ProjectQ: an open source software framework for quantum computing

Damian S. Steiger, Thomas Häner, and Matthias Troyer

Institute for Theoretical Physics, ETH Zurich, 8093 Zurich, Switzerland

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Abstract

We introduce ProjectQ, an open source software effort for quantum computing. The first release features a compiler framework capable of targeting various types of hardware, a high-performance simulator with emulation capabilities, and compiler plug-ins for circuit drawing and resource estimation. We introduce our Python-embedded domain-specific language, present the features, and provide example implementations for quantum algorithms. The framework allows testing of quantum algorithms through simulation and enables running them on actual quantum hardware using a back-end connecting to the IBM Quantum Experience cloud service. Through extension mechanisms, users can provide back-ends to further quantum hardware, and scientists working on quantum compilation can provide plug-ins for additional compilation, optimization, gate synthesis, and layout strategies.

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► References

[1] IBM Quantum Experience. http:/​/​research.ibm.com/​quantum/​.
http:/​/​research.ibm.com/​quantum/​

[2] Thomas Häner, Damian S. Steiger, Krysta Svore, and Matthias Troyer. A software methodology for compiling quantum programs. Quantum Science and Technology, 2018. https:/​/​doi.org/​10.1088/​2058-9565/​aaa5cc.
https:/​/​doi.org/​10.1088/​2058-9565/​aaa5cc

[3] pybind. https:/​/​github.com/​pybind.
https:/​/​github.com/​pybind

[4] Thomas Häner, Damian S. Steiger, Mikhail Smelyanskiy, and Matthias Troyer. High performance emulation of quantum circuits. In Proceedings of the International Conference for High Performance Computing, Networking, Storage and Analysis, SC '16, pages 74:1–74:9, Piscataway, NJ, USA, 2016. IEEE Press. ISBN 978-1-4673-8815-3. 10.1109/​SC.2016.73.
https:/​/​doi.org/​10.1109/​SC.2016.73

[5] Alexander S. Green, Peter LeFanu Lumsdaine, Neil J. Ross, Peter Selinger, and Benoit Valiron. Quipper: a scalable quantum programming language. In ACM SIGPLAN Notices, volume 48, pages 333–342. ACM, 2013. 10.1145/​2499370.2462177.
https:/​/​doi.org/​10.1145/​2499370.2462177

[6] Ali JavadiAbhari, Shruti Patil, Daniel Kudrow, Jeff Heckey, Alexey Lvov, Frederic T. Chong, and Margaret Martonosi. Scaffcc: a framework for compilation and analysis of quantum computing programs. In Proceedings of the 11th ACM Conference on Computing Frontiers, page 1. ACM, 2014. 10.1145/​2597917.2597939.
https:/​/​doi.org/​10.1145/​2597917.2597939

[7] Dave Wecker and Krysta M. Svore. LIQ$Ui|>$: A software design architecture and domain-specific language for quantum computing. arXiv preprint arXiv:1402.4467, 2014.
arXiv:1402.4467

[8] ProjectQ website. www.projectq.ch.
http:/​/​www.projectq.ch

[9] Peter W. Shor. Algorithms for quantum computation: Discrete logarithms and factoring. In Foundations of Computer Science, 1994 Proceedings., 35th Annual Symposium on, pages 124–134. IEEE, 1994. 10.1109/​SFCS.1994.365700.
https:/​/​doi.org/​10.1109/​SFCS.1994.365700

[10] Stephane Beauregard. Circuit for shor's algorithm using 2n+ 3 qubits. Quantum Information and Computation, 3 (2): 175–185, 2003.

[11] Yasuhiro Takahashi, Seiichiro Tani, and Noboru Kunihiro. Quantum addition circuits and unbounded fan-out. Quantum Information and Computation, 10 (9&10): 0872–0890, 2010.

[12] Thomas Häner, Martin Roetteler, and Krysta M. Svore. Factoring using 2n+2 qubits with Toffoli based modular multiplication. Quantum Information and Computation, 17 (7&8): 0673–0684, 2017. 10.26421/​QIC17.7-8.
https:/​/​doi.org/​10.26421/​QIC17.7-8

[13] Thomas G. Draper. Addition on a quantum computer. arXiv preprint quant-ph/​0008033, 2000.
arXiv:quant-ph/0008033

[14] Adriano Barenco, Charles H. Bennett, Richard Cleve, David P. DiVincenzo, Norman Margolus, Peter Shor, Tycho Sleator, John A. Smolin, and Harald Weinfurter. Elementary gates for quantum computation. Physical Review A, 52 (5): 3457, 1995. 10.1103/​PhysRevA.52.3457.
https:/​/​doi.org/​10.1103/​PhysRevA.52.3457

[15] Anders Sørensen and Klaus Mølmer. Quantum computation with ions in thermal motion. Physical Review Letters, 82 (9): 1971, 1999. 10.1103/​PhysRevLett.82.1971.
https:/​/​doi.org/​10.1103/​PhysRevLett.82.1971

[16] Ryan Babbush, Dominic W. Berry, Ian D. Kivlichan, Annie Y. Wei, Peter J. Love, and Alán Aspuru-Guzik. Exponentially more precise quantum simulation of fermions in second quantization. New Journal of Physics, 18 (3): 033032, 2016. 10.1088/​1367-2630/​18/​3/​033032.
https:/​/​doi.org/​10.1088/​1367-2630/​18/​3/​033032

[17] Fermilib. https:/​/​github.com/​projectq-framework/​fermilib.
https:/​/​github.com/​projectq-framework/​fermilib

[18] Ludwig E. de Clercq, Hsiang-Yu Lo, Matteo Marinelli, David Nadlinger, Robin Oswald, Vlad Negnevitsky, Daniel Kienzler, Ben Keitch, and Jonathan P. Home. Parallel transport quantum logic gates with trapped ions. Physical Review Letters, 116 (8): 080502, 2016. 10.1103/​PhysRevLett.116.080502.
https:/​/​doi.org/​10.1103/​PhysRevLett.116.080502

[19] Thomas Häner and Damian S. Steiger. 0.5 petabyte simulation of a 45-qubit quantum circuit. In Proceedings of the International Conference for High Performance Computing, Networking, Storage and Analysis, SC '17, pages 33:1–33:10, New York, NY, USA, 2017. ACM. ISBN 978-1-4503-5114-0. 10.1145/​3126908.3126947.
https:/​/​doi.org/​10.1145/​3126908.3126947

[20] Lov K. Grover. A fast quantum mechanical algorithm for database search. In Proceedings of the twenty-eighth annual ACM Symposium on Theory of Computing, pages 212–219. ACM, 1996. 10.1145/​237814.237866.
https:/​/​doi.org/​10.1145/​237814.237866

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[1] Zhiqian Xu, Honghui Shang, Yi Fan, Xiongzhi Zeng, Yunquan Zhang, and Chu Guo, 2024 IEEE International Parallel and Distributed Processing Symposium (IPDPS) 230 (2024) ISBN:979-8-3503-8711-7.

[2] C. Ryan-Anderson, J. G. Bohnet, K. Lee, D. Gresh, A. Hankin, J. P. Gaebler, D. Francois, A. Chernoguzov, D. Lucchetti, N. C. Brown, T. M. Gatterman, S. K. Halit, K. Gilmore, J. A. Gerber, B. Neyenhuis, D. Hayes, and R. P. Stutz, "Realization of Real-Time Fault-Tolerant Quantum Error Correction", Physical Review X 11 4, 041058 (2021).

[3] Giovanni Di Bartolomeo, Michele Vischi, Francesco Cesa, Roman Wixinger, Michele Grossi, Sandro Donadi, and Angelo Bassi, "Noisy gates for simulating quantum computers", Physical Review Research 5 4, 043210 (2023).

[4] Chansreynich Huot, Kimleang Kea, Tae-Kyung Kim, and Youngsun Han, "Enhancing Knapsack-Based Financial Portfolio Optimization Using Quantum Approximate Optimization Algorithm", IEEE Access 12, 183779 (2024).

[5] Leanghok Hour, Myeongseong Go, and Youngsun Han, "Improving Zero-Noise Extrapolation for Quantum-Gate Error Mitigation Using a Noise-Aware Folding Method", IEEE Access 14, 37362 (2026).

[6] Mingsheng Ying, Li Zhou, and Gilles Barthe, "Laws of Quantum Programming", ACM Transactions on Software Engineering and Methodology 35 7, 1 (2026).

[7] Hussain Shaik, Morampudi Rajitha, K. Priyamvada, R. Naveena Bhargavi, G. Sree Lakshmi, Ch. Lokeshwar Reddy, and K. Shashidhar Reddy, "Optimization Techniques on Quantum and Classical Systems: A Comprehensive Comparative Study", E3S Web of Conferences 616, 02024 (2025).

[8] Austin J. Adams, Sharjeel Khan, Arjun S. Bhamra, Ryan R. Abusaada, Travis S. Humble, Jeffrey S. Young, and Thomas M. Conte, 2025 IEEE International Conference on Quantum Computing and Engineering (QCE) 804 (2025) ISBN:979-8-3315-5736-2.

[9] Gian Giacomo Guerreschi and Jongsoo Park, "Two-step approach to scheduling quantum circuits", Quantum Science and Technology 3 4, 045003 (2018).

[10] Harrison Ball, Michael J Biercuk, Andre R R Carvalho, Jiayin Chen, Michael Hush, Leonardo A De Castro, Li Li, Per J Liebermann, Harry J Slatyer, Claire Edmunds, Virginia Frey, Cornelius Hempel, and Alistair Milne, "Software tools for quantum control: improving quantum computer performance through noise and error suppression", Quantum Science and Technology 6 4, 044011 (2021).

[11] T. L. M. Guedes, D. Winter, and M. Müller, "Quantum Cellular Automata for Quantum Error Correction and Density Classification", Physical Review Letters 133 15, 150601 (2024).

[12] Bettina Heim, Mathias Soeken, Sarah Marshall, Chris Granade, Martin Roetteler, Alan Geller, Matthias Troyer, and Krysta Svore, "Quantum programming languages", Nature Reviews Physics 2 12, 709 (2020).

[13] Tim Coopmans, Robert Knegjens, Axel Dahlberg, David Maier, Loek Nijsten, Julio de Oliveira Filho, Martijn Papendrecht, Julian Rabbie, Filip Rozpędek, 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, 164 (2021).

[14] Abdulah Fawaz, Paul Klein, Sebastien Piat, Simone Severini, and Peter Mountney, Proceedings of the 25th ACM SIGKDD International Conference on Knowledge Discovery & Data Mining 1674 (2019) ISBN:9781450362016.

[15] Arnaud Gazda and Océane Koska, "A pragma based C++ framework for hybrid quantum/classical computation", Science of Computer Programming 236, 103119 (2024).

[16] Pengzhan Zhao, Zhongtao Miao, Shuhan Lan, and Jianjun Zhao, "Bugs4Q: A benchmark of existing bugs to enable controlled testing and debugging studies for quantum programs", Journal of Systems and Software 205, 111805 (2023).

[17] Seong-Min Cho and Seung-Hyun Seo, "Quantum rectangular MinRank attack on multi-layer UOV signature schemes", Scientific Reports 14 1, 16340 (2024).

[18] Matthew Amy, Lecture Notes in Computer Science 11497, 87 (2019) ISBN:978-3-030-21499-9.

[19] Charles Yuan and Michael Carbin, "The T-Complexity Costs of Error Correction for Control Flow in Quantum Computation", Proceedings of the ACM on Programming Languages 8 PLDI, 492 (2024).

[20] Amit Jamadagni Gangapuram, Andreas Läuchli, and Cornelius Hempel, "Benchmarking quantum computer simulation software packages: State vector simulators", SciPost Physics Core 7 4, 075 (2024).

[21] Stefano Markidis, Gilbert Netzer, Luca Pennati, and Ivy Peng, Proceedings of the SC '25 Workshops of the International Conference for High Performance Computing, Networking, Storage and Analysis 1860 (2025) ISBN:9798400718717.

[22] Gushu Li, Yufei Ding, and Yuan Xie, 2020 57th ACM/IEEE Design Automation Conference (DAC) 1 (2020) ISBN:978-1-7281-1085-1.

[23] Mina Alipour, 2025 IEEE Conference on Cloud and Big Data Computing (CBDCom) 1 (2025) ISBN:979-8-3315-9094-9.

[24] Gyeongju Song, Siwoo Eum, Hyeokdong Kwon, Minjoo Sim, Minwoo Lee, and Hwajeong Seo, "Optimized Quantum Circuit for Quantum Security Strength Analysis of Argon2", Electronics 12 21, 4485 (2023).

[25] Masaya Norimoto, Taku Mikuriya, and Naoki Ishikawa, "Quantum Speedup for Multiuser Detection With Optimized Parameters in Grover Adaptive Search", IEEE Access 12, 83810 (2024).

[26] Matthew Amy and Vlad Gheorghiu, " staq—A full-stack quantum processing toolkit", Quantum Science and Technology 5 3, 034016 (2020).

[27] Jakob S Kottmann, Sumner Alperin-Lea, Teresa Tamayo-Mendoza, Alba Cervera-Lierta, Cyrille Lavigne, Tzu-Ching Yen, Vladyslav Verteletskyi, Philipp Schleich, Abhinav Anand, Matthias Degroote, Skylar Chaney, Maha Kesibi, Naomi Grace Curnow, Brandon Solo, Georgios Tsilimigkounakis, Claudia Zendejas-Morales, Artur F Izmaylov, and Alán Aspuru-Guzik, "TEQUILA: a platform for rapid development of quantum algorithms", Quantum Science and Technology 6 2, 024009 (2021).

[28] Haodong Bian, Jianqiang Huang, Jiahao Tang, Runting Dong, Li Wu, and Xiaoying Wang, "PAS: A new powerful and simple quantum computing simulator", Software: Practice and Experience 53 1, 142 (2023).

[29] Anderson Avila, Helida Santos, Anderson Cruz, Samuel Xavier-de-Souza, Giancarlo Lucca, Bruno Moura, Adenauer Yamin, and Renata Reiser, "HybriD-GM: A Framework for Quantum Computing Simulation Targeted to Hybrid Parallel Architectures", Entropy 25 3, 503 (2023).

[30] Hoa T. Nguyen, Muhammad Usman, and Rajkumar Buyya, "iQuantum: A toolkit for modeling and simulation of quantum computing environments", Software: Practice and Experience 54 6, 1141 (2024).

[31] Daniel Vietz, Johanna Barzen, Frank Leymann, and Karoline Wild, Lecture Notes in Computer Science 12747, 127 (2021) ISBN:978-3-030-77979-5.

[32] Lei Zhang, Guoyuan Li, Jingchen Dai, Ruipeng Hong, Chaoen Xiao, Jianxin Wang, and Yifan Zhang, "Efficient quantum circuit research and implementation for 16-bit S-boxes based on composite field", Journal of King Saud University Computer and Information Sciences 37 4, 55 (2025).

[33] Kesha Hietala, Robert Rand, Liyi Li, Shih-Han Hung, Xiaodi Wu, and Michael Hicks, "A Verified Optimizer for Quantum Circuits", ACM Transactions on Programming Languages and Systems 45 3, 1 (2023).

[34] Christophe Chareton, Sébastien Bardin, François Bobot, Valentin Perrelle, and Benoît Valiron, Lecture Notes in Computer Science 12648, 148 (2021) ISBN:978-3-030-72018-6.

[35] Pedro Parrado-Rodríguez, Ciarán Ryan-Anderson, Alejandro Bermudez, and Markus Müller, "Crosstalk Suppression for Fault-tolerant Quantum Error Correction with Trapped Ions", Quantum 5, 487 (2021).

[36] Anurudh Peduri, Ina Schaefer, and Michael Walter, "QbC: Quantum Correctness by Construction", Proceedings of the ACM on Programming Languages 9 OOPSLA1, 534 (2025).

[37] Marc Illa, Caroline E. P. Robin, and Martin J. Savage, "Quantum simulations of SO(5) many-fermion systems using qudits", Physical Review C 108 6, 064306 (2023).

[38] Manu Chaudhary, Ishraq Islam, David Levy, Alvir Nobel, Dylan Kneidel, Vinayak Jha, and Esam El-Araby, Communications in Computer and Information Science 2257, 69 (2025) ISBN:978-3-031-85883-3.

[39] Will Powell, Jason Riedy, Jeffrey S. Young, and Thomas M. Conte, Proceedings of the Practice and Experience in Advanced Research Computing on Rise of the Machines (learning) 1 (2019) ISBN:9781450372275.

[40] Manuel A. Serrano, José A. Cruz-Lemus, Ricardo Perez-Castillo, and Mario Piattini, "Quantum Software Components and Platforms: Overview and Quality Assessment", ACM Computing Surveys 55 8, 1 (2023).

[41] Antonio D. Corcoles, Abhinav Kandala, Ali Javadi-Abhari, Douglas T. McClure, Andrew W. Cross, Kristan Temme, Paul D. Nation, Matthias Steffen, and Jay M. Gambetta, "Challenges and Opportunities of Near-Term Quantum Computing Systems", Proceedings of the IEEE 108 8, 1338 (2020).

[42] Mariana Filipova, Genadiy Gospodinov, Lyubomir Gotsev, Eugenia Kovatcheva, and Boyan Jekov, "QUANTUM COMPUTING APPLICATIONS FOR ADDRESSING GLOBAL WARMING AND POLLUTION: A COMPREHENSIVE ANALYSIS", ENVIRONMENT. TECHNOLOGY. RESOURCES. Proceedings of the International Scientific and Practical Conference 1, 154 (2024).

[43] Chris Cade, Marten Folkertsma, Ido Niesen, and Jordi Weggemans, "Quantifying Grover speed-ups beyond asymptotic analysis", Quantum 7, 1133 (2023).

[44] Yu-Tsung Wu, Po-Hsuan Huang, Kai-Chieh Chang, Chia-Heng Tu, and Shih-Hao Hung, "QOPS: a compiler framework for quantum circuit simulation acceleration with profile-guided optimizations", The Journal of Supercomputing 81 5, 674 (2025).

[45] Evandro Rosa and Rafael Santiago, "Schrödinger’s bug: a survey on quantum software debugging", Quantum Information Processing 25 3, 96 (2026).

[46] Ehsan Arianyan, Niloofar Gholipour, Davood Maleki, Neda Ghorbani, Abdolah Sepahvand, and Pejman Goudarzi, "A Systematic Review and Classification of HPC-Related Emerging Computing Technologies", Electronics 14 12, 2476 (2025).

[47] Giulia Meuli, Mathias Soeken, Martin Roetteler, and Thomas Häner, "Enabling accuracy-aware Quantum compilers using symbolic resource estimation", Proceedings of the ACM on Programming Languages 4 OOPSLA, 1 (2020).

[48] Huan-Yu Ku, Neill Lambert, Feng-Jui Chan, Clive Emary, Yueh-Nan Chen, and Franco Nori, "Experimental test of non-macrorealistic cat states in the cloud", npj Quantum Information 6 1, 98 (2020).

[49] Yu Zhang, Haowei Deng, Quanxi Li, Haoze Song, and Leihai Nie, 2019 International Symposium on Theoretical Aspects of Software Engineering (TASE) 184 (2019) ISBN:978-1-7281-3342-3.

[50] Marie Salm, Johanna Barzen, Uwe Breitenbücher, Frank Leymann, Benjamin Weder, and Karoline Wild, Communications in Computer and Information Science 1310, 66 (2020) ISBN:978-3-030-64845-9.

[51] Marcello Caleffi, Michele Amoretti, Davide Ferrari, Jessica Illiano, Antonio Manzalini, and Angela Sara Cacciapuoti, "Distributed quantum computing: A survey", Computer Networks 254, 110672 (2024).

[52] Suryansh Upadhyay, Mahabubul Alam, and Swaroop Ghosh, Handbook of Computer Architecture 723 (2025) ISBN:978-981-97-9313-6.

[53] Jayesh Hire, Vaidehi Gawande, and Sagar Dhande, "Quantum-Accelerated Flight Selection: Probing Grover's Algorithm and Quantum Device Efficiency", International Journal of Innovative Science and Research Technology (IJISRT) 1255 (2024).

[54] Lukas Burgholzer, Rudy Raymond, Indranil Sengupta, and Robert Wille, Lecture Notes in Computer Science 12805, 227 (2021) ISBN:978-3-030-79836-9.

[55] Tian-Yin Li, Hong-Xi Xing, and Dan-Bo Zhang, "Quantum computing based high-energy nuclear physics", Acta Physica Sinica 72 20, 200303 (2023).

[56] Kyungbae Jang, Sejin Lim, Yujin Oh, Hyunjun Kim, Anubhab Baksi, Sumanta Chakraborty, and Hwajeong Seo, "Quantum Implementation and Analysis of SHA-2 and SHA-3", IEEE Transactions on Emerging Topics in Computing 13 3, 919 (2025).

[57] Anderson Avila, Renata Hax Sander Reiser, Maurício Lima Pilla, and Adenauer Correa Yamin, "Improving in situ GPU simulation of quantum computing in the D-GM environment", The International Journal of High Performance Computing Applications 33 3, 462 (2019).

[58] Ebrahim Ghasemian, Mohammad Kazem Tavassoly, and Habib Rostami, "Implementation of linear optics network for pattern recognition task via the generation of continuous variable entangled states", Neurocomputing 657, 131588 (2025).

[59] Engin Zeydan, Chamitha De Alwis, Rabia Khan, Yekta Turk, Abdullah Aydeger, Thippa Reddy Gadekallu, and Madhusanka Liyanage, "Quantum Technologies for Beyond 5G and 6G Networks: Applications, Opportunities, and Challenges", IEEE Open Journal of the Communications Society 6, 6383 (2025).

[60] Anna Leonteva, Maxime Outteryck, and Guido Masella, Communications in Computer and Information Science 2743, 280 (2026) ISBN:978-3-032-13851-4.

[61] Gian Giacomo Guerreschi, "Fast simulation of quantum algorithms using circuit optimization", Quantum 6, 706 (2022).

[62] Felix Gemeinhardt, Antonio Garmendia, Manuel Wimmer, and Robert Wille, "A Model-Driven Framework for Composition-Based Quantum Circuit Design", ACM Transactions on Quantum Computing 5 4, 1 (2024).

[63] Waylon Luo, Betis Baheri, Travis Humble, Jiapeng Zhao, Tong Zhan, Rajan Maharjan, and Qiang Guan, Proceedings of the 39th ACM SIGSIM Conference on Principles of Advanced Discrete Simulation 165 (2025) ISBN:9798400715914.

[64] Yi-Te Huang, Jhen-Dong Lin, Huan-Yu Ku, and Yueh-Nan Chen, "Benchmarking quantum state transfer on quantum devices", Physical Review Research 3 2, 023038 (2021).

[65] Syivesh Rukmanikanthan, Hayana Dullah, Yun Xin Teoh, and Ali Najah Ahmed, "Quantum Computing Applications in Engineering: Current Status and Future Prospects", Archives of Computational Methods in Engineering 33 5, 7595 (2026).

[66] Chao Ding, Shi Wang, Yaonan Wang, and Weibo Gao, "Quantum machine learning for multiclass classification beyond kernel methods", Physical Review A 111 6, 062410 (2025).

[67] Kai Chen, "Comparison of the Quantum and Conventional Algorithms: Evidence from Genetic Algorithm and Ant Colony Algorithm", Highlights in Science, Engineering and Technology 38, 508 (2023).

[68] James Sharp and Rob Ashmore, "Generic Assurance Topics for Any Type of Programmable Content", Safety-Critical Systems eJournal 1 1(2022).

[69] Peter Nimbe, Benjamin Asubam Weyori, and Adebayo Felix Adekoya, "Models in quantum computing: a systematic review", Quantum Information Processing 20 2, 80 (2021).

[70] Shuang Liang, Yuncheng Lu, Ce Guo, Wayne Luk, and Paul H. J. Kelly, 2024 IEEE 32nd Annual International Symposium on Field-Programmable Custom Computing Machines (FCCM) 24 (2024) ISBN:979-8-3503-7243-4.

[71] Zi-Jian Zhang, Thi Ha Kyaw, Jakob S Kottmann, Matthias Degroote, and Alán Aspuru-Guzik, "Mutual information-assisted adaptive variational quantum eigensolver", Quantum Science and Technology 6 3, 035001 (2021).

[72] Manuel A. Serrano, Luis E. Sánchez, Antonio Santos-Olmo, David García-Rosado, Carlos Blanco, Vita Santa Barletta, Danilo Caivano, and Eduardo Fernández-Medina, "Minimizing incident response time in real-world scenarios using quantum computing", Software Quality Journal 32 1, 163 (2024).

[73] Francisco Orts, Gloria Ortega, Elías F. Combarro, Ignacio F. Rúa, Antonio M. Puertas, and Ester M. Garzón, "Efficient design of a quantum absolute-value circuit using Clifford+T gates", (2022).

[74] Synthesis Lectures on Computer Architecture (2020) ISBN:978-3-031-00637-1.

[75] Gyeongju Song and Hwajeong Seo, "Grover on Scrypt", Electronics 13 16, 3167 (2024).

[76] Neil J. Ross, "The dawn of quantum programming", Quantum Views 2, 4 (2018).

[77] Essam H. Houssein, Zainab Abohashima, Mohamed Elhoseny, and Waleed M. Mohamed, "Machine learning in the quantum realm: The state-of-the-art, challenges, and future vision", Expert Systems with Applications 194, 116512 (2022).

[78] Kiran Mehta and Renuka Sharma, Deep Learning Tools for Predicting Stock Market Movements 39 (2024) ISBN:9781394214303.

[79] Ang Li, Samuel Stein, Sriram Krishnamoorthy, and James Ang, "QASMBench: A Low-Level Quantum Benchmark Suite for NISQ Evaluation and Simulation", ACM Transactions on Quantum Computing 4 2, 1 (2023).

[80] Erik Nielsen, Kenneth Rudinger, Timothy Proctor, Antonio Russo, Kevin Young, and Robin Blume-Kohout, "Probing quantum processor performance with pyGSTi", Quantum Science and Technology 5 4, 044002 (2020).

[81] José A. Cruz-Lemus and Manuel A. Serrano, Quantum Software Engineering 229 (2022) ISBN:978-3-031-05323-8.

[82] Francesco Di Marcantonio, Massimiliano Incudini, Davide Tezza, and Michele Grossi, "Quantum Advantage Seeker with Kernels (QuASK): a software framework to speed up the research in quantum machine learning", Quantum Machine Intelligence 5 1, 20 (2023).

[83] Jun Ye and Jun Yong Khoo, Proceedings of the Supercomputing Asia and International Conference on High Performance Computing in Asia Pacific Region 10 (2026) ISBN:9798400720673.

[84] Liyi Li, Anshu Sharma, Zoukarneini Difaizi Tagba, Sean Frett, and Alex Potanin, Lecture Notes in Computer Science 16501, 432 (2026) ISBN:978-3-032-22719-5.

[85] Neilson Carlos Leite Ramalho, Higor Amario de Souza, and Marcos Lordello Chaim, "Testing and Debugging Quantum Programs: The Road to 2030", ACM Transactions on Software Engineering and Methodology 34 5, 1 (2025).

[86] Philipp Niemann, Alwin Zulehner, Rolf Drechsler, and Robert Wille, "Overcoming the Tradeoff Between Accuracy and Compactness in Decision Diagrams for Quantum Computation", IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems 39 12, 4657 (2020).

[87] Benjamin Bichsel, Maximilian Baader, Timon Gehr, and Martin Vechev, Proceedings of the 41st ACM SIGPLAN Conference on Programming Language Design and Implementation 286 (2020) ISBN:9781450376136.

[88] Huo Chen and Daniel A. Lidar, "Hamiltonian open quantum system toolkit", Communications Physics 5 1, 112 (2022).

[89] Emanuel Colella, Spencer Beloin, Luca Bastianelli, Valter Mariani Primiani, Franco Moglie, and Gabriele Gradoni, "Variational Quantum Shot-Based Simulations for Waveguide Modes", IEEE Transactions on Microwave Theory and Techniques 72 4, 2084 (2024).

[90] Tridiv Swain, Sushruta Mishra, Deepak Gupta, and Ahmed Alkhayyat, Lecture Notes in Networks and Systems 537, 411 (2023) ISBN:978-981-99-3009-8.

[91] Fang Li, Xin Liu, Yong Liu, Pengpeng Zhao, Yuling Yang, Honghui Shang, Weizhe Sun, Zhen Wang, Enming Dong, and Dexun Chen, Proceedings of the International Conference for High Performance Computing, Networking, Storage and Analysis 1 (2021) ISBN:9781450384421.

[92] Zenisha Devani, Zeel Kanudawala, Rohan Thakar, Charmi Padh, and Himani Trivedi, Studies in Computational Intelligence 1256, 265 (2026) ISBN:978-981-95-6275-6.

[93] Yanjun Ji, Sebastian Brandhofer, and Ilia Polian, 2022 IEEE International Conference on Quantum Computing and Engineering (QCE) 204 (2022) ISBN:978-1-6654-9113-6.

[94] Stefan Hillmich, Alwin Zulehner, and Robert Wille, 2020 25th Asia and South Pacific Design Automation Conference (ASP-DAC) 115 (2020) ISBN:978-1-7281-4123-7.

[95] Carlos Riascos-Moreno, Andrés Marino Álvarez-Meza, and German Castellanos-Dominguez, "Pulse-Driven Spin Paradigm for Noise-Aware Quantum Classification", Computers 14 11, 475 (2025).

[96] Salonik Resch and Ulya R. Karpuzcu, "Benchmarking Quantum Computers and the Impact of Quantum Noise", ACM Computing Surveys 54 7, 1 (2022).

[97] Kesha Hietala, Robert Rand, Shih-Han Hung, Xiaodi Wu, and Michael Hicks, "A verified optimizer for Quantum circuits", Proceedings of the ACM on Programming Languages 5 POPL, 1 (2021).

[98] Kyungbae Jang, Gyeongju Song, Hyunjun Kim, Hyeokdong Kwon, Hyunji Kim, and Hwajeong Seo, "Efficient Implementation of PRESENT and GIFT on Quantum Computers", Applied Sciences 11 11, 4776 (2021).

[99] Jinyoung Ha, Jonghyun Lee, and Jun Heo, "Resource analysis and modifications of quantum computing with noisy qubits for elliptic curve discrete logarithms", Scientific Reports 14 1, 3927 (2024).

[100] Kyungbae Jang, Hwajeong Seo, and Anupam Chattopadhyay, "Improved Quantum Cryptanalysis of MD5 and SHA-1", IEEE Access 14, 56694 (2026).

[101] Nicholas H. Stair and Francesco A. Evangelista, "QForte: An Efficient State-Vector Emulator and Quantum Algorithms Library for Molecular Electronic Structure", Journal of Chemical Theory and Computation 18 3, 1555 (2022).

[102] Kyungbae Jang, Yujin Oh, and Hwajeong Seo, "Depth-Optimized Quantum Circuit of Gauss–Jordan Elimination", Applied Sciences 14 19, 8579 (2024).

[103] Yu-Cheng Lin, Chuan-Chi Wang, Chia-Heng Tu, and Shih-Hao Hung, Proceedings of the 39th ACM/SIGAPP Symposium on Applied Computing 1487 (2024) ISBN:9798400702433.

[104] Renke Huang, Chenyang Li, and Francesco A. Evangelista, "Leveraging Small-Scale Quantum Computers with Unitarily Downfolded Hamiltonians", PRX Quantum 4 2, 020313 (2023).

[105] S Vigneshwaran, P Vignesh, R. Anuradha, and N. Sathishkumar, 2023 International Conference on Quantum Technologies, Communications, Computing, Hardware and Embedded Systems Security (iQ-CCHESS) 1 (2023) ISBN:979-8-3503-1494-6.

[106] Prakash Murali, Ali Javadi-Abhari, Frederic T. Chong, and Margaret Martonosi, "Formal constraint-based compilation for noisy intermediate-scale quantum systems", Microprocessors and Microsystems 66, 102 (2019).

[107] Augustin Borgna and Rafael Romero, "Encoding High-level Quantum Programs as SZX-diagrams", Electronic Proceedings in Theoretical Computer Science 394, 141 (2023).

[108] Mehmet KARAKÖSE, Hasan YETİŞ, Osman Furkan KÜÇÜK, Çağatay Umut ÖĞDÜ, and Orhan YAMAN, "Kuantum Programlama Açısından Kuantum Derleyicilerin Karşılaştırmalı Analizi ve IBMQ Uygulaması", Adıyaman Üniversitesi Mühendislik Bilimleri Dergisi 10 21, 227 (2023).

[109] A. Jiménez-Pastor, K. G. Larsen, M. Tribastone, and M. Tschaikowski, Lecture Notes in Computer Science 14571, 343 (2024) ISBN:978-3-031-57248-7.

[110] Gyeongju Song, Kyungbae Jang, Hyunji Kim, Wai-Kong Lee, Zhi Hu, and Hwajeong Seo, Lecture Notes in Computer Science 13218, 421 (2022) ISBN:978-3-031-08895-7.

[111] Ying-Yi Hong and Dylan Josh Domingo Lopez, "A Review on Quantum Machine Learning in Applied Systems and Engineering", IEEE Access 13, 144607 (2025).

[112] Thomas Grurl, Jurgen Fub, and Robert Wille, 2021 IEEE 51st International Symposium on Multiple-Valued Logic (ISMVL) 87 (2021) ISBN:978-1-7281-9224-6.

[113] Wai-Kong Lee, Kyungbae Jang, Gyeongju Song, Hyunji Kim, Seong Oun Hwang, and Hwajeong Seo, "Efficient Implementation of Lightweight Hash Functions on GPU and Quantum Computers for IoT Applications", IEEE Access 10, 59661 (2022).

[114] Corey Trahan, Mark Loveland, and Samuel Dent, "Quantum Physics-Informed Neural Networks", Entropy 26 8, 649 (2024).

[115] Mostafizar Rahman and Goutam Paul, "Grover on KATAN: Quantum Resource Estimation", IEEE Transactions on Quantum Engineering 3, 1 (2022).

[116] Yuhong Song, Edwin Hsing-Mean Sha, Qingfeng Zhuge, Rui Xu, and Han Wang, "Efficient algorithm for full-state quantum circuit simulation with DD compression while maintaining accuracy", Quantum Information Processing 22 11, 413 (2023).

[117] Yudong Cao, Jonathan Romero, Jonathan P. Olson, Matthias Degroote, Peter D. Johnson, Mária Kieferová, Ian D. Kivlichan, Tim Menke, Borja Peropadre, Nicolas P. D. Sawaya, Sukin Sim, Libor Veis, and Alán Aspuru-Guzik, "Quantum Chemistry in the Age of Quantum Computing", Chemical Reviews 119 19, 10856 (2019).

[118] Jingzhe Guo and Mingsheng Ying, "Software Pipelining for Quantum Loop Programs", IEEE Transactions on Software Engineering 49 4, 2815 (2023).

[119] Jinyoung Ha, Yujin Kang, Jonghyun Lee, and Jun Heo, "Architectures for lattice surgery-based surface code quantum computing under 3-dimensional nearest-neighbor connectivity", Quantum Information Processing 24 6, 164 (2025).

[120] Martin Elsman and Troels Henriksen, Proceedings of the 11th ACM SIGPLAN International Workshop on Libraries, Languages and Compilers for Array Programming 28 (2025) ISBN:9798400719271.

[121] Robert Wille, Rod Van Meter, and Yehuda Naveh, 2019 Design, Automation & Test in Europe Conference & Exhibition (DATE) 1234 (2019) ISBN:978-3-9819263-2-3.

[122] Barbora Hrdá and Sascha Wessel, Proceedings of the 18th International Conference on Availability, Reliability and Security 1 (2023) ISBN:9798400707728.

[123] Patrick Rebentrost, Brajesh Gupt, and Thomas R. Bromley, "Quantum computational finance: Monte Carlo pricing of financial derivatives", Physical Review A 98 2, 022321 (2018).

[124] Jin-Guo Liu and Lei Wang, "Differentiable learning of quantum circuit Born machines", Physical Review A 98 6, 062324 (2018).

[125] Jingzhe Guo, Huazhe Lou, Jintao Yu, Riling Li, Wang Fang, Junyi Liu, Peixun Long, Shenggang Ying, and Mingsheng Ying, "isQ: An Integrated Software Stack for Quantum Programming", IEEE Transactions on Quantum Engineering 4, 1 (2023).

[126] Luciano Marrero, Verena Olsowy, Juan Fernández Sosa, Fernando Tesone, Leonardo Corbalán, Pablo Thomas, and Patricia Pesado, Communications in Computer and Information Science 2520, 197 (2026) ISBN:978-3-032-00717-9.

[127] Manuel De Stefano, Fabiano Pecorelli, Dario Di Nucci, Fabio Palomba, and Andrea De Lucia, "Software engineering for quantum programming: How far are we?", Journal of Systems and Software 190, 111326 (2022).

[128] Ercüment Kaya, Burak Mete, Laura Schulz, Muhammad Nufail Farooqi, Jorge Echavarria, and Martin Schulz, 2024 IEEE International Conference on Quantum Computing and Engineering (QCE) 286 (2024) ISBN:979-8-3315-4137-8.

[129] Dhaval Mehta, Amol Ranadive, Jigna B. Prajapati, and Rajiv Pandey, Studies in Computational Intelligence 1085, 311 (2023) ISBN:978-981-19-9529-3.

[130] Thomas Grurl, Jurgen Fus, and Robert Wille, "Noise-Aware Quantum Circuit Simulation With Decision Diagrams", IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems 42 3, 860 (2023).

[131] Khaled Khalfaoui, El Hillali Kerkouche, Tahar Boudjedaa, and Allaoua Chaoui, "Optimized exploration of quantum circuits space based on sub-circuits equivalences", Quantum Information Processing 22 1, 71 (2023).

[132] Mark Fingerhuth, Tomáš Babej, Peter Wittek, and Leonie Anna Mueck, "Open source software in quantum computing", PLOS ONE 13 12, e0208561 (2018).

[133] Alwin Zulehner, Philipp Niemann, Rolf Drechsler, and Robert Wille, 2019 Design, Automation & Test in Europe Conference & Exhibition (DATE) 280 (2019) ISBN:978-3-9819263-2-3.

[134] Matthias Möller and Merel Schalkers, Lecture Notes in Computer Science 12142, 451 (2020) ISBN:978-3-030-50432-8.

[135] M. P. Madhu and Sunanda Dixit, Lecture Notes on Data Engineering and Communications Technologies 44, 714 (2020) ISBN:978-3-030-37050-3.

[136] David Wierichs, Christian Gogolin, and Michael Kastoryano, "Avoiding local minima in variational quantum eigensolvers with the natural gradient optimizer", Physical Review Research 2 4, 043246 (2020).

[137] Hai-Ling Liu, Yu-Sen Wu, Lin-Chun Wan, Shi-Jie Pan, Su-Juan Qin, Fei Gao, and Qiao-Yan Wen, "Variational quantum algorithm for the Poisson equation", Physical Review A 104 2, 022418 (2021).

[138] Yukio Kawashima, Erika Lloyd, Marc P. Coons, Yunseong Nam, Shunji Matsuura, Alejandro J. Garza, Sonika Johri, Lee Huntington, Valentin Senicourt, Andrii O. Maksymov, Jason H. V. Nguyen, Jungsang Kim, Nima Alidoust, Arman Zaribafiyan, and Takeshi Yamazaki, "Optimizing electronic structure simulations on a trapped-ion quantum computer using problem decomposition", Communications Physics 4 1, 245 (2021).

[139] Prakash Verma, Lee Huntington, Marc P. Coons, Yukio Kawashima, Takeshi Yamazaki, and Arman Zaribafiyan, "Scaling up electronic structure calculations on quantum computers: The frozen natural orbital based method of increments", The Journal of Chemical Physics 155 3, 034110 (2021).

[140] Krishanu Sankar, Artur Scherer, Satoshi Kako, Sam Reifenstein, Navid Ghadermarzy, Willem B. Krayenhoff, Yoshitaka Inui, Edwin Ng, Tatsuhiro Onodera, Pooya Ronagh, and Yoshihisa Yamamoto, "A benchmarking study of quantum algorithms for combinatorial optimization", npj Quantum Information 10 1, 64 (2024).

[141] Alexander McCaskey, Eugene Dumitrescu, Dmitry Liakh, and Travis Humble, 2018 IEEE International Conference on Rebooting Computing (ICRC) 1 (2018) ISBN:978-1-5386-9170-0.

[142] Vikas Hassija, Vinay Chamola, Vikas Saxena, Vaibhav Chanana, Prakhar Parashari, Shahid Mumtaz, and Mohsen Guizani, "Present landscape of quantum computing", IET Quantum Communication 1 2, 42 (2020).

[143] Debjyoti Bhattacharjee, Amit Saha, Junde Li, Koustubh Phalak, Avimita Chatterjee, Jeremie Pope, Swaroop Ghosh, and Anupam Chattopadhyay, Communications in Computer and Information Science 2377, 206 (2025) ISBN:978-3-031-81980-3.

[144] Samuel Jaques and Thomas Häner, "Leveraging State Sparsity for More Efficient Quantum Simulations", ACM Transactions on Quantum Computing 3 3, 1 (2022).

[145] Yunya Liu, Jiakun Liu, Jordan R. Raney, and Pai Wang, "Quantum computing for solid mechanics and structural engineering – A demonstration with Variational Quantum Eigensolver", Extreme Mechanics Letters 67, 102117 (2024).

[146] Chenyang Jiao, Weihua Zhang, and Li Shen, "Communication-Partition Co-Optimization for Quantum Circuit Simulation on CPU+GPU Clusters", IEEE Transactions on Parallel and Distributed Systems 37 6, 1280 (2026).

[147] Tuan Hai Vu, Vu Trung Duong Le, Hoai Luan Pham, Quoc Chuong Nguyen, and Yasuhiko Nakashima, "FQsun: A Configurable Wave Function-Based Quantum Emulator for Power-Efficient Quantum Simulations", IEEE Access 13, 93271 (2025).

[148] Siyi Wang and Anupam Chattopadhyay, Computer Architecture and Design Methodologies 119 (2026) ISBN:978-981-95-6038-7.

[149] Shaun Miller, 2020 IEEE Computer Society Annual Symposium on VLSI (ISVLSI) 141 (2020) ISBN:978-1-7281-5775-7.

[150] Vincent Russo, "toqito -- Theory of quantum information toolkit: A Python package for studying quantum information", Journal of Open Source Software 6 61, 3082 (2021).

[151] Róbert Izsák, Christoph Riplinger, Nick S. Blunt, Bernardo de Souza, Nicole Holzmann, Ophelia Crawford, Joan Camps, Frank Neese, and Patrick Schopf, "Quantum computing in pharma: A multilayer embedding approach for near future applications", Journal of Computational Chemistry 44 3, 406 (2023).

[152] Pranav Gokhale, Yongshan Ding, Thomas Propson, Christopher Winkler, Nelson Leung, Yunong Shi, David I. Schuster, Henry Hoffmann, and Frederic T. Chong, Proceedings of the 52nd Annual IEEE/ACM International Symposium on Microarchitecture 266 (2019) ISBN:9781450369381.

[153] Hao Tang, José Leonardo Simancas-García, Jianming Mai, Minghao Cheng, Imran Iqbal, and Lip Yee Por, "Overview of Digital Quantum Simulator: Applications and Comparison with Latest Methods", SPIN 15 02, 2440004 (2025).

[154] Ilya G. Ryabinkin, Tzu-Ching Yen, Scott N. Genin, and Artur F. Izmaylov, "Qubit Coupled Cluster Method: A Systematic Approach to Quantum Chemistry on a Quantum Computer", Journal of Chemical Theory and Computation 14 12, 6317 (2018).

[155] Oumarou Oumarou, Alexandru Paler, and Robert Basmadjian, 2020 IEEE Computer Society Annual Symposium on VLSI (ISVLSI) 126 (2020) ISBN:978-1-7281-5775-7.

[156] Yuan-Hung Tsai, Jie-Hong R. Jiang, and Chiao-Shan Jhang, 2021 58th ACM/IEEE Design Automation Conference (DAC) 439 (2021) ISBN:978-1-6654-3274-0.

[157] Axel Dahlberg, Bart van der Vecht, Carlo Delle Donne, Matthew Skrzypczyk, Ingmar te Raa, Wojciech Kozlowski, and Stephanie Wehner, "NetQASM—a low-level instruction set architecture for hybrid quantum–classical programs in a quantum internet", Quantum Science and Technology 7 3, 035023 (2022).

[158] Yi Fan, Jie Liu, Xiongzhi Zeng, Zhiqian Xu, Honghui Shang, Zhenyu Li, and Jinlong Yang, "Q<sup>2</sup>Chemistry: A quantum computation platform for quantum chemistry", JUSTC 52 12, 2 (2022).

[159] Peng Fu, Kohei Kishida, Neil J. Ross, and Peter Selinger, "Proto-Quipper with Reversing and Control", Electronic Proceedings in Theoretical Computer Science 426, 1 (2025).

[160] Oscar Higgott, Daochen Wang, and Stephen Brierley, "Variational Quantum Computation of Excited States", Quantum 3, 156 (2019).

[161] Zhenyu Huang, Fuxin Zhang, and Dongdai Lin, Lecture Notes in Computer Science 15601, 155 (2025) ISBN:978-3-031-91106-4.

[162] Yasunari Suzuki, Yoshiaki Kawase, Yuya Masumura, Yuria Hiraga, Masahiro Nakadai, Jiabao Chen, Ken M. Nakanishi, Kosuke Mitarai, Ryosuke Imai, Shiro Tamiya, Takahiro Yamamoto, Tennin Yan, Toru Kawakubo, Yuya O. Nakagawa, Yohei Ibe, Youyuan Zhang, Hirotsugu Yamashita, Hikaru Yoshimura, Akihiro Hayashi, and Keisuke Fujii, "Qulacs: a fast and versatile quantum circuit simulator for research purpose", Quantum 5, 559 (2021).

[163] Yujin Oh, Kyungbae Jang, Sejin Lim, Yujin Yang, and Hwajeong Seo, 2023 International Conference on Platform Technology and Service (PlatCon) 67 (2023) ISBN:979-8-3503-0599-9.

[164] Quoc Chuong Nguyen, Le Bin Ho, Lan Nguyen Tran, and Hung Q Nguyen, "Qsun: an open-source platform towards practical quantum machine learning applications", Machine Learning: Science and Technology 3 1, 015034 (2022).

[165] Waylon Luo, Cheng-Chang Lu, Tong Zhan, and Qiang Guan, Proceedings of the SC '25 Workshops of the International Conference for High Performance Computing, Networking, Storage and Analysis 1851 (2025) ISBN:9798400718717.

[166] Matthew Otten and Stephen K. Gray, "Accounting for errors in quantum algorithms via individual error reduction", npj Quantum Information 5 1, 11 (2019).

[167] Thomas Ayral, François-Marie Le Régent, Zain Saleem, Yuri Alexeev, and Martin Suchara, "Quantum Divide and Compute: Exploring the Effect of Different Noise Sources", SN Computer Science 2 3, 132 (2021).

[168] Archita Bhattacharyya, Mrinal Kanti Debbarma, and Rabindra K. Barik, 2025 International Conference on Networks and Cryptology (NETCRYPT) 1324 (2025) ISBN:979-8-3315-2605-4.

[169] Ang Li, Omer Subasi, Xiu Yang, and Sriram Krishnamoorthy, SC20: International Conference for High Performance Computing, Networking, Storage and Analysis 1 (2020) ISBN:978-1-7281-9998-6.

[170] Thomas Häner, Damian S. Steiger, Torsten Hoefler, and Matthias Troyer, Proceedings of the International Conference for High Performance Computing, Networking, Storage and Analysis 1 (2021) ISBN:9781450384421.

[171] Kanishk Dwivedi, Majid Haghparast, and Tommi Mikkonen, "Quantum software engineering and quantum software development lifecycle: a survey", Cluster Computing 27 6, 7127 (2024).

[172] Peter Horoschenkoff, Jasper Rödiger, and Martin Wilske, "A new control and management architecture for SDN-enabled quantum key distribution networks", Journal of Optical Communications and Networking 17 3, 209 (2025).

[173] Ivan Cvitić, Dragan Peraković, and Josip Vladava, Lecture Notes of the Institute for Computer Sciences, Social Informatics and Telecommunications Engineering 542, 3 (2024) ISBN:978-3-031-50050-3.

[174] Aravind Aji, Kurunandan Jain, and Prabhakar Krishnan, 2021 2nd Global Conference for Advancement in Technology (GCAT) 1 (2021) ISBN:978-1-6654-1836-2.

[175] Maria Belkhir, Haroun Benkaouha, and Elhadj Benkhelifa, 2022 Ninth International Conference on Software Defined Systems (SDS) 1 (2022) ISBN:979-8-3503-4671-8.

[176] Davide Ferrari and Michele Amoretti, "Efficient and effective quantum compiling for entanglement-based machine learning on IBM Q devices", International Journal of Quantum Information 16 08, 1840006 (2018).

[177] Yun-Zhuo Fan and Dan-Bo Zhang, "Full counting statistics of particle distribution on a digital quantum computer", Physical Review A 109 1, 012412 (2024).

[178] He-Liang Huang, Xiao-Yue Xu, Chu Guo, Guojing Tian, Shi-Jie Wei, Xiaoming Sun, Wan-Su Bao, and Gui-Lu Long, "Near-term quantum computing techniques: Variational quantum algorithms, error mitigation, circuit compilation, benchmarking and classical simulation", Science China Physics, Mechanics & Astronomy 66 5, 250302 (2023).

[179] Armin Ahmadzadeh and Hamid Sarbazi-Azad, "Fast and scalable quantum computing simulation on multi-core and many-core platforms", Quantum Information Processing 22 5, 215 (2023).

[180] Agustín Borgna, Simon Perdrix, and Benoît Valiron, Lecture Notes in Computer Science 13008, 121 (2021) ISBN:978-3-030-89050-6.

[181] Zihao Li, Ji Guan, and Mingsheng Ying, Lecture Notes in Computer Science 16556, 578 (2026) ISBN:978-3-032-26203-5.

[182] Kyungbae Jang, Wonwoong Kim, Sejin Lim, Yeajun Kang, Yujin Yang, and Hwajeong Seo, Lecture Notes in Computer Science 13720, 251 (2023) ISBN:978-3-031-25658-5.

[183] Stavros Efthymiou, Marco Lazzarin, Andrea Pasquale, and Stefano Carrazza, "Quantum simulation with just-in-time compilation", Quantum 6, 814 (2022).

[184] Kyungbae Jang, Gyeongju Song, Hyunjun Kim, Hyeokdong Kwon, Hyunji Kim, and Hwajeong Seo, "Parallel quantum addition for Korean block ciphers", Quantum Information Processing 21 11, 373 (2022).

[185] Amr Elsharkawy, Xiao-Ting Michelle To, Philipp Seitz, Yanbin Chen, Yannick Stade, Manuel Geiger, Qunsheng Huang, Xiaorang Guo, Muhammad Arslan Ansari, Christian B. Mendl, Dieter Kranzlmüller, and Martin Schulz, "Integration of Quantum Accelerators with High Performance Computing—A Review of Quantum Programming Tools", ACM Transactions on Quantum Computing 6 3, 1 (2025).

[186] Nicholas Meinhardt, Bastiaan Dekker, Niels M. P. Neumann, and Frank Phillipson, "Implementation of a Variational Quantum Circuit for Machine Learning with Compact Data Representation", Digitale Welt 4 1, 95 (2020).

[187] Bui Cuong Nguyen, Van Long Nguyen, T A Nguyen, Sy Nam Tran, D L Tran, and D L Hoang, "MKV: a new block cipher for the post-quantum cryptography transition", Математические вопросы криптографии 16 2, 113 (2025).

[188] Shubham, Prachi Sajwan, and N. Jayapandian, 2019 Third International conference on I-SMAC (IoT in Social, Mobile, Analytics and Cloud) (I-SMAC) 598 (2019) ISBN:978-1-7281-4365-1.

[189] Liyi Li, David Young, James Bryan Graves, Chandeepa Dissanayake, and Amr Sabry, "A Haskell Adiabatic DSL: Solving Classical Optimization Problems on Quantum Hardware", Proceedings of the ACM on Programming Languages 9 ICFP, 479 (2025).

[190] Raphael Seidel, René Zander, Matic Petrič, Niklas Steinmann, David Liu, Nikolay Tcholtchev, and Manfred Hauswirth, "Quantum Backtracking in Qrisp Applied to Sudoku Problems", ACM Transactions on Quantum Computing 7 3, 1 (2026).

[191] Diksha Chawla, Khushboo Jain, Pawan Singh Mehra, Ashok Kumar Das, and Basudeb Bera, "Quantum cryptography as a solution for secure Wireless Sensor Networks: Roadmap, challenges and solutions", Internet of Things 32, 101610 (2025).

[192] Haodong Bian, Jianqiang Huang, Runting Dong, Yuluo Guo, and Xiaoying Wang, Lecture Notes in Computer Science 12453, 111 (2020) ISBN:978-3-030-60238-3.

[193] Călin A. Georgescu, Merel A. Schalkers, and Matthias Möller, "qlbm – A quantum lattice Boltzmann software framework", Computer Physics Communications 315, 109699 (2025).

[194] Kyungbae Jang, Wonwoong Kim, Sejin Lim, Yeajun Kang, Yujin Yang, and Hwajeong Seo, "Quantum Binary Field Multiplication with Optimized Toffoli Depth and Extension to Quantum Inversion", Sensors 23 6, 3156 (2023).

[195] Nathan Killoran, Josh Izaac, Nicolás Quesada, Ville Bergholm, Matthew Amy, and Christian Weedbrook, "Strawberry Fields: A Software Platform for Photonic Quantum Computing", Quantum 3, 129 (2019).

[196] Sabia Hassan and Kaisar J. Giri, "Q-ST: A Comprehensive Review of Quantum Software and Toolchains, Ecosystems, and Technologies", Archives of Computational Methods in Engineering (2026).

[197] Shallu Saini, Manuj Saini, Hardeep Singh Tuli, Jatin Saini, Shreya Nagpal, Priti Duhan, and Poonam Bansal, Artificial Intelligence in Biotechnology 283 (2026) ISBN:9783119145183.

[198] David Plankensteiner, Christoph Hotter, and Helmut Ritsch, "QuantumCumulants.jl: A Julia framework for generalized mean-field equations in open quantum systems", Quantum 6, 617 (2022).

[199] Maria Heloísa Fraga da Silva, Gleydson Fernandes de Jesus, and Clebson Cruz, "Effect of Pure Dephasing Quantum Noise in the Quantum Search Algorithm Using Atos Quantum Assembly", Entropy 26 8, 668 (2024).

[200] Wei-You Liao, Xiang Wang, Xiao-Yue Xu, Chen Ding, Shuo Zhang, He-Liang Huang, and Chu Guo, "JuliVQC.jl: an efficient variational quantum circuit simulator for near-term quantum algorithms", The European Physical Journal Special Topics 234 20, 6223 (2025).

[201] Michael Kühn, Sebastian Zanker, Peter Deglmann, Michael Marthaler, and Horst Weiß, "Accuracy and Resource Estimations for Quantum Chemistry on a Near-Term Quantum Computer", Journal of Chemical Theory and Computation 15 9, 4764 (2019).

[202] Suryansh Upadhyay, Mahabubul Alam, and Swaroop Ghosh, Handbook of Computer Architecture 1 (2023) ISBN:978-981-15-6401-7.

[203] Alessio Cicero, Mohammad Ali Maleki, Muhammad Waqar Azhar, Anton Frisk Kockum, and Pedro Trancoso, "Simulation of Quantum Computers: Review and Acceleration Opportunities", ACM Transactions on Quantum Computing 7 1, 1 (2026).

[204] Taoreed A. Akinola, Xiangfang Li, Richard Wilkins, Pamela H. Obiomon, and Lijun Qian, "Robust Inverse Quantum Fourier Transform Inspired Algorithm for Unsupervised Image Segmentation", IEEE Access 12, 99029 (2024).

[205] Giulia Meuli, Mathias Soeken, and Giovanni De Micheli, "Xor-And-Inverter Graphs for Quantum Compilation", npj Quantum Information 8 1, 7 (2022).

[206] Tianyin Li, Wai Kin Lai, Enke Wang, and Hongxi Xing, "Scattering amplitude from quantum computing with reduction formula", Physical Review D 109 3, 036025 (2024).

[207] Mathias Soeken, Martin Roetteler, Nathan Wiebe, and Giovanni De Micheli, "LUT-Based Hierarchical Reversible Logic Synthesis", IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems 38 9, 1675 (2019).

[208] Xiu-Zhe Luo, Jin-Guo Liu, Pan Zhang, and Lei Wang, "Yao.jl: Extensible, Efficient Framework for Quantum Algorithm Design", Quantum 4, 341 (2020).

[209] Yongsoo Hwang, Taewan Kim, Chungheon Baek, and Byung-Soo Choi, "Integrated Analysis of Performance and Resources in Large-Scale Quantum Computing", Physical Review Applied 13 5, 054033 (2020).

[210] Xuan-Bach Le, Shang-Wei Lin, Jun Sun, and David Sanan, "A Quantum interpretation of separating conjunction for local reasoning of Quantum programs based on separation logic", Proceedings of the ACM on Programming Languages 6 POPL, 1 (2022).

[211] Dayton C. Closser and Zbigniew J. Kabala, "Pushing the Limits of Large Language Models in Quantum Operations", Quantum Reports 8 1, 7 (2026).

[212] Ussama Assad, Muhammad Arshad Shehzad Hassan, Umar Farooq, Asif Kabir, Muhammad Zeeshan Khan, S. Sabahat H. Bukhari, Zain ul Abidin Jaffri, Judit Oláh, and József Popp, "Smart Grid, Demand Response and Optimization: A Critical Review of Computational Methods", Energies 15 6, 2003 (2022).

[213] Leon Riesebos, Brad Bondurant, Jacob Whitlow, Junki Kim, Mark Kuzyk, Tianyi Chen, Samuel Phiri, Ye Wang, Chao Fang, Andrew Van Horn, Jungsang Kim, and Kenneth R. Brown, 2022 IEEE International Conference on Quantum Computing and Engineering (QCE) 545 (2022) ISBN:978-1-6654-9113-6.

[214] Eduard Grigoryan, Sachin Kumar, and Placido Rogério Pinheiro, "A Review on Models and Applications of Quantum Computing", Quantum Reports 7 3, 39 (2025).

[215] Johanna Barzen, Frank Leymann, Michael Falkenthal, Daniel Vietz, Benjamin Weder, and Karoline Wild, Communications in Computer and Information Science 1399, 25 (2021) ISBN:978-3-030-72368-2.

[216] Ritvik Sharma and Sara Achour, "Optimizing Ancilla-Based Quantum Circuits with SPARE", Proceedings of the ACM on Programming Languages 9 PLDI, 176 (2025).

[217] Michael L. Wall, Matthew R. Abernathy, and Gregory Quiroz, "Generative machine learning with tensor networks: Benchmarks on near-term quantum computers", Physical Review Research 3 2, 023010 (2021).

[218] Lukas Burgholzer, Antonio Jimenez-Pastor, Kim Guldstrand Larsen, Mirco Tribastone, Max Tschaikowski, and Robert Wille, "Forward and Backward Constrained Bisimulations for Quantum Circuits Using Decision Diagrams", ACM Transactions on Quantum Computing 6 2, 1 (2025).

[219] Stavros Efthymiou, Sergi Ramos-Calderer, Carlos Bravo-Prieto, Adrián Pérez-Salinas, Diego García-Martín, Artur Garcia-Saez, José Ignacio Latorre, and Stefano Carrazza, " Qibo: a framework for quantum simulation with hardware acceleration", Quantum Science and Technology 7 1, 015018 (2022).

[220] Shabnam Sodagari and Ali Rezaei, 2025 IEEE Integrated STEM Education Conference (ISEC) 1 (2025) ISBN:979-8-3315-1343-6.

[221] Christopher John Wright, Mikel Luján, Pavlos Petoumenos, and John Goodacre, Proceedings of the 21st ACM SIGPLAN International Conference on Managed Programming Languages and Runtimes 65 (2024) ISBN:9798400711183.

[222] Usha Giri and Fathi Amsaad, NAECON 2025 - IEEE National Aerospace and Electronics Conference 1 (2025) ISBN:979-8-3315-3813-2.

[223] Nguyen Tan Viet, Nguyen Thi Chuong, Vu Thi Ngoc Huyen, and Le Bin Ho, "tqix.pis: A toolbox for quantum dynamics simulation of spin ensembles in Dicke basis", Computer Physics Communications 286, 108686 (2023).

[224] Siyi Wang, Kyungbae Jang, Anubhab Baksi, Sumanta Chakraborty, Bryan Lee, Anupam Chattopadhyay, and Hwajeong Seo, Lecture Notes in Computer Science 16372, 339 (2026) ISBN:978-3-032-13300-7.

[225] Jonathan Romero and Alán Aspuru‐Guzik, "Variational Quantum Generators: Generative Adversarial Quantum Machine Learning for Continuous Distributions", Advanced Quantum Technologies 4 1, 2000003 (2021).

[226] Felipe Ferreira and José Campos, "An exploratory study on the usage of quantum programming languages", Science of Computer Programming 240, 103217 (2025).

[227] Ludwig Schmid, David F Locher, Manuel Rispler, Sebastian Blatt, Johannes Zeiher, Markus Müller, and Robert Wille, "Computational capabilities and compiler development for neutral atom quantum processors—connecting tool developers and hardware experts", Quantum Science and Technology 9 3, 033001 (2024).

[228] Pavlo V. Zahorodk, Yevhenii O. Modlo, Olga O. Kalinichenko, Tetiana V. Selivanova, and Serhiy O. Semerikov, Quantum enhanced machine learning: An overview (2021).

[229] Yongshan Ding, Xin-Chuan Wu, Adam Holmes, Ash Wiseth, Diana Franklin, Margaret Martonosi, and Frederic T. Chong, 2020 ACM/IEEE 47th Annual International Symposium on Computer Architecture (ISCA) 570 (2020) ISBN:978-1-7281-4661-4.

[230] Tom Krüger and Wolfgang Mauerer, Proceedings of the IEEE/ACM 42nd International Conference on Software Engineering Workshops 445 (2020) ISBN:9781450379632.

[231] Thomas Häner, Torsten Hoefler, and Matthias Troyer, "Assertion-based optimization of Quantum programs", Proceedings of the ACM on Programming Languages 4 OOPSLA, 1 (2020).

[232] Gabriel Greene‐Diniz and David Muñoz Ramo, "Generalized unitary coupled cluster excitations for multireference molecular states optimized by the variational quantum eigensolver", International Journal of Quantum Chemistry 121 4, e26352 (2021).

[233] Damian S. Steiger, Thomas Häner, and Matthias Troyer, "Advantages of a modular high-level quantum programming framework", Microprocessors and Microsystems 66, 81 (2019).

[234] Tianyin Li, Xingyu Guo, Wai Kin Lai, Xiaohui Liu, Enke Wang, Hongxi Xing, Dan-Bo Zhang, and Shi-Liang Zhu, "Partonic collinear structure by quantum computing", Physical Review D 105 11, L111502 (2022).

[235] Yanjun Ji, Kathrin F. Koenig, and Ilia Polian, "Optimizing quantum algorithms on bipotent architectures", Physical Review A 108 2, 022610 (2023).

[236] Zhi-Quan Shi, Fang-Gang Duan, and Dan-Bo Zhang, "Locating quantum critical points with shallow quantum circuits", Physics Letters A 463, 128683 (2023).

[237] Chenyang Jiao, Weihua Zhang, and Li Shen, Proceedings of the 52nd International Conference on Parallel Processing 203 (2023) ISBN:9798400708435.

[238] Philipp Altmann, Jonas Stein, Michael Kölle, Adelina Bärligea, Maximilian Zorn, Thomas Gabor, Thomy Phan, Sebastian Feld, and Claudia Linnhoff-Popien, 2024 IEEE International Conference on Quantum Computing and Engineering (QCE) 1600 (2024) ISBN:979-8-3315-4137-8.

[239] X. Fu, Jintao Yu, Xing Su, Hanru Jiang, Hua Wu, Fucheng Cheng, Xi Deng, Jinrong Zhang, Lei Jin, Yihang Yang, Le Xu, Chunchao Hu, Anqi Huang, Guangyao Huang, Xiaogang Qiang, Mingtang Deng, Ping Xu, Weixia Xu, Wanwei Liu, Yu Zhang, Yuxin Deng, Junjie Wu, and Yuan Feng, "Quingo: A Programming Framework for Heterogeneous Quantum-Classical Computing with NISQ Features", ACM Transactions on Quantum Computing 2 4, 1 (2021).

[240] Geng-Li Zhang, Di Liu, and Man-Hong Yung, "Observation of exceptional point in a PT broken non-Hermitian system simulated using a quantum circuit", Scientific Reports 11 1, 13795 (2021).

[241] Antonio García de la Barrera, Ignacio García-Rodríguez de Guzmán, Macario Polo, and José A. Cruz-Lemus, Quantum Software Engineering 167 (2022) ISBN:978-3-031-05323-8.

[242] Muhammad Hamid, Bashir Alam, and Om Pal, Communications in Computer and Information Science 2126, 87 (2025) ISBN:978-3-031-80841-8.

[243] Chuan-Chi Wang, Yan-Jie Wang, Yu-Cheng Lin, Chia-Heng Tu, and Shih-Hao Hung, Proceedings of the 41st ACM/SIGAPP Symposium on Applied Computing 1375 (2026) ISBN:9798400722943.

[244] Marie Salm, Johanna Barzen, Frank Leymann, Benjamin Weder, and Karoline Wild, Communications in Computer and Information Science 1429, 64 (2021) ISBN:978-3-030-87567-1.

[245] Mir Mohammad Yousuf and Shabir Ahmad Sofi, "A systematic exploration of quantum software engineering in the NISQ era: Methods, lifecycle practices, and a taxonomy of challenges", Neurocomputing 673, 132809 (2026).

[246] Waylon Luo, Jiapeng Zhao, Tong Zhan, and Qiang Guan, Proceedings of the 54th International Conference on Parallel Processing 658 (2025) ISBN:9798400720741.

[247] J. A. Bravo-Montes, Miriam Bastante, Guillermo Botella, Alberto del Barrio, and F. García-Herrero, "A methodology to select and adjust quantum noise models through emulators: benchmarking against real backends", EPJ Quantum Technology 11 1, 71 (2024).

[248] Priyanka Mukhopadhyay, "Composability of global phase invariant distance and its application to approximation error management", Journal of Physics Communications 5 11, 115017 (2021).

[249] Rozhin Eskandarpour, Kumar Jang Bahadur Ghosh, Amin Khodaei, Aleksi Paaso, and Liuxi Zhang, "Quantum-Enhanced Grid of the Future: A Primer", IEEE Access 8, 188993 (2020).

[250] Christina Petschnigg, Mathias Brandstotter, Horst Pichler, Michael Hofbaur, and Bernhard Dieber, 2019 International Conference on Robotics and Automation (ICRA) 803 (2019) ISBN:978-1-5386-6027-0.

[251] Alwin Zulehner and Robert Wille, 2019 Design, Automation & Test in Europe Conference & Exhibition (DATE) 90 (2019) ISBN:978-3-9819263-2-3.

[252] Nirupma Pathak, Neeraj Kumar Misra, Bandan Kumar Bhoi, and Santosh Kumar, Smart Innovation, Systems and Technologies 235, 523 (2022) ISBN:978-981-16-2876-4.

[253] Thien Nguyen and Alexander J. McCaskey, "Extending Python for Quantum-classical Computing via Quantum Just-in-time Compilation", ACM Transactions on Quantum Computing 3 4, 1 (2022).

[254] P. Krantz, M. Kjaergaard, F. Yan, T. P. Orlando, S. Gustavsson, and W. D. Oliver, "A quantum engineer's guide to superconducting qubits", Applied Physics Reviews 6 2, 021318 (2019).

[255] Tyson Jones, Anna Brown, Ian Bush, and Simon C. Benjamin, "QuEST and High Performance Simulation of Quantum Computers", Scientific Reports 9 1, 10736 (2019).

[256] Martin Kong, "On the Impact of Affine Loop Transformations in Qubit Allocation", ACM Transactions on Quantum Computing 2 3, 1 (2021).

[257] Anbang Wu, Liqiang Lu, Jianwei Yin, Jingwen Leng, and Minyi Guo, 2026 IEEE International Symposium on High Performance Computer Architecture (HPCA) 1 (2026) ISBN:979-8-3315-9302-5.

[258] Antonio García de la Barrera, Ignacio García‐Rodríguez de Guzmán, Macario Polo, and Mario Piattini, "Quantum software testing: State of the art", Journal of Software: Evolution and Process 35 4, e2419 (2023).

[259] Saumya Priyadarshini, Chandrashekar Jatoth, Rajesh Doriya, and Rajkumar Buyya, "Optimizing qubit transfer in multi-host quantum network using security-oriented entanglement routing algorithm", Optics Communications 596, 132549 (2025).

[260] Win Mathew John, "Quantum Computing Explained: A Beginner's Guide to the Future of Processing", International Journal of Information Technology Research Studies (IJITRS) 1 3, 149 (2025).

[261] Khaled Khalfaoui, Tahar Boudjedaa, and El Hillali Kerkouche, "Automatic design of quantum circuits", Quantum Information Processing 20 9, 283 (2021).

[262] Armin Ahmadzadeh and Hamid Sarbazi-Azad, "Fast scalable and low-power quantum circuit simulation on the cluster of GPUs platforms", Optical and Quantum Electronics 56 10, 1646 (2024).

[263] Zhiqian Xu, Yi Fan, Chu Guo, and Honghui Shang, "MPS-VQE: A variational quantum computational chemistry simulator with matrix product states", Computer Physics Communications 294, 108897 (2024).

[264] Wonho Jang, Koji Terashi, Masahiko Saito, Christian W. Bauer, Benjamin Nachman, Yutaro Iiyama, Ryunosuke Okubo, and Ryu Sawada, "Initial-State Dependent Optimization of Controlled Gate Operations with Quantum Computer", Quantum 6, 798 (2022).

[265] Yuhong Song, Edwin Hsing-Mean Sha, Qingfeng Zhuge, Wenlong Xiao, Qijun Dai, and Longshan Xu, "QuanPath: achieving one-step communication for distributed quantum circuit simulation", Quantum Information Processing 23 1, 1 (2023).

[266] Riya Bansal, Megha Khanna, and Nikhil Kumar Rajput, 2024 2nd International Conference on Advances in Computation, Communication and Information Technology (ICAICCIT) 1296 (2024) ISBN:979-8-3315-4121-7.

[267] F. Orts, E. Filatovas, G. Ortega, J. F. SanJuan-Estrada, and E. M. Garzón, "Improving the number of T gates and their spread in integer multipliers on quantum computing", Physical Review A 107 4, 042621 (2023).

[268] Hua Wu, Yuxin Deng, Ming Xu, and Wenjie Du, Lecture Notes in Computer Science 12545, 307 (2020) ISBN:978-3-030-64275-4.

[269] Vijayarangan Natarajan, Quantum Artificial Intelligence 77 (2025) ISBN:978-981-96-5050-7.

[270] Nan JIANG, XiaoYu CHENG, Jian WANG, and ZiChen WANG, "Quantum programs debug using quantum probabilistic cloning", SCIENTIA SINICA Physica, Mechanica & Astronomica 55 4, 240309 (2025).

[271] Cupjin Huang, Fang Zhang, Michael Newman, Xiaotong Ni, Dawei Ding, Junjie Cai, Xun Gao, Tenghui Wang, Feng Wu, Gengyan Zhang, Hsiang-Sheng Ku, Zhengxiong Tian, Junyin Wu, Haihong Xu, Huanjun Yu, Bo Yuan, Mario Szegedy, Yaoyun Shi, Hui-Hai Zhao, Chunqing Deng, and Jianxin Chen, "Efficient parallelization of tensor network contraction for simulating quantum computation", Nature Computational Science 1 9, 578 (2021).

[272] Jarosław Adam Miszczak, Companion Proceedings of the 7th International Conference on the Art, Science, and Engineering of Programming 101 (2023) ISBN:9798400707551.

[273] JA Bravo-Montes, Miriam Bastante, Cyril Allouche, Stanley Cheah, Cyprien Lambert, Arnaud Gazda, Guillermo Botella, Alberto del Barrio, and F García-Herrero, "Comparative analysis of quantum emulation for high-performance computing centers", SIMULATION 102 7, 449 (2026).

[274] Damien Nguyen, Dmitry Mikushin, and Yung Man-Hong, 2021 Design, Automation & Test in Europe Conference & Exhibition (DATE) 1056 (2021) ISBN:978-3-9819263-5-4.

[275] Hoa T. Nguyen, Muhammad Usman, and Rajkumar Buyya, 2023 IEEE International Conference on Quantum Software (QSW) 21 (2023) ISBN:979-8-3503-0479-4.

[276] Stephen Diadamo, Janis Nötzel, Benjamin Zanger, and Mehmet Mert Beşe, "QuNetSim: A Software Framework for Quantum Networks", IEEE Transactions on Quantum Engineering 2, 1 (2021).

[277] Jorge Vázquez-Pérez, César Piñeiro, Juan C. Pichel, Tomás F. Pena, and Andrés Gómez, "QPU integration in OpenCL for heterogeneous programming", The Journal of Supercomputing 80 8, 11682 (2024).

[278] Michael L. Wall and Giuseppe D'Aguanno, "Tree-tensor-network classifiers for machine learning: From quantum inspired to quantum assisted", Physical Review A 104 4, 042408 (2021).

[279] Paramita Basak Upama, Md Jobair Hossain Faruk, Mohammad Nazim, Mohammad Masum, Hossain Shahriar, Gias Uddin, Shabir Barzanjeh, Sheikh Iqbal Ahamed, and Akond Rahman, 2022 IEEE 46th Annual Computers, Software, and Applications Conference (COMPSAC) 520 (2022) ISBN:978-1-6654-8810-5.

[280] XiaoYu Jing, YanJun Li, GuangYue Zhao, Huiqin Xie, and Qi Wang, "Quantum circuit implementation and resource analysis of LBlock and LiCi", Quantum Information Processing 22 9, 347 (2023).

[281] Stavros Efthymiou, Alvaro Orgaz-Fuertes, Rodolfo Carobene, Juan Cereijo, Andrea Pasquale, Sergi Ramos-Calderer, Simone Bordoni, David Fuentes-Ruiz, Alessandro Candido, Edoardo Pedicillo, Matteo Robbiati, Yuanzheng Paul Tan, Jadwiga Wilkens, Ingo Roth, José Ignacio Latorre, and Stefano Carrazza, "Qibolab: an open-source hybrid quantum operating system", Quantum 8, 1247 (2024).

[282] Ryan LaRose, "Overview and Comparison of Gate Level Quantum Software Platforms", Quantum 3, 130 (2019).

[283] 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 6, 062328 (2018).

[284] P. S. Aithal, "Advances and New Research Opportunities in Quantum Computing Technology by Integrating it with Other ICCT Underlying Technologies", International Journal of Case Studies in Business, IT, and Education 314 (2023).

[285] Jianjun Zhao, 2025 40th IEEE/ACM International Conference on Automated Software Engineering (ASE) 3886 (2025) ISBN:979-8-3503-5733-2.

[286] Niels M. P. Neumann, Maran P. P. van Heesch, Frank Phillipson, and Antoine A. P. Smallegange, 2021 International Conference on Military Communication and Information Systems (ICMCIS) 1 (2021) ISBN:978-1-6654-4586-3.

[287] Aeyoung Kim, Seong-Min Cho, Chang-Bae Seo, Sokjoon Lee, and Seung-Hyun Seo, "Quantum Modular Adder over GF(2n − 1) without Saving the Final Carry", Applied Sciences 11 7, 2949 (2021).

[288] Ellis Wilson, Frank Mueller, and Scott Pakin, SC22: International Conference for High Performance Computing, Networking, Storage and Analysis 1 (2022) ISBN:978-1-6654-5444-5.

[289] Neill Lambert, Eric Giguère, Paul Menczel, Boxi Li, Patrick Hopf, Gerardo Suárez, Marc Gali, Jake Lishman, Rushiraj Gadhvi, Rochisha Agarwal, Asier Galicia, Nathan Shammah, Paul Nation, J.R. Johansson, Shahnawaz Ahmed, Simon Cross, Alexander Pitchford, and Franco Nori, "QuTiP 5: The Quantum Toolbox in Python", Physics Reports 1153, 1 (2026).

[290] Nai-Wei Hsu, Chuan-Chi Wang, Chia-Hsin Hsu, Chia-Heng Tu, and Shih-Hao Hung, "Toward cost-effective quantum circuit simulation with performance tuning techniques", Connection Science 36 1, 2349541 (2024).

[291] Mao Zhang, Huai-Ming Yu, Haidong Yuan, Xiaoguang Wang, Rafał Demkowicz-Dobrzański, and Jing Liu, "QuanEstimation: An open-source toolkit for quantum parameter estimation", Physical Review Research 4 4, 043057 (2022).

[292] Tianyin Li, Xingyu Guo, Wai Kin Lai, Xiaohui Liu, Enke Wang, Hongxi Xing, Dan-Bo Zhang, and Shi-Liang Zhu, "Exploring light-cone distribution amplitudes from quantum computing", Science China Physics, Mechanics & Astronomy 66 8, 281011 (2023).

[293] Bhaskara Narottama, Sonia Aïssa, and Zina Mohamed, "AI-Enabled Framework for Energy Sustainability Evaluation and Enhancement of Wireless Networks", IEEE Transactions on Green Communications and Networking 10, 978 (2026).

[294] Thomas Grurl, Jurgen Fus, Stefan Hillmich, Lukas Burgholzer, and Robert Wille, 2020 IEEE 50th International Symposium on Multiple-Valued Logic (ISMVL) 176 (2020) ISBN:978-1-7281-5406-0.

[295] Iskren Vankov, Daniel Mills, Petros Wallden, and Elham Kashefi, "Methods for classically simulating noisy networked quantum architectures", Quantum Science and Technology 5 1, 014001 (2020).

[296] Ahmed Abid Moueddene, Nader Khammassi, Koen Bertels, and Carmen G. Almudever, "Realistic simulation of quantum computation using unitary and measurement channels", Physical Review A 102 5, 052608 (2020).

[297] Francisco Orts, Gloria Ortega, Elías F. Combarro, Ignacio F. Rúa, and Ester M. Garzón, "Optimized quantum leading zero detector circuits", Quantum Information Processing 22 1, 28 (2022).

[298] Simone Cantori, David Vitali, and Sebastiano Pilati, "Supervised learning of random quantum circuits via scalable neural networks", Quantum Science and Technology 8 2, 025022 (2023).

[299] Kyungbae Jang, Gyeongju Song, Hyeokdong Kwon, Siwoo Uhm, Hyunji Kim, Wai-Kong Lee, and Hwajeong Seo, "Grover on PIPO", Electronics 10 10, 1194 (2021).

[300] Manuel De Stefano, Fabiano Pecorelli, Dario Di Nucci, Fabio Palomba, and Andrea De Lucia, "The quantum frontier of software engineering: A systematic mapping study", Information and Software Technology 175, 107525 (2024).

[301] Albert T. Schmitz, Nicolas P. D. Sawaya, Sonika Johri, and A. Y. Matsuura, "Graph optimization perspective for low-depth Trotter-Suzuki decomposition", Physical Review A 109 4, 042418 (2024).

[302] Evandro Rosa, Eduardo Lussi, Jerusa Marchi, Rafael de Santiago, and Eduardo Duzzioni, "Full Quantum Stack: Ket Platform", Brazilian Journal of Physics 56 1, 45 (2026).

[303] Seyoung Yoon, Gyeongju Song, Kyungbae Jang, Sangmin Cha, and Hwajeong Seo, Lecture Notes in Computer Science 16434, 182 (2026) ISBN:978-981-95-6856-7.

[304] Sukhpal Singh Gill, Adarsh Kumar, Harvinder Singh, Manmeet Singh, Kamalpreet Kaur, Muhammad Usman, and Rajkumar Buyya, "Quantum computing: A taxonomy, systematic review and future directions", Software: Practice and Experience 52 1, 66 (2022).

[305] Evandro C. R. Rosa, Eduardo I. Duzzioni, and Rafael de Santiago, "Optimizing Gate Decomposition for High-Level Quantum Programming", Quantum 9, 1659 (2025).

[306] Axel Dahlberg and Stephanie Wehner, "SimulaQron—a simulator for developing quantum internet software", Quantum Science and Technology 4 1, 015001 (2019).

[307] Qun Liu, Bart Preneel, Zheng Zhao, and Meiqin Wang, Lecture Notes in Computer Science 14440, 67 (2023) ISBN:978-981-99-8726-9.

[308] Zhihao Wu, Junjie Wu, and Anqi Huang, "PhotoniQLAB: a framework for simulating photonic quantum information processing experiments", Quantum Science and Technology 6 2, 024001 (2021).

[309] Haotian Shi and Xiutao Feng, Lecture Notes in Computer Science 15491, 358 (2025) ISBN:978-981-96-0943-7.

[310] Junyi Liu, Bohua Zhan, Shuling Wang, Shenggang Ying, Tao Liu, Yangjia Li, Mingsheng Ying, and Naijun Zhan, Lecture Notes in Computer Science 11562, 187 (2019) ISBN:978-3-030-25542-8.

[311] F. Javier Cardama, Jorge Vázquez-Pérez, Tomás F. Pena, Juan C. Pichel, and Andrés Gómez, Lecture Notes in Computer Science 15385, 100 (2025) ISBN:978-3-031-90199-7.

[312] Thomas Grurl, Richard Kueng, Jurgen FuB, and Robert Wille, 2021 Design, Automation & Test in Europe Conference & Exhibition (DATE) 194 (2021) ISBN:978-3-9819263-5-4.

[313] Boxi Li, Shahnawaz Ahmed, Sidhant Saraogi, Neill Lambert, Franco Nori, Alexander Pitchford, and Nathan Shammah, "Pulse-level noisy quantum circuits with QuTiP", Quantum 6, 630 (2022).

[314] Shi-Xin Zhang, Jonathan Allcock, Zhou-Quan Wan, Shuo Liu, Jiace Sun, Hao Yu, Xing-Han Yang, Jiezhong Qiu, Zhaofeng Ye, Yu-Qin Chen, Chee-Kong Lee, Yi-Cong Zheng, Shao-Kai Jian, Hong Yao, Chang-Yu Hsieh, and Shengyu Zhang, "TensorCircuit: a Quantum Software Framework for the NISQ Era", Quantum 7, 912 (2023).

[315] Honghui Shang, Li Shen, Yi Fan, Zhiqian Xu, Chu Guo, Jie Liu, Wenhao Zhou, Huan Ma, Rongfen Lin, Yuling Yang, Fang Li, Zhuoya Wang, Yunquan Zhang, and Zhenyu Li, SC22: International Conference for High Performance Computing, Networking, Storage and Analysis 1 (2022) ISBN:978-1-6654-5444-5.

[316] David Ittah, Thomas Häner, Vadym Kliuchnikov, and Torsten Hoefler, "QIRO: A Static Single Assignment-based Quantum Program Representation for Optimization", ACM Transactions on Quantum Computing 3 3, 1 (2022).

[317] Jarrod R. McClean, Nicholas C. Rubin, Kevin J. Sung, Ian D. Kivlichan, Xavier Bonet-Monroig, Yudong Cao, Chengyu Dai, E. Schuyler Fried, Craig Gidney, Brendan Gimby, Pranav Gokhale, Thomas Häner, Tarini Hardikar, Vojtěch Havlíček, Oscar Higgott, Cupjin Huang, Josh Izaac, Zhang Jiang, Xinle Liu, Sam McArdle, Matthew Neeley, Thomas O'Brien, Bryan O'Gorman, Isil Ozfidan, Maxwell D. Radin, Jhonathan Romero, Nicolas P. D. Sawaya, Bruno Senjean, Kanav Setia, Sukin Sim, Damian S. Steiger, Mark Steudtner, Qiming Sun, Wei Sun, Daochen Wang, Fang Zhang, and Ryan Babbush, "OpenFermion: the electronic structure package for quantum computers", Quantum Science and Technology 5 3, 034014 (2020).

[318] Seyon Sivarajah, Silas Dilkes, Alexander Cowtan, Will Simmons, Alec Edgington, and Ross Duncan, "t|ket⟩: a retargetable compiler for NISQ devices", Quantum Science and Technology 6 1, 014003 (2021).

[319] Andrew W. Cross, Lev S. Bishop, John A. Smolin, and Jay M. Gambetta, "Open Quantum Assembly Language", arXiv:1707.03429, (2017).

[320] Jarrod R. McClean, Kevin J. Sung, Ian D. Kivlichan, Yudong Cao, Chengyu Dai, E. Schuyler Fried, Craig Gidney, Brendan Gimby, Pranav Gokhale, Thomas Häner, Tarini Hardikar, Vojtěch Havlíček, Oscar Higgott, Cupjin Huang, Josh Izaac, Zhang Jiang, Xinle Liu, Sam McArdle, Matthew Neeley, Thomas O'Brien, Bryan O'Gorman, Isil Ozfidan, Maxwell D. Radin, Jhonathan Romero, Nicholas Rubin, Nicolas P. D. Sawaya, Kanav Setia, Sukin Sim, Damian S. Steiger, Mark Steudtner, Qiming Sun, Wei Sun, Daochen Wang, Fang Zhang, and Ryan Babbush, "OpenFermion: The Electronic Structure Package for Quantum Computers", arXiv:1710.07629, (2017).

[321] Frederic T. Chong, Diana Franklin, and Margaret Martonosi, "Programming languages and compiler design for realistic quantum hardware", Nature 549 7671, 180 (2017).

[322] Kanav Setia and James D. Whitfield, "Bravyi-Kitaev Superfast simulation of electronic structure on a quantum computer", Journal of Chemical Physics 148 16, 164104 (2018).

[323] Davide Venturelli, Minh Do, Eleanor Rieffel, and Jeremy Frank, "Compiling quantum circuits to realistic hardware architectures using temporal planners", Quantum Science and Technology 3 2, 025004 (2018).

[324] Krysta M. Svore, Alan Geller, Matthias Troyer, John Azariah, Christopher Granade, Bettina Heim, Vadym Kliuchnikov, Mariia Mykhailova, Andres Paz, and Martin Roetteler, "Q#: Enabling scalable quantum computing and development with a high-level domain-specific language", arXiv:1803.00652, (2018).

[325] Thomas Häner and Damian S. Steiger, "0.5 Petabyte Simulation of a 45-Qubit Quantum Circuit", arXiv:1704.01127, (2017).

[326] Randy Lewis and R. M. Woloshyn, "A qubit model for U(1) lattice gauge theory", arXiv:1905.09789, (2019).

[327] Amr Elsharkawy, Xiao-Ting Michelle To, Philipp Seitz, Yanbin Chen, Yannick Stade, Manuel Geiger, Qunsheng Huang, Xiaorang Guo, Muhammad Arslan Ansari, Christian B. Mendl, Dieter Kranzlmüller, and Martin Schulz, "Integration of Quantum Accelerators with High Performance Computing -- A Review of Quantum Programming Tools", arXiv:2309.06167, (2023).

[328] E. Schuyler Fried, Nicolas P. D. Sawaya, Yudong Cao, Ian D. Kivlichan, Jhonathan Romero, and Alán Aspuru-Guzik, "qTorch: The quantum tensor contraction handler", PLoS ONE 13 12, e0208510 (2018).

[329] Alexander McCaskey, Eugene Dumitrescu, Mengsu Chen, Dmitry Lyakh, and Travis Humble, "Validating quantum-classical programming models with tensor network simulations", PLoS ONE 13 12, e0206704 (2018).

[330] Kyle E. C. Booth, Minh Do, J. Christopher Beck, Eleanor Rieffel, Davide Venturelli, and Jeremy Frank, "Comparing and Integrating Constraint Programming and Temporal Planning for Quantum Circuit Compilation", arXiv:1803.06775, (2018).

[331] Jin-Guo Liu and Lei Wang, "Differentiable Learning of Quantum Circuit Born Machine", arXiv:1804.04168, (2018).

[332] Brandon Langenberg, Hai Pham, and Rainer Steinwandt, "Reducing the Cost of Implementing the Advanced Encryption Standard as a Quantum Circuit", IEEE Transactions on Quantum Engineering 1, TQE.2020.2965697 (2020).

[333] Alwin Zulehner and Robert Wille, "Advanced Simulation of Quantum Computations", IEEE Transactions on Computer Aided Design 38 5, 848 (2019).

[334] E. Schuyler Fried, Nicolas P. D. Sawaya, Yudong Cao, Ian D. Kivlichan, Jhonathan Romero, and Alán Aspuru-Guzik, "qTorch: The Quantum Tensor Contraction Handler", arXiv:1709.03636, (2017).

[335] Kieran Young, Marcus Scese, and Ali Ebnenasir, "Simulating Quantum Computations on Classical Machines: A Survey", arXiv:2311.16505, (2023).

[336] Alexander Singh, Konstantinos Giannakis, and Theodore Andronikos, "Qumin, a minimalist quantum programming language", arXiv:1704.04460, (2017).

[337] Adarsh Kumar, Ali Ismail Awad, Gaurav Sharma, Rajalakshmi Krishnamurthi, Saurabh Jain, P. Srikanth, Kriti Sharma, Mustapha Hedabou, and Surinder Sood, "Revolutionizing Modern Networks: Advances in AI, Machine Learning, and Blockchain for Quantum Satellites and UAV-based Communication", arXiv:2303.11753, (2023).

[338] Evandro Chagas Ribeiro da Rosa and Bruno G. Taketani, "QSystem: bitwise representation for quantum circuit simulations", arXiv:2004.03560, (2020).

[339] Peng Fu, Kohei Kishida, Neil J. Ross, and Peter Selinger, "A tutorial introduction to quantum circuit programming in dependently typed Proto-Quipper", arXiv:2005.08396, (2020).

[340] Youssef Moawad, Wim Vanderbauwhede, and René Steijl, "Transformations for accelerator-based quantum circuit simulation in Haskell", arXiv:2210.12703, (2022).

[341] Hao Tang, Yan-Yan Zhu, Jun Gao, Marcus Lee, Peng-Cheng Lai, and Xian-Min Jin, "FeynmanPAQS: A Graphical Interface Program for Photonic Analog Quantum Computing", arXiv:1810.02289, (2018).

[342] Alwin Zulehner and Robert Wille, "Advanced Simulation of Quantum Computations", arXiv:1707.00865, (2017).

[343] Mathias Soeken and Mariia Mykhailova, "Automatic oracle generation in Microsoft's Quantum Development Kit using QIR and LLVM passes", arXiv:2212.01740, (2022).

[344] Anurudh Peduri, Ina Schaefer, and Michael Walter, "QbC: Quantum Correctness by Construction", arXiv:2307.15641, (2023).

[345] Prakash Murali, Ali Javadi-Abhari, Frederic T. Chong, and Margaret Martonosi, "Formal Constraint-based Compilation for Noisy Intermediate-Scale Quantum Systems", arXiv:1903.03276, (2019).

[346] Hao Tang, Xiao-Jun Xu, Yan-Yan Zhu, Jun Gao, Xuan Chen, Marcus Lee, Peng-Cheng Lai, and Xian-Min Jin, "FeynmanPAQS: a graphical interface program for photonic analog quantum computing", Optical Engineering 61, 081804 (2022).

[347] Augustin Borgna and Rafael Romero, "Encoding High-level Quantum Programs as SZX-diagrams", arXiv:2206.09376, (2022).

[348] Mathias Soeken, Thomas Häner, and Martin Roetteler, "Programming Quantum Computers Using Design Automation", arXiv:1803.01022, (2018).

[349] Charles Yuan and Michael Carbin, "The T-Complexity Costs of Error Correction for Control Flow in Quantum Computation", arXiv:2311.12772, (2023).

[350] Yu-Cheng Lin, Chuan-Chi Wang, Chia-Heng Tu, and Shih-Hao Hung, "Towards Optimizations of Quantum Circuit Simulation for Solving Max-Cut Problems with QAOA", arXiv:2312.03019, (2023).

[351] X. Fu, M. A. Rol, C. C. Bultink, J. van Someren, N. Khammassi, I. Ashraf, R. F. L. Vermeulen, J. C. de Sterke, W. J. Vlothuizen, R. N. Schouten, C. G. Almudever, L. DiCarlo, and K. Bertels, "An Experimental Microarchitecture for a Superconducting Quantum Processor", arXiv:1708.07677, (2017).

[352] Evandro Chagas Ribeiro da Rosa and Rafael de Santiago, "Classical and Quantum Data Interaction in Programming Languages: A Runtime Architecture", arXiv:2006.00131, (2020).

[353] Jarosław Adam Miszczak, "Symbolic quantum programming for supporting applications of quantum computing technologies", arXiv:2302.09401, (2023).

[354] Keith A. Britt, Fahd A. Mohiyaddin, and Travis S. Humble, "Quantum Accelerators for High-Performance Computing Systems", arXiv:1712.01423, (2017).

[355] Osman Ceylan and Ihsan Yilmaz, "Simulation Tests of Tokyo Quantum Network", Materials Science and Engineering Conference Series 1187 1, 012023 (2021).

[356] Jun Ye and Jun Yong Khoo, "EmuPlat: A Framework-Agnostic Platform for Quantum Hardware Emulation with Validated Transpiler-to-Pulse Pipeline", arXiv:2509.12639, (2025).

[357] Alessio Cicero, Mohammad Ali Maleki, Muhammad Waqar Azhar, Anton Frisk Kockum, and Pedro Trancoso, "Simulation of Quantum Computers: Review and Acceleration Opportunities", arXiv:2410.12660, (2024).

[358] Mark Koch, Alan Lawrence, Kartik Singhal, Seyon Sivarajah, and Ross Duncan, "GUPPY: Pythonic Quantum-Classical Programming", arXiv:2510.12582, (2025).

[359] Neilson Carlos Leite Ramalho, Higor Amario de Souza, and Marcos Lordello Chaim, "Testing and Debugging Quantum Programs: The Road to 2030", arXiv:2405.09178, (2024).

[360] Po-Hsuan Huang, Xie-Ru Li, Chi Chuang, Chia-Heng Tu, and Shih-Hao Hung, "ParaQAOA: Efficient Parallel Divide-and-Conquer QAOA for Large-Scale Max-Cut Problems Beyond 10,000 Vertices", arXiv:2603.26232, (2026).

[361] Youssef Moawad, Andrew Brown, René Steijl, and Wim Vanderbauwhede, "Optimising Iteration Scheduling for Full-State Vector Simulation of Quantum Circuits on FPGAs", arXiv:2411.18354, (2024).

[362] Ali Rezaei, Luc Jaulmes, Maria Bahna, Oliver Thomson Brown, and Antonio Barbalace, "Low-Level and NUMA-Aware Optimization for High-Performance Quantum Simulation", arXiv:2506.09198, (2025).

[363] Julien Gacon, "Scalable Quantum Algorithms for Noisy Quantum Computers", arXiv:2403.00940, (2024).

[364] Anurudh Peduri, Jam Kabeer Ali Khan, Gilles Barthe, and Michael Walter, "Traq: Estimating the Quantum Cost of Classical Programs", arXiv:2509.01508, (2025).

[365] Peng Fu, Kohei Kishida, Neil J. Ross, and Peter Selinger, "Proto-Quipper with Reversing and Control", arXiv:2410.22261, (2024).

[366] Chuan-Chi Wang, Yu-Cheng Lin, Yan-Jie Wang, Chia-Heng Tu, and Shih-Hao Hung, "Queen: A quick, scalable, and comprehensive quantum circuit simulation for supercomputing", arXiv:2406.14084, (2024).

[367] Le Chang, Saitej Yavvari, Rance Cleaveland, Samik Basu, Runzhou Tao, and Liyi Li, "DisQ: A Model of Distributed Quantum Processors (Extended Version)", arXiv:2407.09710, (2024).

[368] Mingsheng Ying, Li Zhou, and Gilles Barthe, "Laws of Quantum Programming", arXiv:2412.19463, (2024).

[369] Benoît Valiron, "On Quantum Programming Languages", arXiv:2410.13337, (2024).

[370] Dayton C. Closser and Zbigniew J. Kabala, "Pushing the Limits of LLMs in Quantum Operations", arXiv:2507.21327, (2025).

[371] Liyi Li, Anshu Sharma, Zoukarneini Difaizi Tagba, Sean Frett, and Alex Potanin, "Validating Quantum State Preparation Programs (Extended Version)", arXiv:2501.05616, (2025).

[372] Luke Southall, Joshua Ammermann, Rinor Kelmendi, Domenik Eichhorn, and Ina Schaefer, "Investigating Retargetability Claims for Quantum Compilers", arXiv:2601.16779, (2026).

The above citations are from Crossref's cited-by service (last updated successfully 2026-07-15 13:52:36) and SAO/NASA ADS (last updated successfully 2026-07-15 13:52:38). The list may be incomplete as not all publishers provide suitable and complete citation data.

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