Error mitigation with Clifford quantum-circuit data

Piotr Czarnik; Andrew Arrasmith; Patrick J. Coles; Lukasz Cincio

doi:10.22331/q-2021-11-26-592

Error mitigation with Clifford quantum-circuit data

Piotr Czarnik, Andrew Arrasmith, Patrick J. Coles, and Lukasz Cincio

Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM 87545, USA.

Published:	2021-11-26, volume 5, page 592
Eprint:	arXiv:2005.10189v3
Doi:	https://doi.org/10.22331/q-2021-11-26-592
Citation:	Quantum 5, 592 (2021).

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Abstract

Achieving near-term quantum advantage will require accurate estimation of quantum observables despite significant hardware noise. For this purpose, we propose a novel, scalable error-mitigation method that applies to gate-based quantum computers. The method generates training data $\{X_i^{\text{noisy}},X_i^{\text{exact}}\}$ via quantum circuits composed largely of Clifford gates, which can be efficiently simulated classically, where $X_i^{\text{noisy}}$ and $X_i^{\text{exact}}$ are noisy and noiseless observables respectively. Fitting a linear ansatz to this data then allows for the prediction of noise-free observables for arbitrary circuits. We analyze the performance of our method versus the number of qubits, circuit depth, and number of non-Clifford gates. We obtain an order-of-magnitude error reduction for a ground-state energy problem on 16 qubits in an IBMQ quantum computer and on a 64-qubit noisy simulator.

► BibTeX data

@article{Czarnik2021errormitigation,
  doi = {10.22331/q-2021-11-26-592},
  url = {https://doi.org/10.22331/q-2021-11-26-592},
  title = {Error mitigation with {C}lifford quantum-circuit data},
  author = {Czarnik, Piotr and Arrasmith, Andrew and Coles, Patrick J. and Cincio, Lukasz},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {5},
  pages = {592},
  month = nov,
  year = {2021}
}

► References

[1] Scott Aaronson and Daniel Gottesman. Improved simulation of stabilizer circuits. Phys. Rev. A, 70: 052328, Nov 2004. 10.1103/PhysRevA.70.052328.
https://doi.org/10.1103/PhysRevA.70.052328

[2] Frank Arute, Kunal Arya, Ryan Babbush, Dave Bacon, Joseph C Bardin, Rami Barends, Rupak Biswas, Sergio Boixo, Fernando GSL Brandao, David A Buell, et al. Quantum supremacy using a programmable superconducting processor. Nature, 574 (7779): 505–510, 2019. https://doi.org/10.5061/dryad.k6t1rj8.
https://doi.org/10.5061/dryad.k6t1rj8

[3] Kishor Bharti, Alba Cervera-Lierta, Thi Ha Kyaw, Tobias Haug, Sumner Alperin-Lea, Abhinav Anand, Matthias Degroote, Hermanni Heimonen, Jakob S. Kottmann, Tim Menke, Wai-Keong Mok, Sukin Sim, Leong-Chuan Kwek, and Alán Aspuru-Guzik. Noisy intermediate-scale quantum (nisq) algorithms. arXiv preprint arXiv:2101.08448, 2021. URL https://arxiv.org/abs/2101.08448.
arXiv:2101.08448

[4] Xavi Bonet-Monroig, Ramiro Sagastizabal, M Singh, and TE O'Brien. Low-cost error mitigation by symmetry verification. Physical Review A, 98 (6): 062339, 2018. 10.1103/PhysRevA.98.062339.
https://doi.org/10.1103/PhysRevA.98.062339

[5] Sergey Bravyi, Sarah Sheldon, Abhinav Kandala, David C. Mckay, and Jay M. Gambetta. Mitigating measurement errors in multiqubit experiments. Phys. Rev. A, 103: 042605, Apr 2021. 10.1103/PhysRevA.103.042605.
https://doi.org/10.1103/PhysRevA.103.042605

[6] Zhenyu Cai. Multi-exponential error extrapolation and combining error mitigation techniques for nisq applications. npj Quantum Information, 7 (1): 80, May 2021a. ISSN 2056-6387. 10.1038/s41534-021-00404-3.
https://doi.org/10.1038/s41534-021-00404-3

[7] Zhenyu Cai. Quantum error mitigation using symmetry expansion. arXiv preprint arXiv:2101.03151, 2021b. URL https://arxiv.org/abs/2101.03151. 10.22331/q-2021-09-21-548.
https://doi.org/10.22331/q-2021-09-21-548
arXiv:2101.03151

[8] Yudong Cao, Jonathan Romero, Jonathan P Olson, Matthias Degroote, Peter D Johnson, Mária Kieferová, Ian D Kivlichan, Tim Menke, Borja Peropadre, Nicolas PD Sawaya, et al. Quantum chemistry in the age of quantum computing. Chemical reviews, 119 (19): 10856–10915, 2019. 10.1021/acs.chemrev.8b00803.
https://doi.org/10.1021/acs.chemrev.8b00803

[9] M Cerezo, Kunal Sharma, Andrew Arrasmith, and Patrick J Coles. Variational quantum state eigensolver. arXiv preprint arXiv:2004.01372, 2020. URL https://arxiv.org/abs/2004.01372.
arXiv:2004.01372

[10] M. Cerezo, Andrew Arrasmith, Ryan Babbush, Simon C. Benjamin, Suguru Endo, Keisuke Fujii, Jarrod R. McClean, Kosuke Mitarai, Xiao Yuan, Lukasz Cincio, and Patrick J. Coles. Variational quantum algorithms. Nature Reviews Physics, 3 (9): 625–644, Sep 2021. ISSN 2522-5820. 10.1038/s42254-021-00348-9.
https://doi.org/10.1038/s42254-021-00348-9

[11] J. M. Chow, L. DiCarlo, J. M. Gambetta, A. Nunnenkamp, Lev S. Bishop, L. Frunzio, M. H. Devoret, S. M. Girvin, and R. J. Schoelkopf. Detecting highly entangled states with a joint qubit readout. Phys. Rev. A, 81: 062325, Jun 2010. 10.1103/PhysRevA.81.062325.
https://doi.org/10.1103/PhysRevA.81.062325

[12] L. Cincio, Y. Subaşı, A. T. Sornborger, and P. J. Coles. Learning the quantum algorithm for state overlap. New Journal of Physics, 20 (11): 113022, 2018. 10.1088/1367-2630/aae94a.
https://doi.org/10.1088/1367-2630/aae94a

[13] Lukasz Cincio, Kenneth Rudinger, Mohan Sarovar, and Patrick J. Coles. Machine learning of noise-resilient quantum circuits. PRX Quantum, 2: 010324, Feb 2021. 10.1103/PRXQuantum.2.010324.
https://doi.org/10.1103/PRXQuantum.2.010324

[14] G. E. Crooks. Performance of the quantum approximate optimization algorithm on the maximum cut problem. arXiv preprint arXiv:1811.08419, 2018. URL https://arxiv.org/abs/1811.0841. 10.1126/sciadv.aaz0418.
https://doi.org/10.1126/sciadv.aaz0418
arXiv:1811.08419
https://arxiv.org/abs/1811.0841

[15] Andrew W. Cross, Lev S. Bishop, Sarah Sheldon, Paul D. Nation, and Jay M. Gambetta. Validating quantum computers using randomized model circuits. Phys. Rev. A, 100: 032328, Sep 2019. 10.1103/PhysRevA.100.032328.
https://doi.org/10.1103/PhysRevA.100.032328

[16] Eugene F Dumitrescu, Alex J McCaskey, Gaute Hagen, Gustav R Jansen, Titus D Morris, T Papenbrock, Raphael C Pooser, David Jarvis Dean, and Pavel Lougovski. Cloud quantum computing of an atomic nucleus. Physical review letters, 120 (21): 210501, 2018. 10.1103/PhysRevLett.120.210501.
https://doi.org/10.1103/PhysRevLett.120.210501

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

[18] Suguru Endo, Zhenyu Cai, Simon C Benjamin, and Xiao Yuan. Hybrid quantum-classical algorithms and quantum error mitigation. Journal of the Physical Society of Japan, 90 (3): 032001, 2021. 10.7566/JPSJ.90.032001.
https://doi.org/10.7566/JPSJ.90.032001

[19] Héctor Abraham et. al. Qiskit: An open-source framework for quantum computing, 2019. URL https://zenodo.org/record/2562111. 10.5281/zenodo.2562111.
https://doi.org/10.5281/zenodo.2562111
https://zenodo.org/record/2562111

[20] M. Fannes, B. Nachtergaele, and R. F. Werner. Finitely correlated states on quantum spin chains. Communications in Mathematical Physics, 144 (3): 443–490, Mar 1992. ISSN 1432-0916. 10.1007/BF02099178.
https://doi.org/10.1007/BF02099178

[21] E. Farhi, J. Goldstone, and S. Gutmann. A quantum approximate optimization algorithm. arXiv preprint arXiv:1411.4028, 2014. URL https://arxiv.org/abs/1411.4028.
arXiv:1411.4028

[22] Andrew J. Ferris and Guifre Vidal. Perfect sampling with unitary tensor networks. Phys. Rev. B, 85: 165146, Apr 2012. 10.1103/PhysRevB.85.165146.
https://doi.org/10.1103/PhysRevB.85.165146

[23] Tudor Giurgica-Tiron, Yousef Hindy, Ryan LaRose, Andrea Mari, and William J. Zeng. Digital zero noise extrapolation for quantum error mitigation. pages 306–316, Oct 2020. 10.1109/QCE49297.2020.00045.
https://doi.org/10.1109/QCE49297.2020.00045

[24] Daniel Gottesman. An introduction to quantum error correction and fault-tolerant quantum computation. arXiv preprint arXiv:0904.2557, 2009. URL https://arxiv.org/abs/0904.2557.
arXiv:0904.2557

[25] Stuart Hadfield, Zhihui Wang, Bryan O’Gorman, Eleanor G. Rieffel, Davide Venturelli, and Rupak Biswas. From the quantum approximate optimization algorithm to a quantum alternating operator ansatz. Algorithms, 12 (2), 2019. ISSN 1999-4893. 10.3390/a12020034.
https://doi.org/10.3390/a12020034

[26] Andre He, Benjamin Nachman, Wibe A. de Jong, and Christian W. Bauer. Zero-noise extrapolation for quantum-gate error mitigation with identity insertions. Phys. Rev. A, 102: 012426, Jul 2020. 10.1103/PhysRevA.102.012426.
https://doi.org/10.1103/PhysRevA.102.012426

[27] Abhijith J., Adetokunbo Adedoyin, John Ambrosiano, Petr Anisimov, Andreas Bärtschi, William Casper, Gopinath Chennupati, Carleton Coffrin, Hristo Djidjev, David Gunter, Satish Karra, Nathan Lemons, Shizeng Lin, Alexander Malyzhenkov, David Mascarenas, Susan Mniszewski, Balu Nadiga, Daniel O'Malley, Diane Oyen, Scott Pakin, Lakshman Prasad, Randy Roberts, Phillip Romero, Nandakishore Santhi, Nikolai Sinitsyn, Pieter J. Swart, James G. Wendelberger, Boram Yoon, Richard Zamora, Wei Zhu, Stephan Eidenbenz, Patrick J. Coles, Marc Vuffray, and Andrey Y. Lokhov. Quantum algorithm implementations for beginners, 2018. URL https://arxiv.org/abs/1804.03719.
arXiv:1804.03719

[28] 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 (7749): 491–495, 2019. 10.1038/s41586-019-1040-7.
https://doi.org/10.1038/s41586-019-1040-7

[29] S. Khatri, R. LaRose, A. Poremba, L. Cincio, A. T. Sornborger, and P. J. Coles. Quantum-assisted quantum compiling. Quantum, 3: 140, May 2019. ISSN 2521-327X. 10.22331/q-2019-05-13-140.
https://doi.org/10.22331/q-2019-05-13-140

[30] Ryan LaRose, Arkin Tikku, Étude O'Neel-Judy, Lukasz Cincio, and Patrick J. Coles. Variational quantum state diagonalization. npj Quantum Information, 5 (1): 57, Jun 2019. ISSN 2056-6387. 10.1038/s41534-019-0167-6.
https://doi.org/10.1038/s41534-019-0167-6

[31] Y. Li and S. C. Benjamin. Efficient variational quantum simulator incorporating active error minimization. Phys. Rev. X, 7: 021050, Jun 2017. 10.1103/PhysRevX.7.021050.
https://doi.org/10.1103/PhysRevX.7.021050

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

[33] Sam McArdle, Suguru Endo, Alan Aspuru-Guzik, Simon C Benjamin, and Xiao Yuan. Quantum computational chemistry. Reviews of Modern Physics, 92 (1): 015003, 2020. https://doi.org/10.1103/RevModPhys.92.015003.
https://doi.org/10.1103/RevModPhys.92.015003

[34] Jarrod R McClean, Jonathan Romero, Ryan Babbush, and Alán Aspuru-Guzik. The theory of variational hybrid quantum-classical algorithms. 18 (2): 023023, feb 2016. 10.1088/1367-2630/18/2/023023.
https://doi.org/10.1088/1367-2630/18/2/023023

[35] Prakash Murali, Jonathan M Baker, Ali Javadi-Abhari, Frederic T Chong, and Margaret Martonosi. Noise-adaptive compiler mappings for noisy intermediate-scale quantum computers. In Proceedings of the Twenty-Fourth International Conference on Architectural Support for Programming Languages and Operating Systems, pages 1015–1029, 2019. https://doi.org/10.1145/3297858.3304075.
https://doi.org/10.1145/3297858.3304075

[36] Michael A Nielsen. Neural networks and deep learning, volume 2018. Determination press San Francisco, CA, USA:, 2015.

[37] Matthew Otten and Stephen K Gray. Recovering noise-free quantum observables. Physical Review A, 99 (1): 012338, 2019. 10.1103/PhysRevA.99.012338.
https://doi.org/10.1103/PhysRevA.99.012338

[38] Matthew Otten, Cristian L Cortes, and Stephen K Gray. Noise-resilient quantum dynamics using symmetry-preserving ansatzes. arXiv preprint arXiv:1910.06284, 2019. URL https://arxiv.org/abs/1910.06284.
arXiv:1910.06284

[39] Hakop Pashayan, Oliver Reardon-Smith, Kamil Korzekwa, and Stephen D. Bartlett. Fast estimation of outcome probabilities for quantum circuits. arXiv:2101.12223, 2021. URL https://arxiv.org/abs/2101.12223.
arXiv:2101.12223

[40] A. Peruzzo, J. McClean, P. Shadbolt, M.-H. Yung, X.-Q. Zhou, P. J. Love, A. Aspuru-Guzik, and J. L. O'Brien. A variational eigenvalue solver on a photonic quantum processor. Nature Communications, 5: 4213, 2014. 10.1038/ncomms5213.
https://doi.org/10.1038/ncomms5213

[41] John Preskill. Quantum computing in the NISQ era and beyond. Quantum, 2: 79, 2018. 10.22331/q-2018-08-06-79.
https://doi.org/10.22331/q-2018-08-06-79

[42] Kunal Sharma, Sumeet Khatri, M Cerezo, and Patrick J Coles. Noise resilience of variational quantum compiling. 22 (4): 043006, apr 2020. 10.1088/1367-2630/ab784c.
https://doi.org/10.1088/1367-2630/ab784c

[43] Rolando D Somma. Quantum eigenvalue estimation via time series analysis. New Journal of Physics, 21 (12): 123025, 2019. https://doi.org/10.1088/1367-2630/ab5c60.
https://doi.org/10.1088/1367-2630/ab5c60

[44] Armands Strikis, Dayue Qin, Yanzhu Chen, Simon C. Benjamin, and Ying Li. Learning-based quantum error mitigation. PRX Quantum, 2: 040330, Nov 2021. 10.1103/PRXQuantum.2.040330.
https://doi.org/10.1103/PRXQuantum.2.040330

[45] Kristan Temme, Sergey Bravyi, and Jay M Gambetta. Error mitigation for short-depth quantum circuits. Physical review letters, 119 (18): 180509, 2017. 10.1103/PhysRevLett.119.180509.
https://doi.org/10.1103/PhysRevLett.119.180509

[46] Giacomo Torlai, Guglielmo Mazzola, Giuseppe Carleo, and Antonio Mezzacapo. Precise measurement of quantum observables with neural-network estimators. Phys. Rev. Research, 2: 022060, Jun 2020. 10.1103/PhysRevResearch.2.022060.
https://doi.org/10.1103/PhysRevResearch.2.022060

[47] Don Van Ravenzwaaij, Pete Cassey, and Scott D Brown. A simple introduction to markov chain monte–carlo sampling. Psychonomic bulletin & review, 25 (1): 143–154, 2018. 10.3758/s13423-016-1015-8.
https://doi.org/10.3758/s13423-016-1015-8

[48] Xiao Yuan, Suguru Endo, Qi Zhao, Ying Li, and Simon C Benjamin. Theory of variational quantum simulation. Quantum, 3: 191, 2019. https://doi.org/10.22331/q-2019-10-07-191.
https://doi.org/10.22331/q-2019-10-07-191

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

[2] Yuchen Guo and Shuo Yang, "Quantum Error Mitigation via Matrix Product Operators", PRX Quantum 3 4, 040313 (2022).

[3] Kun Wang, Yu-Ao Chen, and Xin Wang, "Mitigating quantum errors via truncated Neumann series", Science China Information Sciences 66 8, 180508 (2023).

[4] M. Cerezo, Guillaume Verdon, Hsin-Yuan Huang, Lukasz Cincio, and Patrick J. Coles, "Challenges and opportunities in quantum machine learning", Nature Computational Science 2 9, 567 (2022).

[5] Benchen Huang, Marco Govoni, and Giulia Galli, "Simulating the Electronic Structure of Spin Defects on Quantum Computers", PRX Quantum 3 1, 010339 (2022).

[6] 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, and William J. Zeng, "Mitiq: A software package for error mitigation on noisy quantum computers", Quantum 6, 774 (2022).

[7] Yue Ruan, Zhiqiang Yuan, Xiling Xue, and Zhihao Liu, "Quantum approximate optimization for combinatorial problems with constraints", Information Sciences 619, 98 (2023).

[8] Alistair W. R. Smith, Kiran E. Khosla, Chris N. Self, and M. S. Kim, "Qubit readout error mitigation with bit-flip averaging", Science Advances 7 47, eabi8009 (2021).

[9] Zongkang Zhang, Yongdan Yang, Xiaosi Xu, and Ying Li, "Quantum algorithms for Schrieffer-Wolff transformation", Physical Review Research 4 4, 043023 (2022).

[10] Mingxia Huo and Ying Li, "Dual-state purification for practical quantum error mitigation", Physical Review A 105 2, 022427 (2022).

[11] Yuki Takeuchi, Yasuhiro Takahashi, Tomoyuki Morimae, and Seiichiro Tani, "Divide-and-conquer verification method for noisy intermediate-scale quantum computation", Quantum 6, 758 (2022).

[12] Daniel Bultrini, Max Hunter Gordon, Esperanza López, and Germán Sierra, "Simple Mitigation Strategy for a Systematic Gate Error in IBMQ", Journal of Applied Mathematics and Physics 09 06, 1215 (2021).

[13] Ryuji Takagi, Suguru Endo, Shintaro Minagawa, and Mile Gu, "Fundamental limits of quantum error mitigation", npj Quantum Information 8 1, 114 (2022).

[14] Lorcán O. Conlon, Tobias Vogl, Christian D. Marciniak, Ivan Pogorelov, Simon K. Yung, Falk Eilenberger, Dominic W. Berry, Fabiana S. Santana, Rainer Blatt, Thomas Monz, Ping Koy Lam, and Syed M. Assad, "Approaching optimal entangling collective measurements on quantum computing platforms", Nature Physics 19 3, 351 (2023).

[15] 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).

[16] Ali Shaib, Mohamad Hussein Naim, Mohammed E. Fouda, Rouwaida Kanj, and Fadi Kurdahi, "Efficient noise mitigation technique for quantum computing", Scientific Reports 13 1, 3912 (2023).

[17] Yifeng Xiong, Daryus Chandra, Soon Xin Ng, and Lajos Hanzo, "Circuit Symmetry Verification Mitigates Quantum-Domain Impairments", IEEE Transactions on Signal Processing 71, 477 (2023).

[18] Thomas Steckmann, Trevor Keen, Efekan Kökcü, Alexander F. Kemper, Eugene F. Dumitrescu, and Yan Wang, "Mapping the metal-insulator phase diagram by algebraically fast-forwarding dynamics on a cloud quantum computer", Physical Review Research 5 2, 023198 (2023).

[19] Phalgun Lolur, Mårten Skogh, Werner Dobrautz, Christopher Warren, Janka Biznárová, Amr Osman, Giovanna Tancredi, Göran Wendin, Jonas Bylander, and Martin Rahm, "Reference-State Error Mitigation: A Strategy for High Accuracy Quantum Computation of Chemistry", Journal of Chemical Theory and Computation 19 3, 783 (2023).

[20] Poulami Das, Eric Kessler, and Yunong Shi, 2023 IEEE International Symposium on High-Performance Computer Architecture (HPCA) 787 (2023) ISBN:978-1-6654-7652-2.

[21] Vedika Saravanan and Samah Mohamed Saeed, Proceedings of the 41st IEEE/ACM International Conference on Computer-Aided Design 1 (2022) ISBN:9781450392174.

[22] Bo Yang, Rudy Raymond, and Shumpei Uno, "Efficient quantum readout-error mitigation for sparse measurement outcomes of near-term quantum devices", Physical Review A 106 1, 012423 (2022).

[23] Vincent R. Pascuzzi, Andre He, Christian W. Bauer, Wibe A. de Jong, and Benjamin Nachman, "Computationally efficient zero-noise extrapolation for quantum-gate-error mitigation", Physical Review A 105 4, 042406 (2022).

[24] Erik Lötstedt, Lidong Wang, Ryuhei Yoshida, Youyuan Zhang, and Kaoru Yamanouchi, "Error-mitigated quantum computing of Heisenberg spin chain dynamics", Physica Scripta 98 3, 035111 (2023).

[25] Lindsay Bassman Oftelie, Katherine Klymko, Diyi Liu, Norm M. Tubman, and Wibe A. de Jong, "Computing Free Energies with Fluctuation Relations on Quantum Computers", Physical Review Letters 129 13, 130603 (2022).

[26] Francisco Orts, Gloria Ortega, Ernestas Filatovas, and Ester M. Garzón, "Implementation of three efficient 4-digit fault-tolerant quantum carry lookahead adders", The Journal of Supercomputing 78 11, 13323 (2022).

[27] Eliott Rosenberg, Paul Ginsparg, and Peter L McMahon, "Experimental error mitigation using linear rescaling for variational quantum eigensolving with up to 20 qubits", Quantum Science and Technology 7 1, 015024 (2022).

[28] Dax Enshan Koh and Sabee Grewal, "Classical Shadows With Noise", Quantum 6, 776 (2022).

[29] Hiroshi Ohno, "A direct error correction method for quantum machine learning", Quantum Information Processing 22 2, 119 (2023).

[30] 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).

[31] Gokul Subramanian Ravi, Pranav Gokhale, Yi Ding, William Kirby, Kaitlin Smith, Jonathan M. Baker, Peter J. Love, Henry Hoffmann, Kenneth R. Brown, and Frederic T. Chong, Proceedings of the 28th ACM International Conference on Architectural Support for Programming Languages and Operating Systems, Volume 1 15 (2022) ISBN:9781450399159.

[32] Tianyi Hao, Kun Liu, and Swamit Tannu, Proceedings of the 50th Annual International Symposium on Computer Architecture 1 (2023) ISBN:9798400700958.

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

[34] Yu Zhang, Lukasz Cincio, Christian F. A. Negre, Piotr Czarnik, Patrick J. Coles, Petr M. Anisimov, Susan M. Mniszewski, Sergei Tretiak, and Pavel A. Dub, "Variational quantum eigensolver with reduced circuit complexity", npj Quantum Information 8 1, 96 (2022).

[35] Yuxuan Zhang, Daoheng Niu, Alireza Shabani, and Hassan Shapourian, "Quantum Volume for Photonic Quantum Processors", Physical Review Letters 130 11, 110602 (2023).

[36] Youngseok Kim, Christopher J. Wood, Theodore J. Yoder, Seth T. Merkel, Jay M. Gambetta, Kristan Temme, and Abhinav Kandala, "Scalable error mitigation for noisy quantum circuits produces competitive expectation values", Nature Physics 19 5, 752 (2023).

[37] Rawad Mezher, James Mills, and Elham Kashefi, "Mitigating errors by quantum verification and postselection", Physical Review A 105 5, 052608 (2022).

[38] 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).

[39] Dayue Qin, Yanzhu Chen, and Ying Li, "Error statistics and scalability of quantum error mitigation formulas", npj Quantum Information 9 1, 35 (2023).

[40] Yuxuan Du, Tao Huang, Shan You, Min-Hsiu Hsieh, and Dacheng Tao, "Quantum circuit architecture search for variational quantum algorithms", npj Quantum Information 8 1, 62 (2022).

[41] Sarmed A Rahman, Randy Lewis, Emanuele Mendicelli, and Sarah Powell, "Self-mitigating Trotter circuits for SU(2) lattice gauge theory on a quantum computer", Physical Review D 106 7, 074502 (2022).

[42] Kaitlin N. Smith, Michael A. Perlin, Pranav Gokhale, Paige Frederick, David Owusu-Antwi, Richard Rines, Victory Omole, and Frederic Chong, Proceedings of the 50th Annual International Symposium on Computer Architecture 1 (2023) ISBN:9798400700958.

[43] Gokul Subramanian Ravi, Jonathan M. Baker, Arash Fayyazi, Sophia Fuhui Lin, Ali Javadi-Abhari, Massoud Pedram, and Frederic T. Chong, Proceedings of the 28th ACM International Conference on Architectural Support for Programming Languages and Operating Systems, Volume 2 88 (2023) ISBN:9781450399166.

[44] Ryan Shaffer, Lucas Kocia, and Mohan Sarovar, "Surrogate-based optimization for variational quantum algorithms", Physical Review A 107 3, 032415 (2023).

[45] Erik Lötstedt, Kaoru Yamanouchi, and Yutaka Tachikawa, "Evaluation of vibrational energies and wave functions of CO2 on a quantum computer", AVS Quantum Science 4 3, 036801 (2022).

[46] 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).

[47] Samson Wang, Enrico Fontana, M. Cerezo, Kunal Sharma, Akira Sone, Lukasz Cincio, and Patrick J. Coles, "Noise-induced barren plateaus in variational quantum algorithms", Nature Communications 12 1, 6961 (2021).

[48] Daniel Bultrini, Max Hunter Gordon, Piotr Czarnik, Andrew Arrasmith, M. Cerezo, Patrick J. Coles, and Lukasz Cincio, "Unifying and benchmarking state-of-the-art quantum error mitigation techniques", Quantum 7, 1034 (2023).

[49] Andrey Zhukov and Walter Pogosov, "Quantum error reduction with deep neural network applied at the post-processing stage", Quantum Information Processing 21 3, 93 (2022).

[50] Bharat Thotakura and Tzu-Chieh Wei, "Quantum state transfer: interplay between gate and readout errors", Quantum Information Processing 22 7, 275 (2023).

[51] Takanori Nishi, Erik Lötstedt, and Kaoru Yamanouchi, "Simulation of a laser-driven three-level system by a noisy quantum computer", AVS Quantum Science 4 4, 043801 (2022).

[52] Jessie M. Henderson, Marianna Podzorova, M. Cerezo, John K. Golden, Leonard Gleyzer, Hari S. Viswanathan, and Daniel O’Malley, "Quantum algorithms for geologic fracture networks", Scientific Reports 13 1, 2906 (2023).

[53] Alireza Seif, Ze-Pei Cian, Sisi Zhou, Senrui Chen, and Liang Jiang, "Shadow Distillation: Quantum Error Mitigation with Classical Shadows for Near-Term Quantum Processors", PRX Quantum 4 1, 010303 (2023).

[54] Nhung H. Nguyen, Minh C. Tran, Yingyue Zhu, Alaina M. Green, C. Huerta Alderete, Zohreh Davoudi, and Norbert M. Linke, "Digital Quantum Simulation of the Schwinger Model and Symmetry Protection with Trapped Ions", PRX Quantum 3 2, 020324 (2022).

[55] 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).

[56] Chien-Hung Cho, Chih-Yu Chen, Kuo-Chin Chen, Tsung-Wei Huang, Ming-Chien Hsu, Ning-Ping Cao, Bei Zeng, Seng-Ghee Tan, and Ching-Ray Chang, "Quantum computation: Algorithms and Applications", Chinese Journal of Physics 72, 248 (2021).

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

[58] Mario Motta, Gavin O. Jones, Julia E. Rice, Tanvi P. Gujarati, Rei Sakuma, Ieva Liepuoniute, Jeannette M. Garcia, and Yu-ya Ohnishi, "Quantum chemistry simulation of ground- and excited-state properties of the sulfonium cation on a superconducting quantum processor", Chemical Science 14 11, 2915 (2023).

[59] 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).

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

[61] M. Cerezo, Andrew Arrasmith, Ryan Babbush, Simon C. Benjamin, Suguru Endo, Keisuke Fujii, Jarrod R. McClean, Kosuke Mitarai, Xiao Yuan, Lukasz Cincio, and Patrick J. Coles, "Variational quantum algorithms", Nature Reviews Physics 3 9, 625 (2021).

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

[63] Kishor Bharti, Alba Cervera-Lierta, Thi Ha Kyaw, Tobias Haug, Sumner Alperin-Lea, Abhinav Anand, Matthias Degroote, Hermanni Heimonen, Jakob S. Kottmann, Tim Menke, Wai-Keong Mok, Sukin Sim, Leong-Chuan Kwek, and Alán Aspuru-Guzik, "Noisy intermediate-scale quantum algorithms", Reviews of Modern Physics 94 1, 015004 (2022).

[64] Jules Tilly, Hongxiang Chen, Shuxiang Cao, Dario Picozzi, Kanav Setia, Ying Li, Edward Grant, Leonard Wossnig, Ivan Rungger, George H. Booth, and Jonathan Tennyson, "The Variational Quantum Eigensolver: A review of methods and best practices", Physics Reports 986, 1 (2022).

[65] 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).

[66] Suguru Endo, Zhenyu Cai, Simon C. Benjamin, and Xiao Yuan, "Hybrid Quantum-Classical Algorithms and Quantum Error Mitigation", Journal of the Physical Society of Japan 90 3, 032001 (2021).

[67] M. Cerezo, Andrew Arrasmith, Ryan Babbush, Simon C. Benjamin, Suguru Endo, Keisuke Fujii, Jarrod R. McClean, Kosuke Mitarai, Xiao Yuan, Lukasz Cincio, and Patrick J. Coles, "Variational Quantum Algorithms", arXiv:2012.09265, (2020).

[68] Ryuji Takagi, Hiroyasu Tajima, and Mile Gu, "Universal Sampling Lower Bounds for Quantum Error Mitigation", Physical Review Letters 131 21, 210602 (2023).

[69] Armands Strikis, Dayue Qin, Yanzhu Chen, Simon C. Benjamin, and Ying Li, "Learning-Based Quantum Error Mitigation", PRX Quantum 2 4, 040330 (2021).

[70] Róbert Trényi, Árpád Lukács, Paweł Horodecki, Ryszard Horodecki, Tamás Vértesi, and Géza Tóth, "Activation of metrologically useful genuine multipartite entanglement", New Journal of Physics 26 2, 023034 (2024).

[71] 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", Physical Review X 11 4, 041036 (2021).

[72] Joseph Vovrosh, Kiran E. Khosla, Sean Greenaway, Christopher Self, M. S. Kim, and Johannes Knolle, "Simple mitigation of global depolarizing errors in quantum simulations", Physical Review E 104 3, 035309 (2021).

[73] Bálint Koczor, "Exponential Error Suppression for Near-Term Quantum Devices", Physical Review X 11 3, 031057 (2021).

[74] Samson Wang, Piotr Czarnik, Andrew Arrasmith, M. Cerezo, Lukasz Cincio, and Patrick J. Coles, "Can Error Mitigation Improve Trainability of Noisy Variational Quantum Algorithms?", Quantum 8, 1287 (2024).

[75] Kento Tsubouchi, Takahiro Sagawa, and Nobuyuki Yoshioka, "Universal Cost Bound of Quantum Error Mitigation Based on Quantum Estimation Theory", Physical Review Letters 131 21, 210601 (2023).

[76] Jinzhao Sun, Xiao Yuan, Takahiro Tsunoda, Vlatko Vedral, Simon C. Benjamin, and Suguru Endo, "Mitigating Realistic Noise in Practical Noisy Intermediate-Scale Quantum Devices", Physical Review Applied 15 3, 034026 (2021).

[77] Gokul Subramanian Ravi, Pranav Gokhale, Yi Ding, William M. Kirby, Kaitlin N. Smith, Jonathan M. Baker, Peter J. Love, Henry Hoffmann, Kenneth R. Brown, and Frederic T. Chong, "CAFQA: A classical simulation bootstrap for variational quantum algorithms", arXiv:2202.12924, (2022).

[78] Miroslav Urbanek, Benjamin Nachman, Vincent R. Pascuzzi, Andre He, Christian W. Bauer, and Wibe A. de Jong, "Mitigating Depolarizing Noise on Quantum Computers with Noise-Estimation Circuits", Physical Review Letters 127 27, 270502 (2021).

[79] Angus Lowe, Max Hunter Gordon, Piotr Czarnik, Andrew Arrasmith, Patrick J. Coles, and Lukasz Cincio, "Unified approach to data-driven quantum error mitigation", Physical Review Research 3 3, 033098 (2021).

[80] Ryuji Takagi, "Optimal resource cost for error mitigation", Physical Review Research 3 3, 033178 (2021).

[81] Youngseok Kim, Christopher J. Wood, Theodore J. Yoder, Seth T. Merkel, Jay M. Gambetta, Kristan Temme, and Abhinav Kandala, "Scalable error mitigation for noisy quantum circuits produces competitive expectation values", arXiv:2108.09197, (2021).

[82] 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", arXiv:2201.10672, (2022).

[83] Dayue Qin, Xiaosi Xu, and Ying Li, "An overview of quantum error mitigation formulas", Chinese Physics B 31 9, 090306 (2022).

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

[85] Thomas Ayral, Pauline Besserve, Denis Lacroix, and Edgar Andres Ruiz Guzman, "Quantum computing with and for many-body physics", European Physical Journal A 59 10, 227 (2023).

[86] Alexander Zlokapa and Alexandru Gheorghiu, "A deep learning model for noise prediction on near-term quantum devices", arXiv:2005.10811, (2020).

[87] Piotr Czarnik, Andrew Arrasmith, Lukasz Cincio, and Patrick J. Coles, "Qubit-efficient exponential suppression of errors", arXiv:2102.06056, (2021).

[88] Frédéric Sauvage, Martín Larocca, Patrick J. Coles, and M. Cerezo, "Building spatial symmetries into parameterized quantum circuits for faster training", Quantum Science and Technology 9 1, 015029 (2024).

[89] Nikolay V. Tkachenko, James Sud, Yu Zhang, Sergei Tretiak, Petr M. Anisimov, Andrew T. Arrasmith, Patrick J. Coles, Lukasz Cincio, and Pavel A. Dub, "Correlation-Informed Permutation of Qubits for Reducing Ansatz Depth in the Variational Quantum Eigensolver", PRX Quantum 2 2, 020337 (2021).

[90] Hanrui Wang, Yongshan Ding, Jiaqi Gu, Zirui Li, Yujun Lin, David Z. Pan, Frederic T. Chong, and Song Han, "QuantumNAS: Noise-Adaptive Search for Robust Quantum Circuits", arXiv:2107.10845, (2021).

[91] Steven T. Flammia, "Averaged circuit eigenvalue sampling", arXiv:2108.05803, (2021).

[92] 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, and William J. Zeng, "Mitiq: A software package for error mitigation on noisy quantum computers", arXiv:2009.04417, (2020).

[93] 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", arXiv:2007.10917, (2020).

[94] Yongdan Yang, Bing-Nan Lu, and Ying Li, "Accelerated Quantum Monte Carlo with Mitigated Error on Noisy Quantum Computer", PRX Quantum 2 4, 040361 (2021).

[95] Ashley Montanaro and Stasja Stanisic, "Error mitigation by training with fermionic linear optics", arXiv:2102.02120, (2021).

[96] Daniel Bultrini, Max Hunter Gordon, Piotr Czarnik, Andrew Arrasmith, M. Cerezo, Patrick J. Coles, and Lukasz Cincio, "Unifying and benchmarking state-of-the-art quantum error mitigation techniques", arXiv:2107.13470, (2021).

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

[98] 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).

[99] Xinbiao Wang, Yuxuan Du, Yong Luo, and Dacheng Tao, "Towards understanding the power of quantum kernels in the NISQ era", Quantum 5, 531 (2021).

[100] 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).

[101] 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).

[102] Xuanqiang Zhao, Benchi Zhao, Zihan Xia, and Xin Wang, "Information recoverability of noisy quantum states", Quantum 7, 978 (2023).

[103] 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", arXiv:2305.16507, (2023).

[104] Yunfei Wang and Junyu Liu, "A comprehensive review of Quantum Machine Learning: from NISQ to Fault Tolerance", arXiv:2401.11351, (2024).

[105] Zhenyu Cai, "A Practical Framework for Quantum Error Mitigation", arXiv:2110.05389, (2021).

[106] Laia Domingo, "Classical and quantum reservoir computing: development and applications in machine learning", arXiv:2310.07455, (2023).

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

[108] Jinzhao Sun, Xiao Yuan, Takahiro Tsunoda, Vlatko Vedral, Simon C. Bejamin, and Suguru Endo, "Mitigating realistic noise in practical noisy intermediate-scale quantum devices", arXiv:2001.04891, (2020).

[109] Andrii Maksymov, Jason Nguyen, Yunseong Nam, and Igor Markov, "Enhancing quantum computer performance via symmetrization", arXiv:2301.07233, (2023).

[110] Nick S. Blunt, Laura Caune, Róbert Izsák, Earl T. Campbell, and Nicole Holzmann, "Statistical Phase Estimation and Error Mitigation on a Superconducting Quantum Processor", PRX Quantum 4 4, 040341 (2023).

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

[112] Hugo Perrin, Thibault Scoquart, Alexander Shnirman, Jörg Schmalian, and Kyrylo Snizhko, "Mitigating crosstalk errors by randomized compiling: Simulation of the BCS model on a superconducting quantum computer", Physical Review Research 6 1, 013142 (2024).

[113] Ivan Henao, Jader P. Santos, and Raam Uzdin, "Adaptive quantum error mitigation using pulse-based inverse evolutions", npj Quantum Information 9, 120 (2023).

[114] Lukasz Cincio, Kenneth Rudinger, Mohan Sarovar, and Patrick J. Coles, "Machine learning of noise-resilient quantum circuits", arXiv:2007.01210, (2020).

[115] Kun Wang, Yu-Ao Chen, and Xin Wang, "Measurement Error Mitigation via Truncated Neumann Series", arXiv:2103.13856, (2021).

[116] Yusen Wu and Jingbo B. Wang, "Estimating Gibbs partition function with quantum Clifford sampling", Quantum Science and Technology 7 2, 025006 (2022).

[117] Shichuan Xue, Guangyao Huang, Yong Liu, Dongyang Wang, Weixu Shi, Yingwen Liu, Xiang Fu, Anqi Huang, Mingtang Deng, and Junjie Wu, "Efficient quantum process tomography for Clifford circuits", Physical Review A 108 3, 032419 (2023).

[118] Robin Blume-Kohout, Kenneth Rudinger, Erik Nielsen, Timothy Proctor, and Kevin Young, "Wildcard error: Quantifying unmodeled errors in quantum processors", arXiv:2012.12231, (2020).

[119] Daiqin Su, Robert Israel, Kunal Sharma, Haoyu Qi, Ish Dhand, and Kamil Brádler, "Error mitigation on a near-term quantum photonic device", Quantum 5, 452 (2021).

[120] Michael R. Geller, "Conditionally Rigorous Mitigation of Multiqubit Measurement Errors", Physical Review Letters 127 9, 090502 (2021).

[121] Wentao Chen, Shuaining Zhang, Jialiang Zhang, Xiaolu Su, Yao Lu, Kuan Zhang, Mu Qiao, Ying Li, Jing-Ning Zhang, and Kihwan Kim, "Error-mitigated quantum simulation of interacting fermions with trapped ions", npj Quantum Information 9, 122 (2023).

[122] Enrico Fontana, Ivan Rungger, Ross Duncan, and Cristina Cîrstoiu, "Spectral analysis for noise diagnostics and filter-based digital error mitigation", arXiv:2206.08811, (2022).

[123] Daniel Bultrini, Max Hunter Gordon, Esperanza López, and Germȧn Sierra, "Simple Mitigation Strategy for a Systematic Gate Error in IBMQ", arXiv:2012.00831, (2020).

[124] Tim Weaving, Alexis Ralli, William M. Kirby, Peter J. Love, Sauro Succi, and Peter V. Coveney, "Benchmarking noisy intermediate scale quantum error mitigation strategies for ground state preparation of the HCl molecule", Physical Review Research 5 4, 043054 (2023).

[125] Takanori Nishi and Kaoru Yamanouchi, "Simulation of a spin-boson model by iterative optimization of a parametrized quantum circuit", AVS Quantum Science 6 2, 023801 (2024).

[126] Alistair W. R. Smith, Kiran E. Khosla, Chris N. Self, and M. S. Kim, "Qubit Readout Error Mitigation with Bit-flip Averaging", arXiv:2106.05800, (2021).

[127] Rishabh Gupta, Raphael D. Levine, and Sabre Kais, "Convergence of a Reconstructed Density Matrix to a Pure State Using the Maximal Entropy Approach", Journal of Physical Chemistry A 125 34, 7588 (2021).

[128] Gideon Lee, Connor T. Hann, Shruti Puri, S. M. Girvin, and Liang Jiang, "Error Suppression for Arbitrary-Size Black Box Quantum Operations", Physical Review Letters 131 19, 190601 (2023).

[129] Zhen Wang, Yanzhu Chen, Zixuan Song, Dayue Qin, Hekang Li, Qiujiang Guo, H. Wang, Chao Song, and Ying Li, "Scalable Evaluation of Quantum-Circuit Error Loss Using Clifford Sampling", Physical Review Letters 126 8, 080501 (2021).

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

[131] Kun Wang, Yu-Ao Chen, and Xin Wang, "Mitigating Quantum Errors via Truncated Neumann Series", arXiv:2111.00691, (2021).

[132] Siddharth Dangwal, Gokul Subramanian Ravi, Poulami Das, Kaitlin N. Smith, Jonathan M. Baker, and Frederic T. Chong, "VarSaw: Application-tailored Measurement Error Mitigation for Variational Quantum Algorithms", arXiv:2306.06027, (2023).

[133] V. Leyton-Ortega, S. Majumder, and R. C. Pooser, "Quantum error mitigation by hidden inverses protocol in superconducting quantum devices", Quantum Science and Technology 8 1, 014008 (2023).

[134] Yifeng Xiong, Soon Xin Ng, and Lajos Hanzo, "Quantum Error Mitigation Relying on Permutation Filtering", arXiv:2107.01458, (2021).

[135] Viki Kumar Prasad, Freeman Cheng, Ulrich Fekl, and Hans-Arno Jacobsen, "Applications of noisy quantum computing and quantum error mitigation to "adamantaneland": a benchmarking study for quantum chemistry", Physical Chemistry Chemical Physics (Incorporating Faraday Transactions) 26 5, 4071 (2024).

[136] Javier Argüello-Luengo, Tao Shi, and Alejandro González-Tudela, "Engineering analog quantum chemistry Hamiltonians using cold atoms in optical lattices", Physical Review A 103 4, 043318 (2021).

[137] 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).

[138] Jessie M. Henderson, Marianna Podzorova, M. Cerezo, John K. Golden, Leonard Gleyzer, Hari S. Viswanathan, and Daniel O'Malley, "Quantum Algorithms for Geologic Fracture Networks", arXiv:2210.11685, (2022).

[139] Hrushikesh Patil, Peiyi Li, Ji Liu, and Huiyang Zhou, "Folding-Free ZNE: A Comprehensive Quantum Zero-Noise Extrapolation Approach for Mitigating Depolarizing and Decoherence Noise", arXiv:2305.00622, (2023).

[140] L. Domingo, M. Djukic, C. Johnson, and F. Borondo, "Binding affinity predictions with hybrid quantum-classical convolutional neural networks", Scientific Reports 13, 17951 (2023).

[141] Yifeng Xiong, Daryus Chandra, Soon Xin Ng, and Lajos Hanzo, "Circuit Symmetry Verification Mitigates Quantum-Domain Impairments", arXiv:2112.13904, (2021).

[142] Peiyi Li, Ji Liu, Alvin Gonzales, Zain Hamid Saleem, Huiyang Zhou, and Paul Hovland, "QuTracer: Mitigating Quantum Gate and Measurement Errors by Tracing Subsets of Qubits", arXiv:2404.19712, (2024).

[143] Dror Baron, Hrushikesh Pramod Patil, and Huiyang Zhou, "Maximum Likelihood Quantum Error Mitigation for Algorithms with a Single Correct Output", arXiv:2402.11830, (2024).

[144] Andrey Zhukov and Walter Pogosov, "Quantum error mitigation in the regime of high noise using deep neural network: Trotterized dynamics", Quantum Information Processing 23 3, 80 (2024).

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