https:/​/​qa.qcs.rigetti.com/​qpus (2020). Accessed 2024-08-31.
https:/​/​qa.qcs.rigetti.com/​qpus

[87] Aric Hagberg, Pieter J. Swart, and Daniel A. Schult. ``Exploring network structure, dynamics, and function using networkx''. osti.gov (2008). url: https:/​/​www.osti.gov/​biblio/​960616.
https:/​/​www.osti.gov/​biblio/​960616

[88] David P. Williamson. ``Spectral Graph Theory''. https:/​/​people.orie.cornell.edu/​dpw/​orie6334/​Fall2016/​lecture7.pdf (2016). Scribe: Sam Gutekunst. Accessed 2024-12-12.
https:/​/​people.orie.cornell.edu/​dpw/​orie6334/​Fall2016/​lecture7.pdf

[89] Shlomo Hoory, Nathan Linial, and Avi Wigderson. ``Expander graphs and their applications''. Bulletin of the American Mathematical Society 43, 439–561 (2006).
https:/​/​doi.org/​10.1090/​S0273-0979-06-01126-8

[90] Nikolas P. Breuckmann and Jens Niklas Eberhardt. ``Quantum Low-Density Parity-Check Codes''. PRX Quantum 2, 040101 (2021).
https:/​/​doi.org/​10.1103/​PRXQuantum.2.040101

[91] Michael A. Perlin, Zain H. Saleem, Martin Suchara, and James C. Osborn. ``Quantum circuit cutting with maximum-likelihood tomography''. npj Quantum Information 7, 64 (2021).
https:/​/​doi.org/​10.1038/​s41534-021-00390-6

[92] Tianyi Peng, Aram W. Harrow, Maris Ozols, and Xiaodi Wu. ``Simulating Large Quantum Circuits on a Small Quantum Computer''. Physical Review Letters 125, 150504 (2020).
https:/​/​doi.org/​10.1103/​PhysRevLett.125.150504

[93] Scott Aaronson, Adam Bouland, Bill Fefferman, Soumik Ghosh, Umesh Vazirani, Chenyi Zhang, and Zixin Zhou. ``Quantum Pseudoentanglement''. In 15th Innovations in Theoretical Computer Science Conference (ITCS 2024). Pages 2:1–2:21. Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024).
https:/​/​doi.org/​10.4230/​LIPIcs.ITCS.2024.2

[94] Jan-Niklas Boyn, Aleksandr O. Lykhin, Scott E. Smart, Laura Gagliardi, and David A. Mazziotti. ``Quantum-classical hybrid algorithm for the simulation of all-electron correlation''. The Journal of Chemical Physics 155, 244106 (2021).
https:/​/​doi.org/​10.1063/​5.0074842

[95] John M. Martinis. ``Saving superconducting quantum processors from decay and correlated errors generated by gamma and cosmic rays''. npj Quantum Information 7, 90 (2021).
https:/​/​doi.org/​10.1038/​s41534-021-00431-0

[96] Matt McEwen, Lara Faoro, Kunal Arya, Andrew Dunsworth, Trent Huang, Seon Kim, Brian Burkett, Austin Fowler, Frank Arute, Joseph C. Bardin, Andreas Bengtsson, Alexander Bilmes, Bob B. Buckley, Nicholas Bushnell, Zijun Chen, Roberto Collins, Sean Demura, Alan R. Derk, Catherine Erickson, Marissa Giustina, Sean D. Harrington, Sabrina Hong, Evan Jeffrey, Julian Kelly, Paul V. Klimov, Fedor Kostritsa, Pavel Laptev, Aditya Locharla, Xiao Mi, Kevin C. Miao, Shirin Montazeri, Josh Mutus, Ofer Naaman, Matthew Neeley, Charles Neill, Alex Opremcak, Chris Quintana, Nicholas Redd, Pedram Roushan, Daniel Sank, Kevin J. Satzinger, Vladimir Shvarts, Theodore White, Z. Jamie Yao, Ping Yeh, Juhwan Yoo, Yu Chen, Vadim Smelyanskiy, John M. Martinis, Hartmut Neven, Anthony Megrant, Lev Ioffe, and Rami Barends. ``Resolving catastrophic error bursts from cosmic rays in large arrays of superconducting qubits''. Nature PhysicsPages 1–5 (2021).
https:/​/​doi.org/​10.1038/​s41567-021-01432-8

[97] S. Krinner, S. Storz, P. Kurpiers, P. Magnard, J. Heinsoo, R. Keller, J. Lütolf, C. Eichler, and A. Wallraff. ``Engineering cryogenic setups for 100-qubit scale superconducting circuit systems''. EPJ Quantum Technology 6, 1–29 (2019).
https:/​/​doi.org/​10.1140/​epjqt/​s40507-019-0072-0

[98] Austin G. Fowler, Matteo Mariantoni, John M. Martinis, and Andrew N. Cleland. ``Surface codes: Towards practical large-scale quantum computation''. Physical Review A 86, 032324 (2012).
https:/​/​doi.org/​10.1103/​PhysRevA.86.032324

[99] Olivia Lanes, Kallie Ferguson, Abe Asfaw, and Luuk Ament. ``Announcing the winners of the IBM Quantum Open Science Prize''. https:/​/​research.ibm.com/​blog/​quantum-open-science-prize-winners (2021). Accessed 2021-11-30.
https:/​/​research.ibm.com/​blog/​quantum-open-science-prize-winners

[100] Yuval R Sanders, Joel J Wallman, and Barry C Sanders. ``Bounding quantum gate error rate based on reported average fidelity''. New Journal of Physics 18, 012002 (2015).
https:/​/​doi.org/​10.1088/​1367-2630/​18/​1/​012002

[101] ``Quantum tomography''. https:/​/​qiskit.org/​documentation/​tutorials/​noise/​8_tomography.html. Accessed: 2021-09-13.
https:/​/​qiskit.org/​documentation/​tutorials/​noise/​8_tomography.html

[102] ``Measurement Error Mitigation''. https:/​/​community.qiskit.org/​textbook/​ch-quantum-hardware/​measurement-error-mitigation.html. accessed 2021-12-30.
https:/​/​community.qiskit.org/​textbook/​ch-quantum-hardware/​measurement-error-mitigation.html

[103] ``IBM Quantum Experience''. https:/​/​quantum-computing.ibm.com. Accessed: 2021-09-11.
https:/​/​quantum-computing.ibm.com

[104] Kaitlin N Smith, Joshua Viszlai, Lennart Maximilian Seifert, Jonathan M Baker, Jakub Szefer, and Frederic T Chong. ``Fast fingerprinting of cloud-based nisq quantum computers''. In 2023 IEEE International Symposium on Hardware Oriented Security and Trust (HOST). Pages 1–12. IEEE (2023).
https:/​/​doi.org/​10.1109/​HOST55118.2023.10133778

[105] ``Retired qpus''. https:/​/​docs.quantum.ibm.com/​guides/​retired-qpus . Accessed: 2024-09-14.
https:/​/​docs.quantum.ibm.com/​guides/​retired-qpus

[106] Isaac L. Chuang, Debbie W. Leung, and Yoshihisa Yamamoto. ``Bosonic quantum codes for amplitude damping''. Physical Review A 56, 1114–1125 (1997).
https:/​/​doi.org/​10.1103/​PhysRevA.56.1114

[107] A. S. Fletcher, P. W. Shor, and M. Z. Win. ``Channel-Adapted Quantum Error Correction for the Amplitude Damping Channel''. IEEE Transactions on Information Theory 54, 5705–5718 (2008).
https:/​/​doi.org/​10.1109/​TIT.2008.2006458

[108] P. W. Shor, G. Smith, J. A. Smolin, and B. Zeng. ``High Performance Single-Error-Correcting Quantum Codes for Amplitude Damping''. IEEE Transactions on Information Theory 57, 7180–7188 (2011).
https:/​/​doi.org/​10.1109/​TIT.2011.2165149

[109] M. Grassl, Z. Wei, Z. Yin, and B. Zeng. ``Quantum error-correcting codes for amplitude damping''. In 2014 IEEE International Symposium on Information Theory. Pages 906–910. (2014).
https:/​/​doi.org/​10.1109/​ISIT.2014.6874964

[110] Stefano Chessa and Vittorio Giovannetti. ``Quantum capacity analysis of multi-level amplitude damping channels''. Communications Physics 4, 1–12 (2021).
https:/​/​doi.org/​10.1038/​s42005-021-00524-4

[111] Nicholas LaRacuente, Kaitlin N. Smith, Poolad Imany, Kevin L. Silverman, and Frederic T. Chong. ``modeling-links-2024''. https:/​/​github.com/​knsmith/​modeling-links-2024.
https:/​/​github.com/​knsmith/​modeling-links-2024

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[4] Chang Li, "Spin Grouping in Ring Cavity and Its Protection on Entangled States Transfer", Physical Review Letters 134 21, 210803 (2025).

[5] MD Shajalal Forhad, MD AL Mahedi Hassan, Md Forkan Hossain Fahim, and Tanvir Habib Sardar, Signal Processing Roadmap 257 (2026) ISBN:9780443331725.

[6] Hany Khalifa and Matti Silveri, "Gate-based microwave quantum repeater via grid-state encoding", Physical Review Applied 26 2, 024003 (2026).

[7] Sahar Ben Rached, Zezhou Sun, Guilu Long, Santiago Rodrigo, Carmen G. Almudéver, Eduard Alarcón, and Sergi Abadal, 2025 IEEE International Conference on Quantum Computing and Engineering (QCE) 1283 (2025) ISBN:979-8-3315-5736-2.

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[9] Sreraman Muralidharan, "The simulation of distributed quantum algorithms", The Journal of Supercomputing 81 5, 645 (2025).

[10] Bin Cheng, Xiu-Hao Deng, Xiu Gu, Yu He, Guangchong Hu, Peihao Huang, Jun Li, Ben-Chuan Lin, Dawei Lu, Yao Lu, Chudan Qiu, Hui Wang, Tao Xin, Shi Yu, Man-Hong Yung, Junkai Zeng, Song Zhang, Youpeng Zhong, Xinhua Peng, Franco Nori, and Dapeng Yu, "Noisy intermediate-scale quantum computers", Frontiers of Physics 18 2, 21308 (2023).

[11] Chao Zhou, Pinlei Lu, Matthieu Praquin, Tzu-Chiao Chien, Ryan Kaufman, Xi Cao, Mingkang Xia, Roger S. K. Mong, Wolfgang Pfaff, David Pekker, and Michael Hatridge, "Realizing all-to-all couplings among detachable quantum modules using a microwave quantum state router", npj Quantum Information 9 1, 54 (2023).

[12] James Ang, Gabriella Carini, Yanzhu Chen, Isaac Chuang, Michael Austin DeMarco, Sophia E. Economou, Alec Eickbusch, Andrei Faraon, Kai-Mei Fu, Steven M. Girvin, Michael Hatridge, Andrew Houck, Paul Hilaire, Kevin Krsulich, Ang Li, Chenxu Liu, Yuan Liu, Margaret Martonosi, David C. McKay, James Misewich, Mark Ritter, Robert J. Schoelkopf, Samuel A. Stein, Sara Sussman, Hong X. Tang, Wei Tang, Teague Tomesh, Norm M. Tubman, Chen Wang, Nathan Wiebe, Yong-Xin Yao, Dillon C. Yost, and Yiyu Zhou, "Architectures for Multinode Superconducting Quantum Computers", arXiv:2212.06167, (2022).

[13] Hezi Zhang, Keyi Yin, Anbang Wu, Hassan Shapourian, Alireza Shabani, and Yufei Ding, "MECH: Multi-Entry Communication Highway for Superconducting Quantum Chiplets", arXiv:2305.05149, (2023).

[14] Liang Xiang, Jiachen Chen, Zitian Zhu, Zixuan Song, Zehang Bao, Xuhao Zhu, Feitong Jin, Ke Wang, Shibo Xu, Yiren Zou, Hekang Li, Zhen Wang, Chao Song, Alexander Yue, Justine Partridge, Qiujiang Guo, Rubem Mondaini, H. Wang, and Richard T. Scalettar, "Enhanced quantum state transfer by circumventing quantum chaotic behavior", Nature Communications 15, 4918 (2024).

[15] Anbang Wu, Yufei Ding, and Ang Li, "CollComm: Enabling Efficient Collective Quantum Communication Based on EPR buffering", arXiv:2208.06724, (2022).

[16] Xinyu Chen, Zilu Chen, Pengcheng Zhu, Xueyun Cheng, and Zhijin Guan, "Circuit Partitioning and Transmission Cost Optimization in Distributed Quantum Circuits", IEEE Transactions on Computer Aided Design 44 9, 3350 (2025).

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[20] Zirui Li, Minghao Guo, Mayank Barad, Wei Tang, Eddy Z. Zhang, and Yipeng Huang, "A Case for Quantum Circuit Cutting for NISQ Applications: Impact of topology, determinism, and sparsity", arXiv:2412.17929, (2024).

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[23] Kaitlin N. Smith, Gokul Subramanian Ravi, Jonathan M. Baker, and Frederic T. Chong, "Scaling Superconducting Quantum Computers with Chiplet Architectures", arXiv:2210.10921, (2022).

[24] Pau Escofet, Alejandro Gonzalvo, Eduard Alarcón, Carmen G. Almudéver, and Sergi Abadal, "Route-Forcing: Scalable Quantum Circuit Mapping for Scalable Quantum Computing Architectures", arXiv:2407.17306, (2024).

[25] Pau Escofet, Anabel Ovide, Carmen G. Almudever, Eduard Alarcón, and Sergi Abadal, "Hungarian Qubit Assignment for Optimized Mapping of Quantum Circuits on Multi-Core Architectures", arXiv:2309.12182, (2023).

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