Zephyrnet Logo

Error mitigation with Clifford quantum-circuit data

Date:

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

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

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

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

► 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

Cited by

[1] 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.

[2] 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:2101.08448.

[3] Samson Wang, Enrico Fontana, M. Cerezo, Kunal Sharma, Akira Sone, Lukasz Cincio, and Patrick J. Coles, “Noise-Induced Barren Plateaus in Variational Quantum Algorithms”, arXiv:2007.14384.

[4] 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).

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

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

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

[8] 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).

[9] Yuxuan Du, Tao Huang, Shan You, Min-Hsiu Hsieh, and Dacheng Tao, “Quantum circuit architecture search: error mitigation and trainability enhancement for variational quantum solvers”, arXiv:2010.10217.

[10] 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).

[11] Alexander Zlokapa and Alexandru Gheorghiu, “A deep learning model for noise prediction on near-term quantum devices”, arXiv:2005.10811.

[12] 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).

[13] Keisuke Fujii, 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.

[14] Piotr Czarnik, Andrew Arrasmith, Lukasz Cincio, and Patrick J. Coles, “Qubit-efficient exponential suppression of errors”, arXiv:2102.06056.

[15] 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, Nathan Shammah, and William J. Zeng, “Mitiq: A software package for error mitigation on noisy quantum computers”, arXiv:2009.04417.

[16] Lukasz Cincio, Kenneth Rudinger, Mohan Sarovar, and Patrick J. Coles, “Machine learning of noise-resilient quantum circuits”, arXiv:2007.01210.

[17] Xinbiao Wang, Yuxuan Du, Yong Luo, and Dacheng Tao, “Towards understanding the power of quantum kernels in the NISQ era”, arXiv:2103.16774.

[18] Ashley Montanaro and Stasja Stanisic, “Error mitigation by training with fermionic linear optics”, arXiv:2102.02120.

[19] Mingxia Huo and Ying Li, “Dual-state purification for practical quantum error mitigation”, arXiv:2105.01239.

[20] 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).

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

[22] 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.

[23] Samson Wang, Piotr Czarnik, Andrew Arrasmith, M. Cerezo, Lukasz Cincio, and Patrick J. Coles, “Can Error Mitigation Improve Trainability of Noisy Variational Quantum Algorithms?”, arXiv:2109.01051.

[24] Robin Blume-Kohout, Kenneth Rudinger, Erik Nielsen, Timothy Proctor, and Kevin Young, “Wildcard error: Quantifying unmodeled errors in quantum processors”, arXiv:2012.12231.

[25] Yifeng Xiong, Soon Xin Ng, and Lajos Hanzo, “Quantum Error Mitigation Relying on Permutation Filtering”, arXiv:2107.01458.

[26] Kun Wang, Yu-Ao Chen, and Xin Wang, “Measurement Error Mitigation via Truncated Neumann Series”, arXiv:2103.13856.

[27] 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).

[28] Daniel Bultrini, Max Hunter Gordon, Piotr Czarnik, Andrew Arrasmith, Patrick J. Coles, and Lukasz Cincio, “Unifying and benchmarking state-of-the-art quantum error mitigation techniques”, arXiv:2107.13470.

[29] Yu Zhang, Lukasz Cincio, Christian F. A. Negre, Piotr Czarnik, Patrick Coles, Petr M. Anisimov, Susan M. Mniszewski, Sergei Tretiak, and Pavel A. Dub, “Variational Quantum Eigensolver with Reduced Circuit Complexity”, arXiv:2106.07619.

[30] Daniel Bultrini, Max Hunter Gordon, Esperanza López, and Germȧn Sierra, “Simple Mitigation Strategy for a Systematic Gate Error in IBMQ”, arXiv:2012.00831.

[31] Daiqin Su, Robert Israel, Kunal Sharma, Haoyu Qi, Ish Dhand, and Kamil Brádler, “Error mitigation on a near-term quantum photonic device”, arXiv:2008.06670.

[32] Eliott Rosenberg, Paul Ginsparg, and Peter L. McMahon, “Experimental error mitigation using linear rescaling for variational quantum eigensolving with up to 20 qubits”, arXiv:2106.01264.

[33] Zhenyu Cai, “A Practical Framework for Quantum Error Mitigation”, arXiv:2110.05389.

[34] Yongdan Yang, Bing-Nan Lu, and Ying Li, “Accelerated quantum Monte Carlo with mitigated error on noisy quantum computer”, arXiv:2106.09880.

[35] A. A. Zhukov and W. V. Pogosov, “Quantum error reduction with deep neural network applied at the post-processing stage”, arXiv:2105.07793.

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

[37] 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).

[38] Rawad Mezher, James Mills, and Elham Kashefi, “Mitigating errors by quantum verification and post-selection”, arXiv:2109.14329.

[39] 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”, arXiv:2111.05176.

[40] 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).

[41] 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).

[42] 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.

[43] Yuki Takeuchi, Yasuhiro Takahashi, Tomoyuki Morimae, and Seiichiro Tani, “Divide-and-conquer verification method for noisy intermediate-scale quantum computation”, arXiv:2109.14928.

[44] 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).

[45] 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”, arXiv:2110.13338.

[46] Kun Wang, Yu-Ao Chen, and Xin Wang, “Mitigating Quantum Errors via Truncated Neumann Series”, arXiv:2111.00691.

[47] Hanrui Wang, Jiaqi Gu, Yongshan Ding, Zirui Li, Frederic T. Chong, David Z. Pan, and Song Han, “RoQNN: Noise-Aware Training for Robust Quantum Neural Networks”, arXiv:2110.11331.

[48] 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).

[49] Steven T. Flammia, “Averaged circuit eigenvalue sampling”, arXiv:2108.05803.

The above citations are from SAO/NASA ADS (last updated successfully 2021-11-29 12:07:27). The list may be incomplete as not all publishers provide suitable and complete citation data.

On Crossref’s cited-by service no data on citing works was found (last attempt 2021-11-29 12:07:25). Could not fetch ADS cited-by data during last attempt 2021-11-29 12:07:25: cURL error 28: Operation timed out after 10001 milliseconds with 0 bytes received

PlatoAi. Web3 Reimagined. Data Intelligence Amplified.
Click here to access.

Source: https://quantum-journal.org/papers/q-2021-11-26-592/

spot_img

Latest Intelligence

spot_img