Mitiq: A software package for error mitigation on noisy quantum computers

Ryan LaRose; Andrea Mari; Sarah Kaiser; Peter J. Karalekas; Andre A. Alves; Piotr Czarnik; Mohamed El Mandouh; Max H. Gordon; Yousef Hindy; Aaron Robertson; Purva Thakre; Misty Wahl; Danny Samuel; Rahul Mistri; Maxime Tremblay; Nick Gardner; Nathaniel T. Stemen; Nathan Shammah; William J. Zeng

doi:10.22331/q-2022-08-11-774

Mitiq: A software package for error mitigation on noisy quantum computers

Ryan LaRose^1,2, Andrea Mari¹, Sarah Kaiser¹, Peter J. Karalekas^1,3, Andre A. Alves⁴, Piotr Czarnik⁵, Mohamed El Mandouh⁶, Max H. Gordon⁷, Yousef Hindy⁸, Aaron Robertson⁹, Purva Thakre¹⁰, Misty Wahl¹, Danny Samuel¹, Rahul Mistri¹, Maxime Tremblay¹¹, Nick Gardner⁸, Nathaniel T. Stemen¹, Nathan Shammah¹, and William J. Zeng^1,8,12

¹Unitary Fund
²Michigan State University, East Lansing, MI
³AWS Center for Quantum Computing, Pasadena, CA 91125, USA
⁴Hamburg University of Applied Sciences, Hamburg, Germany
⁵Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM 87545, USA
⁶Institute for Quantum Computing, University of Waterloo, Waterloo, ON, N2L 3G1, Canada
⁷Instituto de Física Teórica, UAM/CSIC, Universidad Autónoma de Madrid, Madrid, Spain
⁸Stanford University, Palo Alto, CA
⁹Independent researcher
¹⁰Southern Illinois University, Carbondale, IL
¹¹Institut quantique, Université de Sherbrooke, Sherbrooke, QC, J1K 2R1, Canada
¹²Goldman, Sachs & Co, New York, NY

Published:	2022-08-11, volume 6, page 774
Eprint:	arXiv:2009.04417v4
Doi:	https://doi.org/10.22331/q-2022-08-11-774
Citation:	Quantum 6, 774 (2022).

Find this paper interesting or want to discuss? Scite or leave a comment on SciRate.

Abstract

We introduce Mitiq, a Python package for error mitigation on noisy quantum computers. Error mitigation techniques can reduce the impact of noise on near-term quantum computers with minimal overhead in quantum resources by relying on a mixture of quantum sampling and classical post-processing techniques. Mitiq is an extensible toolkit of different error mitigation methods, including zero-noise extrapolation, probabilistic error cancellation, and Clifford data regression. The library is designed to be compatible with generic backends and interfaces with different quantum software frameworks. We describe Mitiq using code snippets to demonstrate usage and discuss features and contribution guidelines. We present several examples demonstrating error mitigation on IBM and Rigetti superconducting quantum processors as well as on noisy simulators.

Featured image: Mitiq project logo

Popular summary

In this paper, we introduce Mitiq: a Python toolkit for implementing error mitigation techniques on quantum computers.

Current quantum computers are noisy due to interactions with the environment, imperfect gate applications, state preparation and measurement errors, etc. Error mitigation seeks to reduce these effects with minimal overhead in quantum resources by relying on a mixture of quantum sampling and classical post-processing techniques.

► BibTeX data

@article{LaRose2022mitiqsoftware,
  doi = {10.22331/q-2022-08-11-774},
  url = {https://doi.org/10.22331/q-2022-08-11-774},
  title = {Mitiq: {A} software package for error mitigation on noisy quantum computers},
  author = {LaRose, Ryan and Mari, Andrea and Kaiser, Sarah and Karalekas, Peter J. and Alves, Andre A. and Czarnik, Piotr and El Mandouh, Mohamed and Gordon, Max H. and Hindy, Yousef and Robertson, Aaron and Thakre, Purva and Wahl, Misty and Samuel, Danny and Mistri, Rahul and Tremblay, Maxime and Gardner, Nick and Stemen, Nathaniel T. and Shammah, Nathan and Zeng, William J.},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {6},
  pages = {774},
  month = aug,
  year = {2022}
}

► References

[1] Suguru Endo, Zhenyu Cai, Simon C. Benjamin, and Xiao Yuan. ``Hybrid quantum-classical algorithms and quantum error mitigation''. J. Phys. Soc. Japan 90, 032001 (2021).
https://doi.org/10.7566/jpsj.90.032001

[2] Kristan Temme, Sergey Bravyi, and Jay M. Gambetta. ``Error mitigation for short-depth quantum circuits''. Phys. Rev. Lett. 119, 180509 (2017).
https://doi.org/10.1103/PhysRevLett.119.180509

[3] Ying Li and Simon C. Benjamin. ``Efficient variational quantum simulator incorporating active error minimization''. Phys. Rev. X 7, 021050 (2017).
https://doi.org/10.1103/PhysRevX.7.021050

[4] Suguru Endo, Simon C. Benjamin, and Ying Li. ``Practical quantum error mitigation for near-future applications''. Phys. Rev. X 8, 031027 (2018).
https://doi.org/10.1103/PhysRevX.8.031027

[5] Piotr Czarnik, Andrew Arrasmith, Patrick J Coles, and Lukasz Cincio. ``Error mitigation with Clifford quantum-circuit data'' (2020). arXiv:2005.10189.
https://doi.org/10.22331/q-2021-11-26-592
arXiv:2005.10189

[6] Angus Lowe, Max Hunter Gordon, Piotr Czarnik, Andrew Arrasmith, Patrick J. Coles, and Lukasz Cincio. ``Unified approach to data-driven quantum error mitigation'' (2020). arXiv:2011.01157.
https://doi.org/10.1103/PhysRevResearch.3.033098
arXiv:2011.01157

[7] Lea F. Santos and Lorenza Viola. ``Dynamical control of qubit coherence: Random versus deterministic schemes''. Phys. Rev. A 72, 062303 (2005).
https://doi.org/10.1103/PhysRevA.72.062303

[8] Lorenza Viola and Emanuel Knill. ``Random decoupling schemes for quantum dynamical control and error suppression''. Phys. Rev. Lett. 94, 060502 (2005).
https://doi.org/10.1103/PhysRevLett.94.060502

[9] Bibek Pokharel, Namit Anand, Benjamin Fortman, and Daniel A. Lidar. ``Demonstration of fidelity improvement using dynamical decoupling with superconducting qubits''. Phys. Rev. Lett. 121, 220502 (2018).
https://doi.org/10.1103/PhysRevLett.121.220502

[10] Joel J Wallman and Joseph Emerson. ``Noise tailoring for scalable quantum computation via randomized compiling''. Phys. Rev. A 94, 052325 (2016).
https://doi.org/10.1103/PhysRevA.94.052325

[11] Jarrod R. McClean, Zhang Jiang, Nicholas C. Rubin, Ryan Babbush, and Hartmut Neven. ``Decoding quantum errors with subspace expansions''. Nature Commun. 11 (2020).
https://doi.org/10.1038/s41467-020-14341-w

[12] Abhinav Kandala, Kristan Temme, Antonio D. Córcoles, Antonio Mezzacapo, Jerry M. Chow, and Jay M. Gambetta. ``Error mitigation extends the computational reach of a noisy quantum processor''. Nature 567, 491–495 (2019).
https://doi.org/10.1038/s41586-019-1040-7

[13] Tudor Giurgica-Tiron, Yousef Hindy, Ryan LaRose, Andrea Mari, and William J. Zeng. ``Digital zero noise extrapolation for quantum error mitigation''. 2020 IEEE Int. Conf. Quantum Comp. Eng. (QCE) (2020).
https://doi.org/10.1109/QCE49297.2020.00045

[14] Miroslav Urbanek, Benjamin Nachman, and Wibe A. de Jong. ``Error detection on quantum computers improving the accuracy of chemical calculations''. Phys. Rev. A 102 (2020).
https://doi.org/10.1103/PhysRevA.102.022427

[15] Christophe Vuillot. ``Is error detection helpful on IBM 5Q chips?''. Quantum Inf. Comp. 18 (2018).
https://doi.org/10.26421/qic18.11-12

[16] Google AI Quantum et al. ``Hartree-Fock on a superconducting qubit quantum computer''. Science 369, 1084–1089 (2020).
https://doi.org/10.1126/science.abb9811

[17] Chao Song, Jing Cui, H. Wang, J. Hao, H. Feng, and Ying Li. ``Quantum computation with universal error mitigation on a superconducting quantum processor''. Science Adv. 5 (2019).
https://doi.org/10.1126/sciadv.aaw5686

[18] Shuaining Zhang, Yao Lu, Kuan Zhang, Wentao Chen, Ying Li, Jing-Ning Zhang, and Kihwan Kim. ``Error-mitigated quantum gates exceeding physical fidelities in a trapped-ion system''. Nature Communications 11, 587 (2020).
https://doi.org/10.1038/s41467-020-14376-z

[19] Alan Ho and Dave Bacon. ``Announcing Cirq: An open-source framework for NISQ algorithms''. Google Blog (2018). url: ai.googleblog.com/2018/07/announcing-cirq-open-source-framework.html.
https://ai.googleblog.com/2018/07/announcing-cirq-open-source-framework.html

[20] Héctor Abraham et al. ``Qiskit: An open-source framework for quantum computing'' (2019).
https://doi.org/10.5281/zenodo.2562111

[21] Robert S. Smith, Michael J. Curtis, and William J. Zeng. ``A practical quantum instruction set architecture'' (2016). arXiv:1608.03355.
arXiv:1608.03355

[22] Braket. ``https://github.com/aws/amazon-braket-sdk-python'' (2021).
https://github.com/aws/amazon-braket-sdk-python

[23] Pauli Virtanen et al. ``SciPy 1.0: fundamental algorithms for scientific computing in Python''. Nature Meth. 17, 261–272 (2020).
https://doi.org/10.1038/s41592-019-0686-2

[24] P. J. J. O’Malley, R. Babbush, I. D. Kivlichan, J. Romero, J. R. McClean, R. Barends, J. Kelly, P. Roushan, A. Tranter, N. Ding, and et al. ``Scalable quantum simulation of molecular energies''. Physical Review X 6 (2016).
https://doi.org/10.1103/PhysRevX.6.031007

[25] Alejandro Sopena, Max Hunter Gordon, Germán Sierra, and Esperanza López. ``Simulating quench dynamics on a digital quantum computer with data-driven error mitigation'' (2021). arXiv:2103.12680.
https://doi.org/10.1088/2058-9565/ac0e7a
arXiv:2103.12680

[26] Zhenyu Cai. ``Multi-exponential error extrapolation and combining error mitigation techniques for nisq applications''. npj Quantum Inf. 7, 80 (2021).
https://doi.org/10.1038/s41534-021-00404-3

[27] Jinzhao Sun, Xiao Yuan, Takahiro Tsunoda, Vlatko Vedral, Simon C. Benjamin, and Suguru Endo. ``Mitigating realistic noise in practical noisy intermediate-scale quantum devices''. Phys. Rev. Applied 15, 034026 (2021).
https://doi.org/10.1103/PhysRevApplied.15.034026

[28] Jarrod R. McClean, Mollie E. Kimchi-Schwartz, Jonathan Carter, and Wibe A. de Jong. ``Hybrid quantum-classical hierarchy for mitigation of decoherence and determination of excited states''. Phys. Rev. A 95, 042308 (2017).
https://doi.org/10.1103/PhysRevA.95.042308

[29] X. Bonet-Monroig, R. Sagastizabal, M. Singh, and T. E. O'Brien. ``Low-cost error mitigation by symmetry verification''. Phys. Rev. A 98, 062339 (2018).
https://doi.org/10.1103/PhysRevA.98.062339

[30] Sam McArdle, Xiao Yuan, and Simon Benjamin. ``Error-mitigated digital quantum simulation''. Phys. Rev. Lett. 122, 180501 (2019).
https://doi.org/10.1103/PhysRevLett.122.180501

[31] R. Sagastizabal, X. Bonet-Monroig, M. Singh, M. A. Rol, C. C. Bultink, X. Fu, C. H. Price, V. P. Ostroukh, N. Muthusubramanian, A. Bruno, M. Beekman, N. Haider, T. E. O'Brien, and L. DiCarlo. ``Experimental error mitigation via symmetry verification in a variational quantum eigensolver''. Phys. Rev. A 100, 010302 (2019).
https://doi.org/10.1103/PhysRevA.100.010302

[32] Bálint Koczor. ``Exponential error suppression for near-term quantum devices'' (2021). arXiv:2011.05942.
https://doi.org/10.1103/PhysRevX.11.031057
arXiv:2011.05942

[33] William J. Huggins, Sam McArdle, Thomas E. O'Brien, Joonho Lee, Nicholas C. Rubin, Sergio Boixo, K. Birgitta Whaley, Ryan Babbush, and Jarrod R. McClean. ``Virtual distillation for quantum error mitigation'' (2021). arXiv:2011.07064.
https://doi.org/10.1103/PhysRevX.11.041036
arXiv:2011.07064

[34] Zhenyu Cai. ``Quantum error mitigation using symmetry expansion'' (2021). arXiv:2101.03151.
https://doi.org/10.22331/q-2021-09-21-548
arXiv:2101.03151

[35] Carlo Cafaro and Peter van Loock. ``Approximate quantum error correction for generalized amplitude-damping errors''. Phys. Rev. A 89, 022316 (2014).
https://doi.org/10.1103/PhysRevA.89.022316

[36] Matthew Otten and Stephen K. Gray. ``Recovering noise-free quantum observables''. Phys. Rev. A 99, 012338 (2019).
https://doi.org/10.1103/PhysRevA.99.012338

[37] Sisi Zhou and Liang Jiang. ``Optimal approximate quantum error correction for quantum metrology''. Phys. Rev. Research 2, 013235 (2020).
https://doi.org/10.1103/PhysRevResearch.2.013235

[38] Ming Gong, Xiao Yuan, Shiyu Wang, Yulin Wu, Youwei Zhao, Chen Zha, Shaowei Li, Zhen Zhang, Qi Zhao, Yunchao Liu, Futian Liang, Jin Lin, Yu Xu, Hui Deng, Hao Rong, He Lu, Simon C Benjamin, Cheng-Zhi Peng, Xiongfeng Ma, Yu-Ao Chen, Xiaobo Zhu, and Jian-Wei Pan. ``Experimental exploration of five-qubit quantum error-correcting code with superconducting qubits''. National Science Review 9 (2021).
https://doi.org/10.1093/nsr/nwab011

[39] Philipp Schindler, Julio T. Barreiro, Thomas Monz, Volckmar Nebendahl, Daniel Nigg, Michael Chwalla, Markus Hennrich, and Rainer Blatt. ``Experimental repetitive quantum error correction''. Science 332, 1059 (2011).
https://doi.org/10.1126/science.1203329

[40] E. Knill. ``Quantum computing with realistically noisy devices''. Nature 434, 39 (2005).
https://doi.org/10.1038/nature03350

[41] Constantin Brif, Raj Chakrabarti, and Herschel Rabitz. ``Control of quantum phenomena: past, present and future''. New J. Phys. 12, 075008 (2010).
https://doi.org/10.1088/1367-2630/12/7/075008

[42] Lorenza Viola, Emanuel Knill, and Seth Lloyd. ``Dynamical decoupling of open quantum systems''. Phys. Rev. Lett. 82, 2417 (1999).
https://doi.org/10.1103/physrevlett.82.2417

[43] 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, 044011 (2021).
https://doi.org/10.1088/2058-9565/abdca6

[44] Howard J. Carmichael. ``Statistical methods in quantum optics 1: Master equations and fokker-planck equations''. Springer-Verlag. (1999).
https://doi.org/10.1007/978-3-662-03875-8

[45] H.J. Carmichael. ``Statistical methods in quantum optics 2: Non-classical fields''. Springer Berlin Heidelberg. (2007).
https://doi.org/10.1007/978-3-540-71320-3

[46] H.P. Breuer and F. Petruccione. ``The theory of open quantum systems''. OUP Oxford. (2007).
https://doi.org/10.1093/acprof:oso/9780199213900.001.0001

[47] Prakash Murali, David C. Mckay, Margaret Martonosi, and Ali Javadi-Abhari. ``Software mitigation of crosstalk on noisy intermediate-scale quantum computers''. Proc. Twenty-Fifth Int. Conf. on Architect. Supp. for Progr. Lang. Operat. Syst. (2020).
https://doi.org/10.1145/3373376.3378477

[48] Iulia Buluta, Sahel Ashhab, and Franco Nori. ``Natural and artificial atoms for quantum computation''. Rep. Progr. Phys. 74, 104401 (2011).
https://doi.org/10.1088/0034-4885/74/10/104401

[49] Henrique Silvério, Sebastián Grijalva, Constantin Dalyac, Lucas Leclerc, Peter J. Karalekas, Nathan Shammah, Mourad Beji, Louis-Paul Henry, and Loïc Henriet. ``Pulser: An open-source package for the design of pulse sequences in programmable neutral-atom arrays'' (2021). arXiv:2104.15044.
https://doi.org/10.22331/q-2022-01-24-629
arXiv:2104.15044

[50] Boxi Li, Shahnawaz Ahmed, Sidhant Saraogi, Neill Lambert, Franco Nori, Alexander Pitchford, and Nathan Shammah. ``Pulse-level noisy quantum circuits with QuTiP'' (2021). arXiv:2105.09902.
https://doi.org/10.22331/q-2022-01-24-630
arXiv:2105.09902

[51] Daniel Gottesman, Alexei Kitaev, and John Preskill. ``Encoding a qubit in an oscillator''. Phys. Rev. A 64, 012310 (2001).
https://doi.org/10.1103/PhysRevA.64.012310

[52] Mazyar Mirrahimi, Zaki Leghtas, Victor V Albert, Steven Touzard, Robert J Schoelkopf, Liang Jiang, and Michel H Devoret. ``Dynamically protected cat-qubits: a new paradigm for universal quantum computation''. New J. Phys. 16, 045014 (2014).
https://doi.org/10.1088/1367-2630/16/4/045014

[53] Marios H. Michael, Matti Silveri, R. T. Brierley, Victor V. Albert, Juha Salmilehto, Liang Jiang, and S. M. Girvin. ``New class of quantum error-correcting codes for a bosonic mode''. Phys. Rev. X 6, 031006 (2016).
https://doi.org/10.1103/PhysRevX.6.031006

[54] Victor V. Albert, Jacob P. Covey, and John Preskill. ``Robust encoding of a qubit in a molecule''. Physical Review X 10 (2020).
https://doi.org/10.1103/physrevx.10.031050

[55] Jeffrey M. Gertler, Brian Baker, Juliang Li, Shruti Shirol, Jens Koch, and Chen Wang. ``Protecting a bosonic qubit with autonomous quantum error correction''. Nature 590, 243 (2021).
https://doi.org/10.1038/s41586-021-03257-0

[56] D. A. Lidar, I. L. Chuang, and K. B. Whaley. ``Decoherence-free subspaces for quantum computation''. Phys. Rev. Lett. 81, 2594 (1998).
https://doi.org/10.1103/PhysRevLett.81.2594

[57] Emanuel Knill, Raymond Laflamme, and Lorenza Viola. ``Theory of quantum error correction for general noise''. Phys. Rev. Lett. 84, 2525–2528 (2000).
https://doi.org/10.1103/PhysRevLett.84.2525

[58] Anton Frisk Kockum, Göran Johansson, and Franco Nori. ``Decoherence-free interaction between giant atoms in waveguide quantum electrodynamics''. Phys. Rev. Lett. 120, 140404 (2018).
https://doi.org/10.1103/PhysRevLett.120.140404

[59] Simon Lieu, Ron Belyansky, Jeremy T. Young, Rex Lundgren, Victor V. Albert, and Alexey V. Gorshkov. ``Symmetry breaking and error correction in open quantum systems''. Phys. Rev. Lett. 125, 240405 (2020).
https://doi.org/10.1103/physrevlett.125.240405

[60] Thomas A Alexander, Naoki Kanazawa, Daniel Josef Egger, Lauren Capelluto, Christopher James Wood, Ali Javadi-Abhari, and David McKay. ``Qiskit-Pulse: programming quantum computers through the cloud with pulses''. Quantum Sci. Tech. 5, 044006 (2020).
https://doi.org/10.1088/2058-9565/aba404

[61] Peter J Karalekas, Nikolas A Tezak, Eric C Peterson, Colm A Ryan, Marcus P da Silva, and Robert S Smith. ``A quantum-classical cloud platform optimized for variational hybrid algorithms''. Quantum Sci. Tech. 5, 024003 (2020).
https://doi.org/10.1088/2058-9565/ab7559

Cited by

[1] Chayan Patra, Sonaldeep Halder, and Rahul Maitra, "Projective quantum eigensolver via adiabatically decoupled subsystem evolution: A resource efficient approach to molecular energetics in noisy quantum computers", The Journal of Chemical Physics 160 21, 214122 (2024).

[2] Ratun Rahman and Dinh C. Nguyen, "Quantum Error Mitigation: A Comprehensive Survey", ACM Computing Surveys 58 16, 1 (2026).

[3] Elijah Pelofske, Andreas Bärtschi, and Stephan Eidenbenz, "Short-depth QAOA circuits and quantum annealing on higher-order ising models", npj Quantum Information 10 1, 30 (2024).

[4] Nathan Shammah, Quantum Technologies 45 (2026) ISBN:978-3-031-90726-5.

[5] Teppei Suzuki, Takashi Hasebe, and Tsubasa Miyazaki, "Quantum support vector machines for classification and regression on a trapped-ion quantum computer", (2023).

[6] Doan Hieu Nguyen, Xuan Tung Nguyen, Seon-Geun Jeong, Trinh Van Chien, Lajos Hanzo, and Won-Joo Hwang, "Hybrid Quantum Convolutional Neural Network-Aided Pilot Assignment in Cell-Free Massive MIMO Systems", IEEE Transactions on Vehicular Technology 74 12, 19876 (2025).

[7] 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).

[8] Maria Gragera Garces, IEEE INFOCOM 2026 - IEEE Conference on Computer Communications 1 (2026) ISBN:979-8-3315-4961-9.

[9] Gaurav Saxena and Thi Ha Kyaw, "Constant runtime error mitigation via restricted evolution", npj Quantum Information 12 1, 148 (2026).

[10] Quinn Langfitt, Ji Liu, Benchen Huang, Alvin Gonzales, Kaitlin N. Smith, Nikos Hardavellas, and Zain H. Saleem, "Extrapolating Pauli Checks for Expectation Value Estimation on Noisy Quantum Devices", IEEE Transactions on Quantum Engineering 7, 3103409 (2026).

[11] Anirban Mukherjee, Noah F. Berthusen, João C. Getelina, Peter P. Orth, and Yong-Xin Yao, "Comparative study of adaptive variational quantum eigensolvers for multi-orbital impurity models", Communications Physics 6 1, 4 (2023).

[12] Run-Sheng 润盛 Zhao 赵, Hong-Yang 鸿洋 Ma 马, Tao 涛 Cheng 程, Shuang 爽 Wang 王, and Xing-Kui 兴奎 Fan 范, "Quantum generative adversarial networks based on a readout error mitigation method with fault tolerant mechanism", Chinese Physics B 33 4, 040304 (2024).

[13] Fang Qi, Kaitlin N. Smith, Travis LeCompte, Nian-feng Tzeng, Xu Yuan, Frederic T. Chong, and Lu Peng, "Quantum Vulnerability Analysis to Guide Robust Quantum Computing System Design", IEEE Transactions on Quantum Engineering 5, 1 (2024).

[14] Diego García-Vega, Fernando Plou Llorente, Alejandro Leal Castaño, Elías F. Combarro, and José Ranilla, "pLazyQML: A parallel package for efficient execution of QML models on classical computers", (2025).

[15] Alejandro Sopena, Max Hunter Gordon, Diego García-Martín, Germán Sierra, and Esperanza López, "Algebraic Bethe Circuits", Quantum 6, 796 (2022).

[16] Benjamin McDonough, Andrea Mari, Nathan Shammah, Nathaniel T. Stemen, Misty Wahl, William J. Zeng, and Peter P. Orth, 2022 IEEE/ACM Third International Workshop on Quantum Computing Software (QCS) 83 (2022) ISBN:978-1-6654-7536-5.

[17] Adriano Lusso, Marco Venere, Victor Onofre, Alberto Maldonado-Romo, Alejandro Montanez-Barrera, and Marco D. Santambrogio, 2025 IEEE International Conference on Quantum Computing and Engineering (QCE) 602 (2025) ISBN:979-8-3315-5736-2.

[18] Pegah Mohammadipour and Xiantao Li, "Direct Analysis of Zero-Noise Extrapolation: Polynomial Methods, Error Bounds, and Simultaneous Physical-Algorithmic Error Mitigation", Quantum 9, 1909 (2025).

[19] Abdul Kalam, Shubham Kumar, Ashok Kumar, and Prasanta K. Panigrahi, "Quantum Computation of Hydride Ion using Variational Quantum Algorithm", ChemistrySelect 9 43, e202402699 (2024).

[20] Shengxin Zhuang, John Tanner, Yusen Wu, Du Huynh, Wei Liu, Xavier Cadet, Nicolas Fontaine, Philippe Charton, Cedric Damour, Frederic Cadet, and Jingbo Wang, "Non-hemolytic peptide classification using a quantum support vector machine", Quantum Information Processing 23 11, 379 (2024).

[21] Srushti Patil, Dibyendu Mondal, and Rahul Maitra, "Machine learning approach toward quantum error mitigation for accurate molecular energetics", The Journal of Chemical Physics 163 2, 024129 (2025).

[22] 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 33 7, 10325 (2026).

[23] Yongchun Xu, Zengtao Kuang, Qun Huang, Jie Yang, Hamid Zahrouni, Michel Potier-Ferry, Kaixuan Huang, Jia-Chi Zhang, Heng Fan, and Heng Hu, "Nonlinear path-following via the asymptotic numerical method on a quantum processor", Computational Mechanics (2026).

[24] Almudena Carrera Vazquez, Daniel J. Egger, David Ochsner, and Stefan Woerner, "Well-conditioned multi-product formulas for hardware-friendly Hamiltonian simulation", Quantum 7, 1067 (2023).

[25] Hrushikesh Pramod Patil, Peiyi Li, Ji Liu, and Huiyang Zhou, 2023 IEEE International Conference on Quantum Computing and Engineering (QCE) 898 (2023) ISBN:979-8-3503-4323-6.

[26] Xinyi Wang, Shaukat Ali, Paolo Arcaini, Narasimha Raghavan Veeraragavan, and Jan F. Nygård, "Quantum Neural Network Classifier for Cancer Registry System Testing: A Feasibility Study", ACM Transactions on Software Engineering and Methodology 35 5, 1 (2026).

[27] Alexander Engelsberger and Thomas Villmann, "Quantum Computing Approaches for Vector Quantization—Current Perspectives and Developments", Entropy 25 3, 540 (2023).

[28] Xinyi Wang, Shaukat Ali, and Paolo Arcaini, "Quantum Artificial Intelligence for Software Engineering: The Road Ahead", ACM Transactions on Software Engineering and Methodology 35 9, 1 (2026).

[29] Noah Goss, Samuele Ferracin, Akel Hashim, Arnaud Carignan-Dugas, John Mark Kreikebaum, Ravi K. Naik, David I. Santiago, and Irfan Siddiqi, "Extending the computational reach of a superconducting qutrit processor", npj Quantum Information 10 1, 101 (2024).

[30] Fan Chen, Lei Jiang, Hausi Müller, Philip Richerme, Cheng Chu, Zhenxiao Fu, and Min Yang, "NISQ Quantum Computing: A Security-Centric Tutorial and Survey [Feature]", IEEE Circuits and Systems Magazine 24 1, 14 (2024).

[31] Kevin Schultz, Ryan LaRose, Andrea Mari, Gregory Quiroz, Nathan Shammah, B. David Clader, and William J. Zeng, "Impact of time-correlated noise on zero-noise extrapolation", Physical Review A 106 5, 052406 (2022).

[32] Yuta Shingu, Tetsuro Nikuni, Shiro Kawabata, and Yuichiro Matsuzaki, "Quantum annealing with error mitigation", Physical Review A 109 4, 042606 (2024).

[33] Alexander Miessen, Pauline J. Ollitrault, Francesco Tacchino, and Ivano Tavernelli, "Quantum algorithms for quantum dynamics", Nature Computational Science 3 1, 25 (2022).

[34] Yanbin Chen, Qunyou Liu, Yu Wang, Christian B. Mendl, and Helmut Seidl, Lecture Notes in Computer Science 16977, 558 (2027) ISBN:978-3-032-40373-5.

[35] Daniel T. Chen, Ethan H. Hansen, Xinpeng Li, Vinooth Kulkarni, Vipin Chaudhary, Bin Ren, Qiang Guan, Sanmukh Kuppannagari, Ji Liu, and Shuai Xu, 2023 IEEE International Parallel and Distributed Processing Symposium Workshops (IPDPSW) 517 (2023) ISBN:979-8-3503-1199-0.

[36] Salvatore Certo, Anh Pham, Nicolas Robles, and Andrew Vlasic, "Conditional generative models for learning stochastic processes", Quantum Machine Intelligence 5 2, 42 (2023).

[37] Swarnadeep Majumder, Christopher G. Yale, Titus D. Morris, Daniel S. Lobser, Ashlyn D. Burch, Matthew N. H. Chow, Melissa C. Revelle, Susan M. Clark, and Raphael C. Pooser, "Characterizing and mitigating coherent errors in a trapped ion quantum processor using hidden inverses", Quantum 7, 1006 (2023).

[38] Shi-Xin Zhang and Shuai Yin, "Universal imaginary-time critical dynamics on a quantum computer", Physical Review B 109 13, 134309 (2024).

[39] Michael Krebsbach, Björn Trauzettel, and Alessio Calzona, "Optimization of Richardson extrapolation for quantum error mitigation", Physical Review A 106 6, 062436 (2022).

[40] Elias X. Huber, Benjamin Y. L. Tan, Paul R. Griffin, and Dimitris G. Angelakis, "Exponential qubit reduction in optimization for financial transaction settlement", EPJ Quantum Technology 11 1, 52 (2024).

[41] Marco Venere, Adriano Lusso, Victor Onofre, Alberto Maldonado-Romo, and Marco D. Santambrogio, 2024 IEEE International Conference on Quantum Computing and Engineering (QCE) 426 (2024) ISBN:979-8-3315-4137-8.

[42] Siyuan Niu and Aida Todri-Sanial, Quantum Computing 19 (2024) ISBN:978-3-031-37965-9.

[43] 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).

[44] Xiao-Dao Lin, Hsi-Ming Chang, Jhih-Shih You, and Hsiu-Chuan Hsu, 2025 IEEE International Conference on Quantum Control, Computing and Learning (qCCL) 58 (2025) ISBN:978-1-6654-5782-8.

[45] Juan Borge, Unai Aseguinolaza, Nahual Sobrino, Gabriel Sobrino, and Joaquim Jornet-Somoza, "Error Estimation in Current Noisy Quantum Computers", (2023).

[46] Yusuke Hama and Hirofumi Nishi, "Quantum error mitigation via quantum-noise-effect circuit groups", Scientific Reports 14 1, 6077 (2024).

[47] Saleh Almutairi, Asem Alenaizan, Abduljabar Al-Sayoud, Joakim Beck, Sheikha Lardhi, Shuroog Al-Ogbi, and Muhamad Felemban, "Quantum Computing for Computational Sciences", IEEE Transactions on Quantum Engineering 7, 3103728 (2026).

[48] Peter Annis, Abe Kassem, and Evan Coleman, Proceedings of the 35th International Symposium on High-Performance Parallel and Distributed Computing 659 (2026) ISBN:9798400726408.

[49] Elijah Pelofske, Vincent Russo, Ryan Larose, Andrea Mari, Dan Strano, Andreas Bärtschi, Stephan Eidenbenz, and William Zeng, "Increasing the Measured Effective Quantum Volume with Zero Noise Extrapolation", ACM Transactions on Quantum Computing 5 3, 1 (2024).

[50] Zirui Sheng, Weitang Li, and Zhigang Shuai, "Quantum-computational chemistry in noisy intermediate-scale quantum era: TenCirChem and its application", Chinese Science Bulletin 70 34, 5792 (2025).

[51] Ritajit Majumdar, Pedro Rivero, Friedrike Metz, Areeq Hasan, and Derek S. Wang, 2023 IEEE International Conference on Quantum Computing and Engineering (QCE) 881 (2023) ISBN:979-8-3503-4323-6.

[52] Victor Manuel González-Gorrín and Josep Prieto-Blázquez, "Metamorphic Malware Detection via Graph-Augmented Neural Semantics and Adversarial Hardening: A Comprehensive Framework", Journal of Cybersecurity and Privacy 6 5, 164 (2026).

[53] Emmanouil Giortamis, Francisco Romao, Nathaniel Tornow, Dmitry Lugovoy, and Pramod Bhatotia, Proceedings of the International Conference for High Performance Computing, Networking, Storage and Analysis 728 (2025) ISBN:9798400714665.

[54] Olivia Di Matteo and R. M. Woloshyn, "Quantum computing fidelity susceptibility using automatic differentiation", Physical Review A 106 5, 052429 (2022).

[55] Vincent Russo and Andrea Mari, "Quantum error mitigation by layerwise Richardson extrapolation", Physical Review A 110 6, 062420 (2024).

[56] Takaharu Yoshida, Yuta Shingu, Chihaya Shimada, Tetsuro Nikuni, Hideaki Hakoshima, and Yuichiro Matsuzaki, "Hardware-efficient quantum annealing with error mitigation via classical shadow", Physical Review A 113 6, 062430 (2026).

[57] Nils Quetschlich and Olivia Di Matteo, "An experience-based classification of quantum bugs in quantum software", Computing 107 10, 193 (2025).

[58] Piotr Czarnik, Michael McKerns, Andrew T. Sornborger, and Lukasz Cincio, "Improving the efficiency of learning-based error mitigation", Quantum 9, 1727 (2025).

[59] Yulin Chi, Hongyi Shi, Wen Zheng, Haoyang Cai, Yu Zhang, Xinsheng Tan, Shaoxiong Li, Jianwei Wang, Jiangyu Cui, Man-Hong Yung, and Yang Yu, "Variational quantum algorithms with invariant probabilistic error cancellation on noisy quantum processors", Science China Physics, Mechanics & Astronomy 69 1, 210312 (2026).

[60] Wenbo Shi and Robert Malaney, GLOBECOM 2023 - 2023 IEEE Global Communications Conference 5475 (2023) ISBN:979-8-3503-1090-0.

[61] Simone Cantori, Andrea Mari, David Vitali, and Sebastiano Pilati, "Synergy between noisy quantum computers and scalable classical deep learning for quantum error mitigation", EPJ Quantum Technology 11 1, 45 (2024).

[62] Samudra Dasgupta, Travis S. Humble, and Arshag Danageozian, 2023 IEEE International Conference on Quantum Computing and Engineering (QCE) 99 (2023) ISBN:979-8-3503-4323-6.

[63] Bisma Majid, Shabir Ahmed Sofi, and Zamrooda Jabeen, "Noise resilient quantum learning: Adaptive policy guided error mitigation in quantum reinforcement learning for the traveling salesman problem", Applied Soft Computing 187, 114279 (2026).

[64] Monika Malik, Quantum Ops 97 (2026) ISBN:978-3-032-10774-9.

[65] Teppei Suzuki, Takashi Hasebe, and Tsubasa Miyazaki, "Quantum support vector machines for classification and regression on a trapped-ion quantum computer", Quantum Machine Intelligence 6 1, 31 (2024).

[66] Badhon Rahman, Majid Haghparast, and Tommi Mikkonen, "Classification of security challenges and mitigation approaches in the quantum software engineering", Journal of Systems and Software 238, 112884 (2026).

[67] Boseon Kim, Wooyeong Song, Kwangil Bae, Wonhyuk Lee, and IlKwon Sohn, "Enhanced extrapolation-based quantum error mitigation using repetitive structure in quantum algorithms", Quantum Science and Technology 11 3, 035037 (2026).

[68] Misty A. Wahl, Andrea Mari, Nathan Shammah, William J. Zeng, and Gokul Subramanian Ravi, 2023 IEEE International Conference on Quantum Computing and Engineering (QCE) 888 (2023) ISBN:979-8-3503-4323-6.

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

[70] Stefan H. Sack and Daniel J. Egger, "Large-scale quantum approximate optimization on nonplanar graphs with machine learning noise mitigation", Physical Review Research 6 1, 013223 (2024).

[71] Sorana Catrina and Alexandra Băicoianu, "Quantum Tunneling: From Theory to Error‐Mitigated Quantum Simulation", Advanced Quantum Technologies 8 1, 2400163 (2025).

[72] Kaleb Dias Antoine KODO and Eugène C. EZIN, "Analysis of Innovative Quantum Optimization Solutions for Shor’s Period Finding Algorithm Applied to the Computation of ", Journal of Quantum Computing 7 1, 17 (2025).

[73] I-Chi Chen, Benjamin Burdick, Yongxin Yao, Peter P. Orth, and Thomas Iadecola, "Error-mitigated simulation of quantum many-body scars on quantum computers with pulse-level control", Physical Review Research 4 4, 043027 (2022).

[74] Bojia Duan and Chang-Yu Hsieh, "Hamiltonian-based data loading with shallow quantum circuits", Physical Review A 106 5, 052422 (2022).

[75] Khairil Imran Ghauth and Yanche Ari Kustiawan, "Quantum Machine Learning in Oncology: A Systematic Review of Clinical Applications, Challenges, and Future Research Directions", Machine Learning and Knowledge Extraction 8 8, 242 (2026).

[76] Samudra Dasgupta and Travis S. Humble, "Improving Probabilistic Error Cancellation in the Presence of Nonstationary Noise", IEEE Transactions on Quantum Engineering 5, 1 (2024).

[77] Elijah Pelofske and Vincent Russo, 2025 IEEE International Conference on Quantum Computing and Engineering (QCE) 01 (2025) ISBN:979-8-3315-5736-2.

[78] Jami Rönkkö, Olli Ahonen, Ville Bergholm, Alessio Calzona, Attila Geresdi, Hermanni Heimonen, Johannes Heinsoo, Vladimir Milchakov, Stefan Pogorzalek, Matthew Sarsby, Mykhailo Savytskyi, Stefan Seegerer, Fedor Šimkovic, P. V. Sriluckshmy, Panu T. Vesanen, and Mikio Nakahara, "On-premises superconducting quantum computer for education and research", EPJ Quantum Technology 11 1, 32 (2024).

[79] Wenbo Shi, Neel Kanth Kundu, and Robert Malaney, "Error-mitigated multi-layer quantum routing", APL Quantum 2 1, 016130 (2025).

[80] Emilie Huffman, Miguel García Vera, and Debasish Banerjee, "Toward the real-time evolution of gauge-invariant Z2 and U(1) quantum link models on noisy intermediate-scale quantum hardware with error mitigation", Physical Review D 106 9, 094502 (2022).

[81] 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).

[82] Zhenyu Cai, Ryan Babbush, Simon C. Benjamin, Suguru Endo, William J. Huggins, Ying Li, Jarrod R. McClean, and Thomas E. O’Brien, "Quantum error mitigation", Reviews of Modern Physics 95 4, 045005 (2023).

[83] Xinpeng Li, Vinooth Kulkarni, Daniel T. Chen, Qiang Guan, Weiwen Jiang, Ning Xie, Shuai Xu, and Vipin Chaudhary, 2024 IEEE International Conference on Quantum Computing and Engineering (QCE) 117 (2024) ISBN:979-8-3315-4137-8.

[84] Max Rossmannek, Fabijan Pavošević, Angel Rubio, and Ivano Tavernelli, "Quantum Embedding Method for the Simulation of Strongly Correlated Systems on Quantum Computers", The Journal of Physical Chemistry Letters 14 14, 3491 (2023).

[85] Wenbo Shi, Neel Kanth Kundu, Matthew R. McKay, and Robert Malaney, 2025 International Conference on Quantum Communications, Networking, and Computing (QCNC) 32 (2025) ISBN:979-8-3315-3159-1.

[86] Biswajit Paul and Tapan Mishra, "Realizing nontrivial doublon formation using a quantum computer", Physical Review B 110 2, L020302 (2024).

[87] Elijah Pelofske, Andreas Bärtschi, Lukasz Cincio, John Golden, and Stephan Eidenbenz, "Scaling whole-chip QAOA for higher-order ising spin glass models on heavy-hex graphs", npj Quantum Information 10 1, 109 (2024).

[88] Elijah Pelofske, Andreas Bärtschi, and Stephan Eidenbenz, Lecture Notes in Computer Science 13948, 240 (2023) ISBN:978-3-031-32040-8.

[89] Bo Yang and Naoki Negishi, "Quantum simulation of many-body dynamics with noise-robust Trotter decomposition based on symmetric structures", AVS Quantum Science 8 1, 013802 (2026).

[90] Sonaldeep Halder, Chinmay Shrikhande, and Rahul Maitra, "Development of zero-noise extrapolated projective quantum algorithm for accurate evaluation of molecular energetics in noisy quantum devices", The Journal of Chemical Physics 159 11, 114115 (2023).

[91] José D. Guimarães, Mikhail I. Vasilevskiy, and Luís S. Barbosa, "Digital quantum simulation of non-perturbative dynamics of open systems with orthogonal polynomials", Quantum 8, 1242 (2024).

[92] Sasan Moradi, "Hybrid classical-quantum computation of heat diffusion in multilayer materials", (2025).

[93] Alisa Haukisalmi, Daniel Paz Ramos, Matti Raasakka, Andrea Marchesin, Lauri Ylinen, and Ilkka Tittonen, "Noisy quantum simulation: Performance and resource considerations for the Tavis-Cummings and Heisenberg models", Physical Review Research 7 4, 043254 (2025).

[94] João C. Getelina, Prachi Sharma, Thomas Iadecola, Peter P. Orth, and Yong-Xin Yao, "Quantum subspace expansion in the presence of hardware noise", APL Quantum 1 3, 036127 (2024).

[95] Victor F. dos Santos, Victor P. Brasil, Pedro A. S. Contri, and Jonas Maziero, "Prime Number Identification Demonstrated With Quantum Processors Using a New Rescaling‐Based Noise Mitigation Technique", Advanced Quantum Technologies 9 6, e70342 (2026).

[96] Vincent Russo, Andrea Mari, Nathan Shammah, Ryan LaRose, and William J. Zeng, "Testing Platform-Independent Quantum Error Mitigation on Noisy Quantum Computers", IEEE Transactions on Quantum Engineering 4, 1 (2023).

[97] Andrea Skolik, Stefano Mangini, Thomas Bäck, Chiara Macchiavello, and Vedran Dunjko, "Robustness of quantum reinforcement learning under hardware errors", EPJ Quantum Technology 10 1, 8 (2023).

[98] Hector D. Menendez, Luciano Bello, and David Clark, 2023 IEEE/ACM 4th International Workshop on Quantum Software Engineering (Q-SE) 16 (2023) ISBN:979-8-3503-0180-9.

[99] Asmar Muqeet, Shaukat Ali, and Paolo Arcaini, Proceedings of the 39th IEEE/ACM International Conference on Automated Software Engineering 2130 (2024) ISBN:9798400712487.

[100] Samuele Ferracin, Akel Hashim, Jean-Loup Ville, Ravi Naik, Arnaud Carignan-Dugas, Hammam Qassim, Alexis Morvan, David I. Santiago, Irfan Siddiqi, and Joel J. Wallman, "Efficiently improving the performance of noisy quantum computers", Quantum 8, 1410 (2024).

[101] Andreas Elben and Benoit Vermersch, "RandomMeas.jl: A Julia Package for Randomized Measurements in Quantum Devices", Quantum 10, 2086 (2026).

[102] Massimiliano Incudini, Michele Grossi, Andrea Ceschini, Antonio Mandarino, Massimo Panella, Sofia Vallecorsa, and David Windridge, "Resource saving via ensemble techniques for quantum neural networks", Quantum Machine Intelligence 5 2, 39 (2023).

[103] Arseny Kovyrshin, Dilhan Manawadu, Edoardo Altamura, George Pennington, Benjamin Jaderberg, Sebastian Brandhofer, Anton Nykänen, Aaron Miller, Walter Talarico, Stefan Knecht, Fabijan Pavošević, Alberto Baiardi, Francesco Tacchino, Ivano Tavernelli, Stefano Mensa, Jason Crain, Lars Tornberg, and Anders Broo, "Approximate quantum circuit compilation for proton-transfer kinetics on quantum processors", Physical Chemistry Chemical Physics 28 4, 3035 (2026).

[104] Tao Jiang, John Rogers, Marius S. Frank, Ove Christiansen, Yong-Xin Yao, and Nicola Lanatà, "Error mitigation in variational quantum eigensolvers using tailored probabilistic machine learning", Physical Review Research 6 3, 033069 (2024).

[105] Mathys Rennela and Harold Ollivier, "Low Bit‐Flip Rate Probabilistic Error Cancellation", Advanced Quantum Technologies 8 10, e2500029 (2025).

[106] Swaroop Ghosh, Suryansh Upadhyay, and Abdullah Ash Saki, "A Primer on Security of Quantum Computing Hardware", Proceedings of the IEEE 113 7, 640 (2025).

[107] Asmar Muqeet, Shaukat Ali, and Paolo Arcaini, "Tool: QUIET: A Tool for Sampling-Based Quantum Noise Error Mitigation", IEEE Software 42 6, 28 (2025).

[108] Joshua Viszlai, Satvik Maurya, Swamit Tannu, Margaret Martonosi, and Frederic T. Chong, Proceedings of the 31st ACM International Conference on Architectural Support for Programming Languages and Operating Systems, Volume 2 1476 (2026) ISBN:9798400723599.

[109] Tomis Prajapati, Harsh Mehta, Shreya Banerjee, Prasanta K. Panigrahi, and V. Narayanan, "Evolution of Entanglement Witness of Dicke State under Noise and Error Mitigation", International Journal of Theoretical Physics 64 9, 237 (2025).

[110] Cristina Cirstoiu, Silas Dilkes, Daniel Mills, Seyon Sivarajah, and Ross Duncan, "Volumetric Benchmarking of Error Mitigation with Qermit", Quantum 7, 1059 (2023).

[111] Kimchhor Chiv, Leanghok Hour, Sanghyeon Lee, Tara Kit, Tae-Kyung Kim, and Youngsun Han, "Strategies for Noise-Resilient Quantum Approximate Optimization Algorithms: A Review and Classification of Error Mitigation", IEEE Access 13, 216916 (2025).

[112] Unai Aseguinolaza, Nahual Sobrino, Gabriel Sobrino, Joaquim Jornet-Somoza, and Juan Borge, "Error estimation in current noisy quantum computers", Quantum Information Processing 23 5, 181 (2024).

[113] Andrew Eddins, Mario Motta, Tanvi P. Gujarati, Sergey Bravyi, Antonio Mezzacapo, Charles Hadfield, and Sarah Sheldon, "Doubling the Size of Quantum Simulators by Entanglement Forging", PRX Quantum 3 1, 010309 (2022).

[114] 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).

[115] Zhenyu Cai, "Quantum Error Mitigation using Symmetry Expansion", Quantum 5, 548 (2021).

[116] Changsu Cao, Jiaqi Hu, Wengang Zhang, Xusheng Xu, Dechin Chen, Fan Yu, Jun Li, Han-Shi Hu, Dingshun Lv, and Man-Hong Yung, "Progress toward larger molecular simulation on a quantum computer: Simulating a system with up to 28 qubits accelerated by point-group symmetry", Physical Review A 105 6, 062452 (2022).

[117] Andrea Mari, Nathan Shammah, and William J. Zeng, "Extending quantum probabilistic error cancellation by noise scaling", Physical Review A 104 5, 052607 (2021).

[118] Kamila Zaman, Alberto Marchisio, Muhammad Abdullah Hanif, and Muhammad Shafique, "A Survey on Quantum Machine Learning: Current Trends, Challenges, Opportunities, and the Road Ahead", arXiv:2310.10315, (2023).

[119] Dorit Aharonov, Ori Alberton, Itai Arad, Yosi Atia, Eyal Bairey, Matan Ben Dov, Asaf Berkovitch, Zvika Brakerski, Itsik Cohen, Eran Fuchs, Omri Golan, Or Golan, Barak D. Gur, Ilya Gurwich, Avieli Haber, Rotem Haber, Dorri Halbertal, Yaron Itkin, Barak A. Katzir, Oded Kenneth, Shlomi Kotler, Roei Levi, Eyal Leviatan, Yotam Y. Lifshitz, Adi Ludmer, Shlomi Matityahu, Ron Aharon Melcer, Adiel Meyer, Omrie Ovdat, Aviad Panahi, Gil Ron, Ittai Rubinstein, Gili Schul, Tali Shnaider, Maor Shutman, Asif Sinay, Tasneem Watad, Assaf Zubida, and Netanel H. Lindner, "Reliable high-accuracy error mitigation for utility-scale quantum circuits", arXiv:2508.10997, (2025).

[120] Alejandro Sopena, Max Hunter Gordon, Germán Sierra, and Esperanza López, "Simulating quench dynamics on a digital quantum computer with data-driven error mitigation", Quantum Science and Technology 6 4, 045003 (2021).

[121] Kaoru Yamamoto, Suguru Endo, Hideaki Hakoshima, Yuichiro Matsuzaki, and Yuuki Tokunaga, "Error-Mitigated Quantum Metrology via Virtual Purification", Physical Review Letters 129 25, 250503 (2022).

[122] Noah F. Berthusen, Thaís V. Trevisan, Thomas Iadecola, and Peter P. Orth, "Quantum dynamics simulations beyond the coherence time on noisy intermediate-scale quantum hardware by variational Trotter compression", Physical Review Research 4 2, 023097 (2022).

[123] Yongxin Yao, Feng Zhang, Cai-Zhuang Wang, Kai-Ming Ho, and Peter P. Orth, "Gutzwiller hybrid quantum-classical computing approach for correlated materials", Physical Review Research 3 1, 013184 (2021).

[124] Mirko Consiglio, "Variational Quantum Algorithms for Many-Body Systems", arXiv:2502.11985, (2025).

[125] Ben DalFavero and Ryan LaRose, "Error mitigation for partially error-corrected quantum computers", arXiv:2510.10905, (2025).

[126] Gokul Subramanian Ravi, Kaitlin N. Smith, Pranav Gokhale, Andrea Mari, Nathan Earnest, Ali Javadi-Abhari, and Frederic T. Chong, "VAQEM: A Variational Approach to Quantum Error Mitigation", arXiv:2112.05821, (2021).

[127] Teppei Suzuki, Takashi Hasebe, and Tsubasa Miyazaki, "Quantum support vector machines for classification and regression on a trapped-ion quantum computer", arXiv:2307.02091, (2023).

[128] Martin Rodriguez-Vega, Ella Carlander, Adrian Bahri, Ze-Xun Lin, Nikolai A. Sinitsyn, and Gregory A. Fiete, "Real-time simulation of light-driven spin chains on quantum computers", Physical Review Research 4 1, 013196 (2022).

[129] Ryan LaRose, Andrea Mari, Vincent Russo, Dan Strano, and William J. Zeng, "Error mitigation increases the effective quantum volume of quantum computers", arXiv:2203.05489, (2022).

[130] Emmanouil Giortamis, Francisco Romão, Nathaniel Tornow, Dmitry Lugovoy, and Pramod Bhatotia, "Qonductor: A Cloud Orchestrator for Quantum Computing", arXiv:2408.04312, (2024).

[131] Shweta Sahoo, Utkarsh Azad, and Harjinder Singh, "Quantum phase recognition using quantum tensor networks", European Physical Journal Plus 137 12, 1373 (2022).

[132] Yi Fan, Jie Liu, Zhenyu Li, and Jinlong Yang, "A Quantum Algorithm to Calculate Band Structure at the EOM Level of Theory", arXiv:2109.01318, (2021).

[133] Leanghok Hour, Myeongseong Go, and Youngsun Han, "Improving Zero-noise Extrapolation for Quantum-gate Error Mitigation using a Noise-aware Folding Method", arXiv:2401.12495, (2024).

[134] Simone Cantori, Andrea Mari, David Vitali, and Sebastiano Pilati, "Deep-learned error mitigation via partially knitted circuits for the variational quantum eigensolver", arXiv:2506.04146, (2025).

[135] Misty A. Wahl, Andrea Mari, Nathan Shammah, William J. Zeng, and Gokul Subramanian Ravi, "Zero noise extrapolation on logical qubits by scaling the error correction code distance", arXiv:2304.14985, (2023).

[136] Vasily Sazonov and Mohamed Tamaazousti, "Quantum error mitigation for parametric circuits", Physical Review A 105 4, 042408 (2022).

[137] Himanshu Sahu and Hari Prabhat Gupta, "NAC-QFL: Noise Aware Clustered Quantum Federated Learning", arXiv:2406.14236, (2024).

[138] Cheng-Lin Hong, Ting Tsai, Jyh-Pin Chou, Peng-Jen Chen, Pei-Kai Tsai, Yu-Cheng Chen, En-Jui Kuo, David Srolovitz, Alice Hu, Yuan-Chung Cheng, and Hsi-Sheng Goan, "Accurate and Efficient Quantum Computations of Molecular Properties Using Daubechies Wavelet Molecular Orbitals: A Benchmark Study against Experimental Data", PRX Quantum 3 2, 020360 (2022).

[139] Wilmer Contreras Sepúlveda, Ángel David Torres-Palencia, José Javier Sánchez Mondragón, Braulio Misael Villegas-Martínez, J. Jesús Escobedo-Alatorre, Sandra Gesing, Néstor Lozano-Crisóstomo, Julio César García-Melgarejo, Juan Carlos Sánchez Pérez, Eddie Nelson Palacios- Pérez, and Omar PalilleroSandoval, "Unleashing quantum algorithms with Qinterpreter: bridging the gap between theory and practice across leading quantum computing platforms", arXiv:2310.07173, (2023).

[140] Elijah Pelofske, Andreas Bärtschi, and Stephan Eidenbenz, "Simulating Heavy-Hex Transverse Field Ising Model Magnetization Dynamics Using Programmable Quantum Annealers", arXiv:2311.01657, (2023).

[141] Elijah Pelofske and Vincent Russo, "Digital Zero-Noise Extrapolation with Quantum Circuit Unoptimization", arXiv:2503.06341, (2025).

[142] Olivia Di Matteo, Josh Izaac, Tom Bromley, Anthony Hayes, Christina Lee, Maria Schuld, Antal Száva, Chase Roberts, and Nathan Killoran, "Quantum computing with differentiable quantum transforms", arXiv:2202.13414, (2022).

[143] Elijah Pelofske, Vincent Russo, Ryan LaRose, Andrea Mari, Dan Strano, Andreas Bärtschi, Stephan Eidenbenz, and William J. Zeng, "Increasing the Measured Effective Quantum Volume with Zero Noise Extrapolation", arXiv:2306.15863, (2023).

[144] Daniel Beaulieu, Dylan Miracle, Anh Pham, and William Scherr, "Quantum Kernel for Image Classification of Real World Manufacturing Defects", arXiv:2212.08693, (2022).

[145] Elijah Pelofske, Andreas Bärtschi, and Stephan Eidenbenz, "Quantum Annealing vs. QAOA: 127 Qubit Higher-Order Ising Problems on NISQ Computers", arXiv:2301.00520, (2023).

[146] Asmar Muqeet, Hassan Sartaj, Aitor Arrieta, Shaukat Ali, Paolo Arcaini, Maite Arratibel, Julie Marie Gjøby, Narasimha Raghavan Veeraragavan, and Jan F. Nygård, "Assessing Quantum Extreme Learning Machines for Software Testing in Practice", arXiv:2410.15494, (2024).

[147] Christophe Jurczak, "Investing in the Quantum Future : State of Play and Way Forward for Quantum Venture Capital", arXiv:2311.17187, (2023).

[148] Karan Kendre, "Machine Learning for Quantum Noise Reduction", arXiv:2509.16242, (2025).

[149] Matteo Paltenghi and Michael Pradel, "Bugs in Quantum Computing Platforms: An Empirical Study", arXiv:2110.14560, (2021).

[150] Xinpeng Li, Vinooth Kulkarni, Daniel T. Chen, Qiang Guan, Weiwen Jiang, Ning Xie, Shuai Xu, and Vipin Chaudhary, "Efficient Circuit Wire Cutting Based on Commuting Groups", arXiv:2410.20313, (2024).

[151] Nils Quetschlich and Olivia Di Matteo, "An experience-based classification of quantum bugs in quantum software", arXiv:2509.03280, (2025).

[152] Vicenzo Scavino, "Finite-shot operating windows for probabilistic error cancellation and Clifford data regression", arXiv:2606.21686, (2026).

[153] Asmar Muqeet, Shaukat Ali, and Paolo Arcaini, "Search-Based Quantum Program Testing via Commuting Pauli String", arXiv:2602.11487, (2026).

[154] Carlos-Miguel Lorenzo, "Certifying bipartite entanglement on a superconducting processor from a corrected QAOA cost layer", arXiv:2609.09495, (2026).

[155] Karim Elgammal and Marc Maußner, "Scaling a CUDA-Q GQE + QSCI pipeline to 40 qubits for EUV photoresist chemistry", arXiv:2607.23988, (2026).

[156] Vicenzo Scavino, "Decision Kernels for Quantum Error Mitigation: Why Accuracy Gains Need Not Improve Downstream Decisions", arXiv:2607.02888, (2026).

The above citations are from Crossref's cited-by service (last updated successfully 2026-10-12 21:10:40) and SAO/NASA ADS (last updated successfully 2026-10-12 21:10:42). The list may be incomplete as not all publishers provide suitable and complete citation data.

This Paper is published in Quantum under the Creative Commons Attribution 4.0 International (CC BY 4.0) license. Copyright remains with the original copyright holders such as the authors or their institutions.