Qulacs: a fast and versatile quantum circuit simulator for research purpose

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; Keisuke Fujii

doi:10.22331/q-2021-10-06-559

Qulacs: a fast and versatile quantum circuit simulator for research purpose

Yasunari Suzuki^1,2, Yoshiaki Kawase³, Yuya Masumura⁴, Yuria Hiraga⁵, Masahiro Nakadai⁶, Jiabao Chen⁷, Ken M. Nakanishi^7,8, Kosuke Mitarai^3,7,9, Ryosuke Imai⁷, Shiro Tamiya^7,10, Takahiro Yamamoto⁷, Tennin Yan⁷, Toru Kawakubo⁷, Yuya O. Nakagawa⁷, Yohei Ibe⁷, Youyuan Zhang^7,8, Hirotsugu Yamashita¹¹, Hikaru Yoshimura¹¹, Akihiro Hayashi¹², and Keisuke Fujii^2,3,9,13

¹NTT Computer and Data Science Laboratories, NTT Corporation, Musashino 180-8585, Japan
²JST PRESTO, Kawaguchi, Saitama 332-0012, Japan
³Graduate School of Engineering Science, Osaka University, 1-3 Machikaneyama, Toyonaka, Osaka 560-8531, Japan
⁴Graduate School of Information Science and Technology, Osaka University, 1-1 Yamadaoka, Suita, Osaka 565-0871, Japan
⁵Graduate School of Information and Science, Nara Institute of Science and Technology, Takayama, Ikoma, Nara 630-0192, Japan
⁶Graduate School of Science, Kyoto University, Yoshida-Ushinomiya, Sakyo, Kyoto 606-8302, Japan
⁷QunaSys Inc., Aqua Hakusan Building 9F, 1-13-7 Hakusan, Bunkyo, Tokyo 113-0001, Japan
⁸Graduate School of Science, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan
⁹Center for Quantum Information and Quantum Biology, Institute for Open and Transdisciplinary Research Initiatives, Osaka University, Japan
¹⁰Graduate School of Engineering, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan
¹¹Individual researcher
¹²School of Computer Science, Georgia Institute of Technology, Atlanta, GA, 30332, USA
¹³Center for Emergent Matter Science, RIKEN, Wako Saitama 351-0198, Japan

Published:	2021-10-06, volume 5, page 559
Eprint:	arXiv:2011.13524v4
Doi:	https://doi.org/10.22331/q-2021-10-06-559
Citation:	Quantum 5, 559 (2021).

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Abstract

To explore the possibilities of a near-term intermediate-scale quantum algorithm and long-term fault-tolerant quantum computing, a fast and versatile quantum circuit simulator is needed. Here, we introduce Qulacs, a fast simulator for quantum circuits intended for research purpose. We show the main concepts of Qulacs, explain how to use its features via examples, describe numerical techniques to speed-up simulation, and demonstrate its performance with numerical benchmarks.

► BibTeX data

@article{Suzuki2021qulacsfast,
  doi = {10.22331/q-2021-10-06-559},
  url = {https://doi.org/10.22331/q-2021-10-06-559},
  title = {Qulacs: a fast and versatile quantum circuit simulator for research purpose},
  author = {Suzuki, Yasunari and Kawase, Yoshiaki and Masumura, Yuya and Hiraga, Yuria and Nakadai, Masahiro and Chen, Jiabao and Nakanishi, Ken M. and Mitarai, Kosuke and Imai, Ryosuke and Tamiya, Shiro and Yamamoto, Takahiro and Yan, Tennin and Kawakubo, Toru and Nakagawa, Yuya O. and Ibe, Yohei and Zhang, Youyuan and Yamashita, Hirotsugu and Yoshimura, Hikaru and Hayashi, Akihiro and Fujii, Keisuke},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {5},
  pages = {559},
  month = oct,
  year = {2021}
}

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[9] Ryota Kojima, Masahiko Kamoshita, and Keita Kanno, 2025 IEEE International Conference on Quantum Computing and Engineering (QCE) 2300 (2025) ISBN:979-8-3315-5736-2.

[10] 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).

[11] 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).

[12] Yuichiro Nakano, Hideaki Hakoshima, Kosuke Mitarai, and Keisuke Fujii, "Markov-chain Monte Carlo method enhanced by a quantum alternating operator ansatz", Physical Review Research 6 3, 033105 (2024).

[13] Paulo F. Bedaque, Ratna Khadka, Gautam Rupak, and Muhammad Yusf, "Radiative processes on a quantum computer", Physical Review C 111 3, 034604 (2025).

[14] Rihito Sakurai, Wataru Mizukami, and Hiroshi Shinaoka, "Hybrid quantum-classical algorithm for computing imaginary-time correlation functions", Physical Review Research 4 2, 023219 (2022).

[15] Abhinav Anand, Lasse Bjørn Kristensen, Felix Frohnert, Sukin Sim, and Alán Aspuru-Guzik, "Information flow in parameterized quantum circuits", Quantum Science and Technology 9 3, 035025 (2024).

[16] François Jamet, Lachlan P. Lindoy, Yannic Rath, Connor Lenihan, Abhishek Agarwal, Enrico Fontana, Fedor Simkovic, Baptiste Anselme Martin, and Ivan Rungger, "Anderson impurity solver integrating tensor network methods with quantum computing", APL Quantum 2 1, 016121 (2025).

[17] Hasan Sayginel, Francois Jamet, Abhishek Agarwal, Dan E Browne, and Ivan Rungger, "A fault-tolerant variational quantum algorithm with limited T-depth", Quantum Science and Technology 9 1, 015015 (2024).

[18] Ze‐Tong Li, Fan‐Xu Meng, Han Zeng, Zhai‐Rui Gong, Zai‐Chen Zhang, and Xu‐Tao Yu, "A Gradient‐Cost Multiobjective Alternate Framework for Variational Quantum Eigensolver with Variable Ansatz", Advanced Quantum Technologies 6 5, 2200130 (2023).

[19] Ryohei Niwase, Hikaru Harasawa, Yoshiki Yamaguchi, Kaijie Wei, Hideharu Amano, and Takefumi Miyoshi, 2023 International Conference on Field Programmable Technology (ICFPT) 288 (2023) ISBN:979-8-3503-5911-4.

[20] Ifan Williams and Mathieu Pellen, "A general approach to quantum integration of cross sections in high-energy physics", Quantum Science and Technology 10 4, 045017 (2025).

[21] Mirko Consiglio, Jacopo Settino, Andrea Giordano, Carlo Mastroianni, Francesco Plastina, Salvatore Lorenzo, Sabrina Maniscalco, John Goold, and Tony J. G. Apollaro, "Variational Gibbs state preparation on noisy intermediate-scale quantum devices", Physical Review A 110 1, 012445 (2024).

[22] Emirhan Yılmaz and Elif Kurtaran Özbudak, 2026 5th International Informatics and Software Engineering Conference (IISEC) 672 (2026) ISBN:979-8-3315-8031-5.

[23] Yuichiro Yoshida, Wataru Mizukami, and Norio Yoshida, "Solvent Distribution Effects on Quantum Chemical Calculations with Quantum Computers", Journal of Chemical Theory and Computation 20 5, 1962 (2024).

[24] Kaijie Wei, Hideharu Amano, Ryohei Niwase, Yoshiki Yamaguchi, and Takefumi Miyoshi, "Qu-Trefoil: Large-Scale Quantum Circuit Simulator Working on FPGA With SATA Storages", IEEE Transactions on Computers 74 4, 1306 (2025).

[25] William M. Watkins, Samuel Yen-Chi Chen, and Shinjae Yoo, "Quantum machine learning with differential privacy", Scientific Reports 13 1, 2453 (2023).

[26] Ken N. Okada, Keita Osaki, Kosuke Mitarai, and Keisuke Fujii, "Classically optimized variational quantum eigensolver with applications to topological phases", Physical Review Research 5 4, 043217 (2023).

[27] Mohadeseh Zarei Ghobadi and Elaheh Afsaneh, "Potential of quantum machine learning for solving the real-world problem of cancer classification", Discover Applied Sciences 6 10, 513 (2024).

[28] Stuart Ferguson and Petros Wallden, "Quantum-enhanced Markov chain Monte Carlo for systems larger than a quantum computer", Physical Review Research 7 1, 013231 (2025).

[29] 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).

[30] Sam Westrick, Pengyu Liu, Byeongjee Kang, Colin McDonald, Mike Rainey, Mingkuan Xu, Jatin Arora, Yongshan Ding, and Umut A. Acar, 2024 IEEE International Conference on Quantum Computing and Engineering (QCE) 1132 (2024) ISBN:979-8-3315-4137-8.

[31] 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).

[32] 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).

[33] Kouhei Nakaji, Hiroyuki Tezuka, and Naoki Yamamoto, "Quantum-classical hybrid neural networks in the neural tangent kernel regime", Quantum Science and Technology 9 1, 015022 (2024).

[34] Akihiro Tabuchi, Satoshi Imamura, Masafumi Yamazaki, Takumi Honda, Akihiko Kasagi, Hiroshi Nakao, Naoto Fukumoto, and Kohta Nakashima, 2023 IEEE International Conference on Quantum Computing and Engineering (QCE) 959 (2023) ISBN:979-8-3503-4323-6.

[35] Jingxuan Chen, Hanna Westerheim, Zoë Holmes, Ivy Luo, Theshani Nuradha, Dhrumil Patel, Soorya Rethinasamy, Kathie Wang, and Mark M. Wilde, "Slack-variable approach for variational quantum semidefinite programming", Physical Review A 112 2, 022607 (2025).

[36] Philipp Schleich, Jakob S. Kottmann, and Alán Aspuru-Guzik, "Improving the accuracy of the variational quantum eigensolver for molecular systems by the explicitly-correlated perturbative [2]R12-correction", Physical Chemistry Chemical Physics 24 22, 13550 (2022).

[37] Yuuki Tokunaga, Yasunari Suzuki, Suguru Endo, and Rui Asaoka, "Fault-tolerant Technology for Quantum Information Processing and Its Implementation Methods", NTT Technical Review 19 5, 40 (2021).

[38] Mingkuan Xu, Shiyi Cao, Xupeng Miao, Umut A. Acar, and Zhihao Jia, SC24: International Conference for High Performance Computing, Networking, Storage and Analysis 1 (2024) ISBN:979-8-3503-5291-7.

[39] Kohtaroh Sakaue, Hiroshi Shinaoka, and Rihito Sakurai, "Adaptive sampling-based optimization of quantics tensor trains for noisy functions: Applications to quantum simulations", SciPost Physics 19 2, 038 (2025).

[40] Chenfeng Cao, Hiroshi Yano, and Yuya O. Nakagawa, "Accelerated variational quantum eigensolver with joint Bell measurement", Physical Review Research 6 1, 013205 (2024).

[41] Junpei Yamaguchi, Masafumi Yamazaki, Akihiro Tabuchi, Takumi Honda, Tetsuya Izu, and Noboru Kunihiro, Lecture Notes in Computer Science 14561, 119 (2024) ISBN:978-981-97-1234-2.

[42] Don Arai, Ken N. Okada, Yuichiro Nakano, Kosuke Mitarai, and Keisuke Fujii, "Scalable circuit depth reduction in feedback-based quantum optimization with a quadratic approximation", Physical Review Research 7 1, 013035 (2025).

[43] Kenji Sugisaki and Yuji Mochizuki, "Quantum Applications", The Journal of The Institute of Image Information and Television Engineers 77 1, 47 (2023).

[44] Nobuki Inoue and Hisao Nakamura, "Correction Scheme for Molecular Total Energies From Quantum Phase Estimation Under Limited Qubit Resources", Journal of Computational Chemistry 47 14, e70400 (2026).

[45] Viktor Khinevich and Wataru Mizukami, "Enhancing quantum computations with the synergy of auxiliary field quantum Monte Carlo and computational basis tomography", Physical Review Research 7 4, 043344 (2025).

[46] Maria-Andreea Filip, Nathan Fitzpatrick, David Muñoz Ramo, and Alex J. W. Thom, "Reducing unitary coupled cluster circuit depth by classical stochastic amplitude prescreening", Physical Review Research 4 2, 023243 (2022).

[47] Yusuke Kimura, Shaowen Li, Hiroyuki Sato, Masahiro Fujita, and Robert Wille, "Improving Decision Diagram-Based Quantum Circuit Simulation Using Static Variable Ordering and Multinode Ring Communication", IEEE Transactions on Quantum Engineering 7, 1 (2026).

[48] Samuel Yen-Chi Chen and Shinjae Yoo, "Federated Quantum Machine Learning", Entropy 23 4, 460 (2021).

[49] Masaya Hagai, Mahito Sugiyama, Koji Tsuda, and Takeshi Yanai, "Artificial neural network encoding of molecular wavefunctions for quantum computing", Digital Discovery 2 3, 634 (2023).

[50] Georgia Christopoulou, Cono Di Paola, Floris Eelke Elzinga, Aurelie Jallat, David Muñoz Ramo, and Michal Krompiec, "Quantum hardware calculations of the activation and dissociation of nitrogen on iron clusters and surfaces", Physical Chemistry Chemical Physics 26 7, 5895 (2024).

[51] Masaya Kohda, Ryosuke Imai, Keita Kanno, Kosuke Mitarai, Wataru Mizukami, and Yuya O. Nakagawa, "Quantum expectation-value estimation by computational basis sampling", Physical Review Research 4 3, 033173 (2022).

[52] Hyunjoon Shin, Seokhyeon Lee, Myeongjin Kwak, and Yongtae Kim, Proceedings of the 40th ACM International Conference on Supercomputing 1296 (2026) ISBN:9798400725227.

[53] Yoshiaki Kawase, Kosuke Mitarai, and Keisuke Fujii, "Parametric t-stochastic neighbor embedding with quantum neural network", Physical Review Research 4 4, 043199 (2022).

[54] Koki Chinzei, Quoc Hoan Tran, Yasuhiro Endo, and Hirotaka Oshima, "Resource-efficient equivariant quantum convolutional neural networks", Quantum Machine Intelligence 8 1, 53 (2026).

[55] 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).

[56] Kouhei Nakaji, Suguru Endo, Yuichiro Matsuzaki, and Hideaki Hakoshima, "Measurement optimization of variational quantum simulation by classical shadow and derandomization", Quantum 7, 995 (2023).

[57] Navnil Choudhury, Ameya Bhave, and Kanad Basu, Design Automation for Quantum Computing 207 (2026) ISBN:978-3-032-09302-8.

[58] Koki Chinzei, Quoc Hoan Tran, Kazunori Maruyama, Hirotaka Oshima, and Shintaro Sato, "Splitting and parallelizing of quantum convolutional neural networks for learning translationally symmetric data", Physical Review Research 6 2, 023042 (2024).

[59] Hasitha Muthumala Waidyasooriya, Hiroki Oshiyama, Yuya Kurebayashi, Masanori Hariyama, and Masayuki Ohzeki, "A Scalable Emulator for Quantum Fourier Transform Using Multiple-FPGAs With High-Bandwidth-Memory", IEEE Access 10, 65103 (2022).

[60] A S Rejeesh and Nishant Kumar Shekhar, 2025 Supercomputing India (SCI) 1 (2025) ISBN:979-8-3315-5758-4.

[61] Charles M. Varmantchaonala, Jean Louis K. E. Fendji, Julius Schöning, and Marcellin Atemkeng, "Quantum Natural Language Processing: A Comprehensive Survey", IEEE Access 12, 99578 (2024).

[62] Nicolas Poirier, Jakob S. Kottmann, Alán Aspuru‐Guzik, Luc Mongeau, and Alireza Najafi‐Yazdi, "Range‐separated density functional theory using multiresolution analysis and quantum computing", Journal of Computational Chemistry 45 23, 1987 (2024).

[63] Theofanis Kalampokas, George A. Papakostas, and Pramita Mishra, "Unlocking Nonlinear Dynamics in Fuzzy Cognitive Maps: A Quantum Kernel Approach", Applied Computational Intelligence and Soft Computing 2026 1, 4363446 (2026).

[64] Maurice Weber, Abhinav Anand, Alba Cervera-Lierta, Jakob S. Kottmann, Thi Ha Kyaw, Bo Li, Alán Aspuru-Guzik, Ce Zhang, and Zhikuan Zhao, "Toward reliability in the NISQ era: Robust interval guarantee for quantum measurements on approximate states", Physical Review Research 4 3, 033217 (2022).

[65] Samuel Duffield, Gabriel Matos, and Melf Johannsen, "qujax: Simulating quantum circuits with JAX", Journal of Open Source Software 8 89, 5504 (2023).

[66] Takuya Yoshioka, Keita Sasada, Yuichiro Nakano, and Keisuke Fujii, "Fermionic quantum approximate optimization algorithm", Physical Review Research 5 2, 023071 (2023).

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

[68] Bryan T. Gard and Adam M. Meier, "Classically efficient quantum scalable Fermi-Hubbard benchmark", Physical Review A 105 4, 042602 (2022).

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

[70] Luca Erhart, Kosuke Mitarai, Wataru Mizukami, and Keisuke Fujii, "Constructing Local Bases for a Deep Variational Quantum Eigensolver for Molecular Systems", Physical Review Applied 18 6, 064051 (2022).

[71] Zi-Jian Zhang, Jinzhao Sun, Xiao Yuan, and Man-Hong Yung, "Low-Depth Hamiltonian Simulation by an Adaptive Product Formula", Physical Review Letters 130 4, 040601 (2023).

[72] Kaijie Wei, Hideharu Amano, Ryohei Niwase, and Yoshiki Yamaguchi, 14th International Symposium on Highly Efficient Accelerators and Reconfigurable Technologies (HEART 24)) 63 (2024) ISBN:9798400717277.

[73] Nozomu Kobayashi, Yoshiyuki Suimon, Koichi Miyamoto, and Kosuke Mitarai, "The cross-sectional stock return predictions via quantum neural network and tensor network", Quantum Machine Intelligence 5 2, 46 (2023).

[74] David Barral, F. Javier Cardama, Guillermo Díaz-Camacho, Daniel Faílde, Iago F. Llovo, Mariamo Mussa-Juane, Jorge Vázquez-Pérez, Juan Villasuso, César Piñeiro, Natalia Costas, Juan C. Pichel, Tomás F. Pena, and Andrés Gómez, "Review of Distributed Quantum Computing: From single QPU to High Performance Quantum Computing", Computer Science Review 57, 100747 (2025).

[75] Tatsuhiko N. Ikeda, Hideki Kono, and Keisuke Fujii, "Measuring Trotter error and its application to precision-guaranteed Hamiltonian simulations", Physical Review Research 6 3, 033285 (2024).

[76] 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).

[77] Mohd Jawed Khan, Pankaj Pratap Singh, Biswajeet Pradhan, Abdullah Alamri, and Chang-Wook Lee, "Extraction of Roads Using the Archimedes Tuning Process with the Quantum Dilated Convolutional Neural Network", Sensors 23 21, 8783 (2023).

[78] Ken N. Okada, Hirofumi Nishi, Taichi Kosugi, and Yu-ichiro Matsushita, "Systematic study on the dependence of the warm-start quantum approximate optimization algorithm on approximate solutions", Scientific Reports 14 1, 1167 (2024).

[79] 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).

[80] Nicholas C. Rubin, Klaas Gunst, Alec White, Leon Freitag, Kyle Throssell, Garnet Kin-Lic Chan, Ryan Babbush, and Toru Shiozaki, "The Fermionic Quantum Emulator", Quantum 5, 568 (2021).

[81] Brice Chichereau, Stéphane Vialle, Miwako Tsuji, Patrick Carribault, and Mitsuhisa Sato, 2025 IEEE International Conference on Quantum Computing and Engineering (QCE) 8 (2025) ISBN:979-8-3315-5736-2.

[82] Yuichiro Nakano, Ken N. Okada, and Keisuke Fujii, "Neural-Network-Assisted Monte Carlo Sampling Trained by Quantum Approximate Optimization Algorithm", PRX Quantum 7 1, 010338 (2026).

[83] Mirko Consiglio, Tony J. G. Apollaro, and Marcin Wieśniak, "Variational approach to the quantum separability problem", Physical Review A 106 6, 062413 (2022).

[84] Akihiro Hayashi, Austin Adams, Jeffrey Young, Alexander McCaskey, Eugene Dumitrescu, Vivek Sarkar, and Thomas M. Conte, 2023 IEEE International Parallel and Distributed Processing Symposium Workshops (IPDPSW) 509 (2023) ISBN:979-8-3503-1199-0.

[85] 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).

[86] Zhulu Chu, Xihan Wang, Meilin Jin, Ning Zhang, Quanli Gao, and Lianhe Shao, "An Effective Strategy for Sentiment Analysis Based on Complex-Valued Embedding and Quantum Long Short-Term Memory Neural Network", Axioms 13 3, 207 (2024).

[87] Alex Tritt, Joshua Morris, Joel Hochstetter, R.P. Anderson, James Saunderson, and L.D. Turner, "Spinsim: A GPU optimized python package for simulating spin-half and spin-one quantum systems", Computer Physics Communications 287, 108701 (2023).

[88] Francisco Javier del Arco Santos and Jakob S Kottmann, "A hybrid qubit encoding: splitting Fock space into Fermionic and Bosonic subspaces", Quantum Science and Technology 10 3, 035018 (2025).

[89] Yu Terada, Ken Arai, Yu Tanaka, Yota Maeda, Hiroshi Ueno, and Hiroyuki Tezuka, "Quantum-enhanced causal discovery for a small number of samples", Quantum Machine Intelligence 8 1, 36 (2026).

[90] Jakob S. Kottmann and Alán Aspuru-Guzik, "Optimized low-depth quantum circuits for molecular electronic structure using a separable-pair approximation", Physical Review A 105 3, 032449 (2022).

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

[92] Kaito Kishi, Junpei Yamaguchi, Tetsuya Izu, and Noboru Kunihiro, "Simulation of Shor Algorithm for Discrete Logarithm Problems With Comprehensive Pairs of Modulo $p$ and Order $q$", IEEE Transactions on Quantum Engineering 6, 1 (2025).

[93] Philipp Schleich, Joseph Boen, Lukasz Cincio, Abhinav Anand, Jakob S. Kottmann, Sergei Tretiak, Pavel A. Dub, and Alán Aspuru-Guzik, "Partitioning Quantum Chemistry Simulations with Clifford Circuits", Journal of Chemical Theory and Computation 19 15, 4952 (2023).

[94] Ziqing Guo, Jan Balewski, and Ziwen Pan, Proceedings of the 54th International Conference on Parallel Processing 638 (2025) ISBN:9798400720741.

[95] Soichiro Nishio, Yuki Oba, and Yuki Kurashige, "Statistical errors in reduced density matrices sampled from quantum circuit simulation and the impact on multireference perturbation theory", Physical Chemistry Chemical Physics 25 44, 30525 (2023).

[96] Jie Liu, Huan Ma, Honghui Shang, Zhenyu Li, and Jinlong Yang, "Quantum-centric high performance computing for quantum chemistry", Physical Chemistry Chemical Physics 26 22, 15831 (2024).

[97] Ryo Watanabe, Keisuke Fujii, and Hiroshi Ueda, "Variational quantum eigensolver with embedded entanglement using a tensor-network ansatz", Physical Review Research 6 2, 023009 (2024).

[98] 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).

[99] Seenivasan Hariharan, Sachin Kinge, and Lucas Visscher, "Modeling Heterogeneous Catalysis Using Quantum Computers: An Academic and Industry Perspective", Journal of Chemical Information and Modeling 65 2, 472 (2025).

[100] Keisuke Fujii, Kaoru Mizuta, Hiroshi Ueda, Kosuke Mitarai, Wataru Mizukami, and Yuya O. Nakagawa, "Deep Variational Quantum Eigensolver: A Divide-And-Conquer Method for Solving a Larger Problem with Smaller Size Quantum Computers", PRX Quantum 3 1, 010346 (2022).

[101] Keichi Takahashi, Toshio Mori, and Hiroyuki Takizawa, Proceedings of the SC '23 Workshops of the International Conference on High Performance Computing, Network, Storage, and Analysis 1499 (2023) ISBN:9798400707858.

[102] Takeshi Yoshikawa, Tomoya Takanashi, and Hiromi Nakai, "Quantum Algorithm of the Divide-and-Conquer Unitary Coupled Cluster Method with a Variational Quantum Eigensolver", Journal of Chemical Theory and Computation 18 9, 5360 (2022).

[103] Haruhiko Hasegawa, Masayuki Shimoda, Hiroki Nakahara, and Takefumi Miyoshi, 2025 IEEE 55th International Symposium on Multiple-Valued Logic (ISMVL) 117 (2025) ISBN:979-8-3315-0744-2.

[104] Rihito Sakurai, Oliver J. Backhouse, George H. Booth, Wataru Mizukami, and Hiroshi Shinaoka, "Comparative study on compact quantum circuits of hybrid quantum-classical algorithms for quantum impurity models", Physical Review Research 6 2, 023110 (2024).

[105] Kohdai Kuroiwa and Yuya O. Nakagawa, "Averaging gate approximation error and performance of Unitary Coupled Cluster ansatz in Pre-FTQC Era", Quantum 9, 1800 (2025).

[106] Kamil Wereszczyński, Agnieszka Michalczuk, and Krzysztof A. Cyran, 2025 11th International Conference on Control, Decision and Information Technologies (CoDIT) 942 (2025) ISBN:979-8-3315-0338-3.

[107] Ziqing Guo, Jan Balewski, and Ziwen Pan, Workshop Proceedings of the 54th International Conference on Parallel Processing 200 (2025) ISBN:9798400721090.

[108] Kentaro Yamamoto, David Zsolt Manrique, Irfan T. Khan, Hideaki Sawada, and David Muñoz Ramo, "Quantum hardware calculations of periodic systems with partition-measurement symmetry verification: Simplified models of hydrogen chain and iron crystals", Physical Review Research 4 3, 033110 (2022).

[109] Vu Tuan Hai, Le Vu Trung Duong, Pham Hoai Luan, and Yasuhiko Nakashima, 2024 International Conference on Advanced Technologies for Communications (ATC) 449 (2024) ISBN:979-8-3503-5398-3.

[110] Hayato Higuchi, Yuki Ito, Kazuki Sakamoto, Keisuke Fujii, Juan William Pedersen, and Akimasa Yoshikawa, 2025 IEEE International Conference on Quantum Software (QSW) 35 (2025) ISBN:979-8-3315-6720-0.

[111] Joan Camps, Ophelia Crawford, György P Gehér, Alexander V Gramolin, Matthew P Stafford, and Mark L Turner, "Leakage mobility in superconducting qubits as a leakage reduction unit", Physica Scripta 101 11, 115107 (2026).

[112] Andrea Pizzamiglio, Alessandro Bisio, and Paolo Perinotti, "Classification of Qubit Cellular Automata on Hypercubic Lattices", Physical Review Letters 134 24, 240601 (2025).

[113] Takeru Yokota and Tatsuhiko N. Ikeda, "Unpolarized prethermal discrete time crystal", Physical Review A 112 3, 032212 (2025).

[114] Ali Masoudian, Uffe Jakobsen, and Mohammad Hassan Khooban, "Emulation of Variational Quantum Circuits on Embedded Systems for Real-Time Quantum Machine Learning Applications", Designs 9 4, 87 (2025).

[115] Nobuyuki Yoshioka, Takeshi Sato, Yuya O. Nakagawa, Yu-ya Ohnishi, and Wataru Mizukami, "Variational quantum simulation for periodic materials", Physical Review Research 4 1, 013052 (2022).

[116] Kaoru Mizuta, Mikiya Fujii, Shigeki Fujii, Kazuhide Ichikawa, Yutaka Imamura, Yukihiro Okuno, and Yuya O. Nakagawa, "Deep variational quantum eigensolver for excited states and its application to quantum chemistry calculation of periodic materials", Physical Review Research 3 4, 043121 (2021).

[117] Mathias Mikkelsen and Yuya O. Nakagawa, "Quantum-selected configuration interaction with time-evolved state", Physical Review Research 7 4, 043043 (2025).

[118] Carlos Bistafa, Norihiko Takahashi, Jumpei Koyama, Shintaro Sato, and Yukihiro Okuno, "Accuracy and Potential of Hardware-Efficient Ansätze for Molecular Ground and Excited State Electronic Structure Calculations: Benchmark and Analysis of High-Depth Quantum Circuits", ACS Omega 10 45, 54585 (2025).

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

[120] 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).

[121] Martin Lukac, Naoya Onizawa, and Shinobu Nagayama, 2026 IEEE 56th International Symposium on Multiple-Valued Logic (ISMVL) 152 (2026) ISBN:979-8-3315-5956-4.

[122] Teppei Suzuki, Tsubasa Miyazaki, Toshiki Inaritai, and Takahiro Otsuka, "Quantum AI simulator using a hybrid CPU–FPGA approach", Scientific Reports 13 1, 7735 (2023).

[123] Mohadeseh Zarei Ghoabdi and Elaheh Afsaneh, "Quantum machine learning for untangling the real-world problem of cancers classification based on gene expressions", (2023).

[124] 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.

[125] Mario Ponce, Thomas Cope, Inés de Vega, and Martin Leib, "Performance and scaling analysis of variational quantum simulation", Quantum Science and Technology 10 1, 015027 (2025).

[126] 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).

[127] Tomoya TAKANASHI, Takeshi YOSHIKAWA, and Hiromi NAKAI, "Development of Quantum Algorithm qUCC-LR for Excited-State Calculation Using Dynamic Polarizability", Journal of Computer Chemistry, Japan 20 4, 140 (2021).

[128] Jakob S. Kottmann and Francesco Scala, "Quantum Algorithmic Approach to Multiconfigurational Valence Bond Theory: Insights from Interpretable Circuit Design", Journal of Chemical Theory and Computation 20 9, 3514 (2024).

[129] Kisung Jin, Jinho On, and Gyuil Cha, "Tracking Affine Subspace with Gaussian Elimination for Adaptive Quantum Circuit Simulation", ACM Transactions on Quantum Computing 7 4, 1 (2026).

[130] Nobuyuki Yoshioka, Hideaki Hakoshima, Yuichiro Matsuzaki, Yuuki Tokunaga, Yasunari Suzuki, and Suguru Endo, "Generalized Quantum Subspace Expansion", Physical Review Letters 129 2, 020502 (2022).

[131] Takashi Tsuchimochi, Yoohee Ryo, Seiichiro L. Ten-no, and Kazuki Sasasako, "Improved Algorithms of Quantum Imaginary Time Evolution for Ground and Excited States of Molecular Systems", Journal of Chemical Theory and Computation 19 2, 503 (2023).

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

[133] Yuichiro Mori, Kouhei Nakaji, Yuichiro Matsuzaki, and Shiro Kawabata, "Expressive quantum supervised machine learning using Kerr-nonlinear parametric oscillators", Quantum Machine Intelligence 6 1, 14 (2024).

[134] Shahriar Rizvi and Md. Nazrul Islam Mondal, 2026 5th International Conference on Electrical, Computer & Telecommunication Engineering (ICECTE) 1 (2026) ISBN:979-8-3315-6135-2.

[135] Thi Ha Kyaw, Micheline B Soley, Brandon Allen, Paul Bergold, Chong Sun, Victor S Batista, and Alán Aspuru-Guzik, "Boosting quantum amplitude exponentially in variational quantum algorithms", Quantum Science and Technology 9 1, 01LT01 (2024).

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[137] 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).

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[140] Shui Jiang, Yi-Hua Chung, Chih-Chun Chang, Tsung-Yi Ho, and Tsung-Wei Huang, Proceedings of the 30th ACM International Conference on Architectural Support for Programming Languages and Operating Systems, Volume 2 79 (2025) ISBN:9798400710797.

[141] Ryutaro Sato, Yasuhiro Aota, Takaharu Yoshida, Hideaki Kawaguchi, Yuichiro Mori, Hiroki Kuji, and Yuichiro Matsuzaki, "Quantum circuit learning using complex spectra of non-integrable systems", Japanese Journal of Applied Physics 65 11, 112004 (2026).

[142] Yusei Mori, Hideaki Hakoshima, Kyohei Sudo, Toshio Mori, Kosuke Mitarai, and Keisuke Fujii, "Quantum circuit unoptimization", Physical Review Research 7 2, 023139 (2025).

[143] Yoshiaki Kawase, Kosuke Mitarai, and Keisuke Fujii, "Quantum kernel t-distributed stochastic neighbor embedding", Physical Review Research 6 4, 043234 (2024).

[144] Tomohiro Itogawa, Yugo Takada, Yutaka Hirano, and Keisuke Fujii, "Efficient Magic State Distillation by Zero-Level Distillation", PRX Quantum 6 2, 020356 (2025).

[145] Naihua Ji, Rongyi Bao, Zhao Chen, Yiming Yu, and Hongyang Ma, "Hybrid Quantum Neural Network Image Anti-Noise Classification Model Combined with Error Mitigation", Applied Sciences 14 4, 1392 (2024).

[146] Masahiro Fujita and Yusuke Kimura, Design Automation for Quantum Computing 251 (2026) ISBN:978-3-032-09302-8.

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[149] Vu Tuan Hai, Le Vu Trung Duong, Pham Hoai Luan, and Yasuhiko Nakashima, 2024 RIVF International Conference on Computing and Communication Technologies (RIVF) 419 (2024) ISBN:979-8-3315-0507-3.

[150] Taichi Kosugi, Hirofumi Nishi, and Yu-ichiro Matsushita, "Exhaustive search for optimal molecular geometries using imaginary-time evolution on a quantum computer", npj Quantum Information 9 1, 112 (2023).

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[152] Teodor Parella-Dilmé, Jakob S. Kottmann, and Antonio Acín, "Swap Network Augmented Ansätze on Arbitrary Connectivity", Quantum 10, 2062 (2026).

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

[154] Ryohei Niwase, Hikaru Harasawa, Yoshiki Yamaguchi, Wei Kaijie, and Hideharu Amano, 2023 IEEE 16th International Symposium on Embedded Multicore/Many-core Systems-on-Chip (MCSoC) 51 (2023) ISBN:979-8-3503-9361-3.

[155] Cono Di Paola, Evgeny Plekhanov, Michal Krompiec, Chandan Kumar, Emanuele Marsili, Fengmin Du, Daniel Weber, Jasper Simon Krauser, Elvira Shishenina, and David Muñoz Ramo, "Platinum-based catalysts for oxygen reduction reaction simulated with a quantum computer", npj Computational Materials 10 1, 285 (2024).

[156] Wang Fang and Mingsheng Ying, "Symbolic Execution for Quantum Error Correction Programs", Proceedings of the ACM on Programming Languages 8 PLDI, 1040 (2024).

[157] Benchi Zhao and Keisuke Fujii, "Variational quantum Hamiltonian engineering", Physical Review Research 7 2, 023123 (2025).

[158] Juha Reinikainen, Vlad Stirbu, Teiko Heinosaari, Vesa Lappalainen, and Tommi Mikkonen, "Quantum Computing for All: Online Courses Built Around an Interactive Visual Quantum Circuit Simulator", IEEE Computer Graphics and Applications 44 5, 67 (2024).

[159] 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).

[160] Teodor Parella-Dilmé, Korbinian Kottmann, Leonardo Zambrano, Luke Mortimer, Jakob S. Kottmann, and Antonio Acín, "Reducing Entanglement with Physically Inspired Fermion-To-Qubit Mappings", PRX Quantum 5 3, 030333 (2024).

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

[162] Yosuke Mitsuhashi and Nobuyuki Yoshioka, "Clifford Group and Unitary Designs under Symmetry", PRX Quantum 4 4, 040331 (2023).

[163] Tatsuhiko N. Ikeda, Sho Sugiura, and Anatoli Polkovnikov, "Robust Effective Ground State in a Nonintegrable Floquet Quantum Circuit", Physical Review Letters 133 3, 030401 (2024).

[164] Kosuke Mitarai, Yasunari Suzuki, Wataru Mizukami, Yuya O. Nakagawa, and Keisuke Fujii, "Quadratic Clifford expansion for efficient benchmarking and initialization of variational quantum algorithms", Physical Review Research 4 3, 033012 (2022).

[165] Jakob S. Kottmann, "Molecular Quantum Circuit Design: A Graph-Based Approach", Quantum 7, 1073 (2023).

[166] 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).

[167] Mohamed Tarek Ibn Ziad and Christos Kozyrakis, "Hunting CUDA Bugs at Scale with cuFuzz", Proceedings of the ACM on Programming Languages 10 OOPSLA1, 877 (2026).

[168] Kaijie Wei, Ryohei Niwase, Hideharu Amano, Yoshiki Yamaguchi, and Takefumi Miyoshi, 2023 International Conference on Field Programmable Technology (ICFPT) 272 (2023) ISBN:979-8-3503-5911-4.

[169] Tianyi Li, Yumeng Zeng, Qiming Ding, Zixuan Huo, Xiaosi Xu, Jiajun Ren, Diandong Tang, Xiaoxia Cai, and Xiao Yuan, "Efficient quantum simulation of non-adiabatic molecular dynamics with precise electronic structure", Digital Discovery 5 2, 548 (2026).

[170] Eric B. Jones, Cody James Winkleblack, Colin Campbell, Caleb Rotello, Edward D. Dahl, Matthew Reynolds, Peter Graf, and Wesley Jones, "Dynamic, symmetry-preserving, and hardware-adaptable circuits for quantum computing many-body states and correlators of the Anderson impurity model", Physical Review Research 7 2, 023186 (2025).

[171] Rinka Miura, "Velocity Verlet-based optimization for variational quantum eigensolvers", Quantum Information Processing 25 2, 34 (2026).

[172] Yuya O. Nakagawa, Jiabao Chen, Shotaro Sudo, Yu-ya Ohnishi, and Wataru Mizukami, "Analytical Formulation of the Second-Order Derivative of Energy for the Orbital-Optimized Variational Quantum Eigensolver: Application to Polarizability", Journal of Chemical Theory and Computation 19 7, 1998 (2023).

[173] Norifumi Matsumoto, Shoichiro Tsutsui, Yuya O. Nakagawa, Yuichiro Hidaka, Shota Kanasugi, Kazunori Maruyama, Hirotaka Oshima, and Shintaro Sato, "Quantum many-body simulation of finite-temperature systems with sampling a series expansion of a quantum imaginary-time evolution", Physical Review Research 7 1, 013254 (2025).

[174] Yuncheng Lu, Shuang Liang, Hongxiang Fan, Ce Guo, Wayne Luk, and Paul H. J. Kelly, 2025 62nd ACM/IEEE Design Automation Conference (DAC) 1 (2025) ISBN:979-8-3315-0304-8.

[175] Gabriel Marin-Sanchez and David Amaro, "Performance analysis of a filtering variational quantum algorithm", New Journal of Physics 27 5, 054505 (2025).

[176] Zuoqiang Du, Jiepeng Wang, and Hui Li, "Quantum Firefly Algorithm: A Novel Approach for Quantum Circuit Scheduling Optimization", Electronics 14 11, 2123 (2025).

[177] Abhinav Anand and Kenneth R. Brown, "Hamiltonian-based graph-state ansatz for variational quantum algorithms", Physical Review A 111 1, 012437 (2025).

[178] Haruhiko Hasegawa, Masayuki Shimoda, Hiroki Nakahara, and Takefumi Miyoshi, 2024 International Conference on Field Programmable Technology (ICFPT) 1 (2024) ISBN:979-8-3315-2321-3.

[179] Tomoya Shiota, Kenji Ishihara, and Wataru Mizukami, "Lowering the exponential wall: accelerating high-entropy alloy catalysts screening using local surface energy descriptors from neural network potentials", Digital Discovery 4 3, 738 (2025).

[180] 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).

[181] Chen Zhang, Zeyu Song, Haojie Wang, Kaiyuan Rong, and Jidong Zhai, Proceedings of the ACM International Conference on Supercomputing 443 (2021) ISBN:9781450383356.

[182] Elmin Marevac, Esad Kadušić, Nataša Živić, and Christoph Ruland, "Accelerated Quantum Algorithm Prototyping: Modular Simulation and Noise Modelling with CUDA Support", Journal of Advances in Information Technology 17 6, 1188 (2026).

[183] Abhinav Anand and Kenneth R Brown, "Leveraging commuting groups for an efficient variational Hamiltonian ansatz", Quantum Science and Technology 10 4, 045009 (2025).

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[185] Alexandre Fleury, James Brown, Erika Lloyd, Maritza Hernandez, and Isaac H. Kim, "Nonunitary Coupled Cluster Enabled by Midcircuit Measurements on Quantum Computers", Journal of Chemical Theory and Computation 20 24, 10807 (2024).

[186] Davide Bincoletto and Jakob S. Kottmann, "A physics-informed measurement protocol for expectation values of fermionic observables", Digital Discovery 5 3, 1257 (2026).

[187] Samuel Yen-Chi Chen, Tzu-Chieh Wei, Chao Zhang, Haiwang Yu, and Shinjae Yoo, "Quantum convolutional neural networks for high energy physics data analysis", Physical Review Research 4 1, 013231 (2022).

[188] Yusuke Kimura, Shaowen Li, Hiroyuki Sato, and Masahiro Fujita, 2024 IEEE International Conference on Quantum Software (QSW) 107 (2024) ISBN:979-8-3503-6847-5.

[189] Changjong Kim, Ehan Sohn, Seunghwan Kim, Alex Sim, Kesheng Wu, Houjun Tang, Yongseok Son, and Sunggon Kim, "ScaleQsim: Highly Scalable Quantum Circuit Simulation Framework for Exascale HPC Systems", Proceedings of the ACM on Measurement and Analysis of Computing Systems 9 3, 1 (2025).

[190] Anh Phuong Ngo, Nhat Le, Hieu T. Nguyen, Abdullah Eroglu, and Duong T. Nguyen, 2023 IEEE Green Technologies Conference (GreenTech) 164 (2023) ISBN:978-1-6654-9287-4.

[191] Joseph Peetz, Scott E. Smart, Spyros Tserkis, and Prineha Narang, "Simulation of open quantum systems via low-depth convex unitary evolutions", Physical Review Research 6 2, 023263 (2024).

[192] Yusuke Kimura, Shaowen Li, Hiroyuki Sato, and Masahiro Fujita, 2024 IEEE International Conference on Quantum Computing and Engineering (QCE) 757 (2024) ISBN:979-8-3315-4137-8.

[193] Ikuo Kinoshita, A. Zoia, C.M. Diop, and E. Saikali, "Quantum Circuit Learning for Uncertainty Quantification of RELAP5 Code Analysis of ROSA/LSTF Small Break LOCA Tests", EPJ Web of Conferences 302, 17001 (2024).

[194] 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.

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[196] Xinyi Wang, Shaukat Ali, Aitor Arrieta, Paolo Arcaini, and Maite Arratibel, Companion Proceedings of the 32nd ACM International Conference on the Foundations of Software Engineering 399 (2024) ISBN:9798400706585.

[197] Mallika Chouhan and Sameer G. Kulkarni, 2026 18th International Conference on COMmunication Systems and NETworks (COMSNETS) 807 (2026) ISBN:979-8-3315-9239-4.

[198] Fong Yew Leong, Wei-Bin Ewe, and Dax Enshan Koh, "Variational quantum evolution equation solver", Scientific Reports 12 1, 10817 (2022).

[199] 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).

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[201] Yu Liu, Kazuya Kaneko, Kentaro Baba, Jumpei Koyama, Koichi Kimura, and Naoyuki Takeda, "Analysis of Parameterized Quantum Circuits: On the Connection Between Expressibility and Types of Quantum Gates", IEEE Transactions on Quantum Engineering 6, 1 (2025).

[202] Yusuke Teranishi, Shoma Hiraoka, Wataru Mizukami, Masao Okita, and Fumihiko Ino, "Lazy Qubit Reordering for Accelerating Parallel State-Vector-based Quantum Circuit Simulation", ACM Transactions on Quantum Computing 6 4, 1 (2025).

[203] Chenyang Jiao, Zhikai Qin, and Li Shen, "ScalaQC: a scalability optimization framework for full-state quantum simulation on CPU+GPU heterogeneous clusters", CCF Transactions on High Performance Computing 6 4, 397 (2024).

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[205] Jesús Cerrudo-Herrera, Daniel Talaván-Vega, Paloma Rodríguez-Oliver, Ahmed Ziabat-Ziabat, and Juan Antonio Rico-Gallego, "Benchmarking quantum computing statevector simulators on high-performance computing", SIMULATION 102 7, 493 (2026).

[206] Cenk Tüysüz, Carla Rieger, Kristiane Novotny, Bilge Demirköz, Daniel Dobos, Karolos Potamianos, Sofia Vallecorsa, Jean-Roch Vlimant, and Richard Forster, "Hybrid quantum classical graph neural networks for particle track reconstruction", Quantum Machine Intelligence 3 2, 29 (2021).

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[214] Yixiong Chen, "A novel image classification framework based on variational quantum algorithms", Quantum Information Processing 23 10, 362 (2024).

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[218] Carlos Bistafa, Josh J. M. Kirsopp, Antonio Márquez Romero, Jumpei Koyama, and Michal Krompiec, "A Hybrid Quantum Computing Method for UV–Vis Spectroscopy of Solvated Molecules at Room Temperature", The Journal of Physical Chemistry A 129 43, 9991 (2025).

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[220] 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.

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[222] Yasunari Suzuki, Suguru Endo, Keisuke Fujii, and Yuuki Tokunaga, "Quantum Error Mitigation as a Universal Error Reduction Technique: Applications from the NISQ to the Fault-Tolerant Quantum Computing Eras", PRX Quantum 3 1, 010345 (2022).

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[224] Hirotoshi Hirai, "Practical application of quantum neural network to materials informatics", Scientific Reports 14 1, 8583 (2024).

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[228] Jinpeng Ji, Enmin Zhuo, Lu Wang, Zaichen Zhang, and Xutao Yu, Communications in Computer and Information Science 2733, 58 (2026) ISBN:978-981-95-4790-6.

[229] Leonardo Placidi, Ryuichiro Hataya, Toshio Mori, Koki Aoyama, Hayata Morisaki, Kosuke Mitarai, and Keisuke Fujii, "MNISQ: A Large-Scale Quantum Circuit Dataset for Machine Learning in the NISQ Era", Scientific Data 13 1, 810 (2026).

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[231] Alan Morningstar, Markus Hauru, Jackson Beall, Martin Ganahl, Adam G.M. Lewis, Vedika Khemani, and Guifre Vidal, "Simulation of Quantum Many-Body Dynamics with Tensor Processing Units: Floquet Prethermalization", PRX Quantum 3 2, 020331 (2022).

[232] V. Canivell, P. Forn-Díaz, A. Garcia-Saez, and R. Sagastizabal, "Startup Qilimanjaro—towards a European full-stack coherent quantum annealer platform", EPJ Quantum Technology 8 1, 6 (2021).

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

[234] Kan Hatakeyama-Sato, Yasuhiko Igarashi, Takahiro Kashikawa, Koichi Kimura, and Kenichi Oyaizu, "Quantum circuit learning as a potential algorithm to predict experimental chemical properties", Digital Discovery 2 1, 165 (2023).

[235] Ang Li, Alessandro Baroni, Ionel Stetcu, and Travis S. Humble, "Deep quantum circuit simulations of low-energy nuclear states", The European Physical Journal A 60 5, 106 (2024).

[236] Mikio Morita, Yoshinori Tomita, Junpei Koyama, and Koichi Kimura, "Simulator Demonstration of Large Scale Variational Quantum Algorithm on HPC Cluster", IEEE Access 12, 85219 (2024).

[237] Roberto Campos, P. A. M. Casares, and M. A. Martin-Delgado, "Quantum Metropolis Solver: a quantum walks approach to optimization problems", Quantum Machine Intelligence 5 2, 28 (2023).

[238] 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).

[239] Tomoya Shiota, Kenji Ishihara, and Wataru Mizukami, "Universal neural network potentials as descriptors: towards scalable chemical property prediction using quantum and classical computers", Digital Discovery 3 9, 1714 (2024).

[240] Chen Zhang, Haojie Wang, Zixuan Ma, Lei Xie, Zeyu Song, and Jidong Zhai, SC22: International Conference for High Performance Computing, Networking, Storage and Analysis 1 (2022) ISBN:978-1-6654-5444-5.

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[242] Muhammad Shaeer Moeed, James Brown, Alexander Ibrahim, Estêvão V. B. de Oliveira, and Pierre-Nicholas Roy, "Qubit encodings for lattices of dipolar planar rotors", The Journal of Chemical Physics 163 17, 174103 (2025).

[243] Takahiro Ohgoe, Hokuto Iwakiri, Kazuhide Ichikawa, Sho Koh, and Masaya Kohda, "Quantum Computation of a Quasiparticle Band Structure with the Quantum-Selected Configuration Interaction", Journal of the Physical Society of Japan 94 11, 114002 (2025).

[244] Yohei Ibe, Yuya O. Nakagawa, Nathan Earnest, Takahiro Yamamoto, Kosuke Mitarai, Qi Gao, and Takao Kobayashi, "Calculating transition amplitudes by variational quantum deflation", Physical Review Research 4 1, 013173 (2022).

[245] Akimoto Nakayama, Kosuke Mitarai, Leonardo Placidi, Takanori Sugimoto, and Keisuke Fujii, "VQE-generated quantum circuit dataset for machine learning", Physical Review Research 7 3, 033048 (2025).

[246] Enhua Xu, Yuma Shimomoto, Seiichiro L. Ten-no, and Takashi Tsuchimochi, "Many-Body-Expansion Based on Variational Quantum Eigensolver and Deflation for Dynamical Correlation", The Journal of Physical Chemistry A 128 12, 2507 (2024).

[247] Shuang Liang, Yuncheng Lu, Ce Guo, Paul H. J. Kelly, Wayne Luk, and Hongxiang Fan, 2026 IEEE International Symposium on High Performance Computer Architecture (HPCA) 1 (2026) ISBN:979-8-3315-9302-5.

[248] Kosei Teramoto, Rudy Raymond, and Hiroshi Imai, 2023 IEEE International Conference on Quantum Computing and Engineering (QCE) 543 (2023) ISBN:979-8-3503-4323-6.

[249] Kouhei Nakaji, Mohsen Bagherimehrab, and Alán Aspuru-Guzik, "High-Order Randomized Compiler for Hamiltonian Simulation", PRX Quantum 5 2, 020330 (2024).

[250] Takuya Yoshioka, Keita Sasada, Yuichiro Nakano, and Keisuke Fujii, 2023 IEEE International Conference on Quantum Computing and Engineering (QCE) 300 (2023) ISBN:979-8-3503-4323-6.

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[252] Takashi Tsuchimochi, Yoohee Ryo, Siu Chung Tsang, and Seiichiro L. Ten-no, "Multi-state quantum simulations via model-space quantum imaginary time evolution", npj Quantum Information 9 1, 113 (2023).

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[254] Matthew A. Dorsey, Kelvin Dsouza, Dhruv Ranganath, Joshua S. Harris, Thomas R. Lane, Fabio Urbina, and Sean Ekins, "Near-Term Quantum Classification Algorithms Applied to Antimalarial Drug Discovery", Journal of Chemical Information and Modeling 64 15, 5922 (2024).

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[256] Mitsuki Katsuda, Kosuke Mitarai, and Keisuke Fujii, "Simulation and performance analysis of quantum error correction with a rotated surface code under a realistic noise model", Physical Review Research 6 1, 013024 (2024).

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