Modeling And Mitigation Of Cross-talk Effects In Readout Noise With Applications To The Quantum Approximate Optimization Algorithm

Abstract

Measurement noise is one of the main sources of errors in currently available quantum devices based on superconducting qubits. At the same time, the complexity of its characterization and mitigation often exhibits exponential scaling with the system size. In this work, we introduce a correlated measurement noise model that can be efficiently described and characterized, and which admits effective noise-mitigation on the level of marginal probability distributions. Noise mitigation can be performed up to some error for which we derive upper bounds. Characterization of the model is done efficiently using Diagonal Detector Overlapping Tomography – a generalization of the recently introduced Quantum Overlapping Tomography to the problem of reconstruction of readout noise with restricted locality. The procedure allows to characterize $k$-local measurement cross-talk on $N$-qubit device using $O(k2^klog(N))$ circuits containing random combinations of X and identity gates. We perform experiments on 15 (23) qubits using IBM’s (Rigetti’s) devices to test both the noise model and the error-mitigation scheme, and obtain an average reduction of errors by a factor $>22$ ($>5.5$) compared to no mitigation. Interestingly, we find that correlations in the measurement noise do not correspond to the physical layout of the device. Furthermore, we study numerically the effects of readout noise on the performance of the Quantum Approximate Optimization Algorithm (QAOA). We observe in simulations that for numerous objective Hamiltonians, including random MAX-2-SAT instances and the Sherrington-Kirkpatrick model, the noise-mitigation improves the quality of the optimization. Finally, we provide arguments why in the course of QAOA optimization the estimates of the local energy (or cost) terms often behave like uncorrelated variables, which greatly reduces sampling complexity of the energy estimation compared to the pessimistic error analysis. We also show that similar effects are expected for Haar-random quantum states and states generated by shallow-depth random circuits.

Featured image: The illustration shows correlations in readout noise in IBM’s 15-qubit device. Two orange qubits are strongly correlated with each other, the arrows indicate mild correlations.

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Popular summary

State of the art quantum devices are affected by a significant amount of noise, which often prohibits the implementation of useful quantum information processing tasks. It is, therefore, not surprising that recently the field of characterization and mitigation of various types of noise has been developing rapidly. In this work, we make a few contributions that focus specifically on the characterization and reduction of the noise affecting the quantum measurement process.

We propose a readout noise model that can capture multiqubit cross-talk while remaining efficiently describable under the assumption that the locality of correlations in noise is not too high. Inspired by recent advances of the so-called Quantum Overlapping Tomography, we show how to characterize k-local correlations in measurement noise using random combinations of elementary quantum gates (identity gate and NOT gate), and we prove that the number of circuits required to do so scales only logarithmically with the number of qubits.

The characterization of the noise can be used to perform error mitigation on marginal probability distributions in a manner that does not exhibit exponential sampling complexity – exactly because it is performed on the level of marginals (contrary to standard methods that operate on global probability distributions). While this correction is imperfect, we provide upper bounds on the errors that can be calculated directly from the noise-characterization results. We demonstrate the effectiveness of noise mitigation in experiments on 15- and 23-qubit systems and conclude great improvements.

While mitigating noise on marginals does not allow correcting results of arbitrary experiments, currently the most promising quantum algorithms belong to the class of hybrid quantum-classical variational algorithms, where one usually restricts the locality of the quantities that are to be estimated. Here we investigate an example of such algorithms, i.e., Quantum Approximate Optimization Algorithm (QAOA). We numerically demonstrate that the correlated readout noise affects both the convergence and the final estimation of QAOA, and find that error mitigation helps to reduce such effects.

Finally, we study the sample complexity of estimation of local observables, from the point of view of quantum correlations. Based on recent results on correlations spreading in QAOA circuits, we show that for shallow-depth QAOA, one should expect that the estimators of expected values of local observables will not be correlated. Consequently, such estimators effectively behave as uncorrelated variables, highly reducing the sampling complexity of such estimation. We show that similar effects should be expected also from random quantum states.

Our work is accompanied by an open-source GitHub repository QREM – Quantum Readout Error Mitigation (https://github.com/fbm2718/QREM), where we develop a Python code that allows performing efficient measurement noise characterization and mitigation.

► BibTeX data

@article{Maciejewski2021modelingmitigation, doi = {10.22331/q-2021-06-01-464}, url = {https://doi.org/10.22331/q-2021-06-01-464}, title = {Modeling and mitigation of cross-talk effects in readout noise with applications to the {Q}uantum {A}pproximate {O}ptimization {A}lgorithm}, author = {Maciejewski, Filip B. and Baccari, Flavio and Zimbor{‘{a}}s, Zolt{‘{a}}n and Oszmaniec, Micha{l{}}}, journal = {{Quantum}}, issn = {2521-327X}, publisher = {{Verein zur F{“{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}}, volume = {5}, pages = {464}, month = jun, year = {2021}<br /> }

► References

[1] Frank Arute et al. Quantum supremacy using a programmable superconducting processor. Nature, 574 (7779): 505–510, Oct 2019. ISSN 1476-4687. 10.1038/s41586-019-1666-5. URL https://doi.org/10.1038/s41586-019-1666-5.
https://doi.org/10.1038/s41586-019-1666-5

[2] Benjamin Villalonga, Dmitry Lyakh, Sergio Boixo, Hartmut Neven, Travis S Humble, Rupak Biswas, Eleanor G Rieffel, Alan Ho, and Salvatore Mandrà. Establishing the quantum supremacy frontier with a 281 pflop/s simulation. Quantum Science and Technology, 5 (3): 034003, Apr 2020. ISSN 2058-9565. 10.1088/2058-9565/ab7eeb. URL http://dx.doi.org/10.1088/2058-9565/ab7eeb.
https://doi.org/10.1088/2058-9565/ab7eeb

[3] Edward Farhi and Aram W Harrow. Quantum Supremacy through the Quantum Approximate Optimization Algorithm. arXiv e-prints, art. arXiv:1602.07674, Feb 2016. URL https://arxiv.org/abs/1602.07674.
arXiv:1602.07674

[4] Nikolaj Moll, Panagiotis Barkoutsos, Lev S. Bishop, Jerry M. Chow, Andrew Cross, Daniel J. Egger, Stefan Filipp, Andreas Fuhrer, Jay M. Gambetta, Marc Ganzhorn, Abhinav Kandala, Antonio Mezzacapo, Peter Müller, Walter Riess, Gian Salis, John Smolin, Ivano Tavernelli, and Kristan Temme. Quantum optimization using variational algorithms on near-term quantum devices. Quantum Science and Technology, 3 (3): 030503, Jul 2018. 10.1088/2058-9565/aab822. URL https://arxiv.org/abs/1710.01022v2.
https://doi.org/10.1088/2058-9565/aab822
arXiv:1710.01022v2

[5] John Preskill. Quantum Computing in the NISQ era and beyond. Quantum, 2: 79, August 2018. ISSN 2521-327X. 10.22331/q-2018-08-06-79. URL https://doi.org/10.22331/q-2018-08-06-79.
https://doi.org/10.22331/q-2018-08-06-79

[6] Joel J. Wallman and Joseph Emerson. Noise tailoring for scalable quantum computation via randomized compiling. Physical Review A, 94 (5), Nov 2016. ISSN 2469-9934. 10.1103/physreva.94.052325. URL http://dx.doi.org/10.1103/PhysRevA.94.052325.
https://doi.org/10.1103/physreva.94.052325

[7] Ying Li and Simon C. Benjamin. Efficient variational quantum simulator incorporating active error minimization. Physical Review X, 7 (2), Jun 2017. ISSN 2160-3308. 10.1103/physrevx.7.021050. URL http://dx.doi.org/10.1103/PhysRevX.7.021050.
https://doi.org/10.1103/physrevx.7.021050

[8] Kristan Temme, Sergey Bravyi, and Jay M. Gambetta. Error mitigation for short-depth quantum circuits. Physical Review Letters, 119 (18), Nov 2017. ISSN 1079-7114. 10.1103/physrevlett.119.180509. URL http://dx.doi.org/10.1103/PhysRevLett.119.180509.
https://doi.org/10.1103/physrevlett.119.180509

[9] Suguru Endo, Simon C. Benjamin, and Ying Li. Practical Quantum Error Mitigation for Near-Future Applications. Physical Review X, 8: 031027, Jul 2018. 10.1103/PhysRevX.8.031027.
https://doi.org/10.1103/PhysRevX.8.031027

[10] 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, Mar 2019. ISSN 1476-4687. 10.1038/s41586-019-1040-7. URL http://dx.doi.org/10.1038/s41586-019-1040-7.
https://doi.org/10.1038/s41586-019-1040-7

[11] 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), Mar 2021. ISSN 2331-7019. 10.1103/physrevapplied.15.034026. URL http://dx.doi.org/10.1103/PhysRevApplied.15.034026.
https://doi.org/10.1103/physrevapplied.15.034026

[12] 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. 2020. URL https://arxiv.org/abs/2011.07064.
arXiv:2011.07064

[13] Filip B. Maciejewski, Zoltán Zimborás, and Michał Oszmaniec. Mitigation of readout noise in near-term quantum devices by classical post-processing based on detector tomography. Quantum, 4: 257, April 2020a. ISSN 2521-327X. 10.22331/q-2020-04-24-257. URL https://doi.org/10.22331/q-2020-04-24-257.
https://doi.org/10.22331/q-2020-04-24-257

[14] Yanzhu Chen, Maziar Farahzad, Shinjae Yoo, and Tzu-Chieh Wei. Detector tomography on ibm quantum computers and mitigation of an imperfect measurement. Physical Review A, 100 (5), Nov 2019. ISSN 2469-9934. 10.1103/physreva.100.052315. URL http://dx.doi.org/10.1103/PhysRevA.100.052315.
https://doi.org/10.1103/physreva.100.052315

[15] Sergey Bravyi, Sarah Sheldon, Abhinav Kandala, David C. Mckay, and Jay M. Gambetta. Mitigating measurement errors in multiqubit experiments. Physical Review A, 103 (4), Apr 2021. ISSN 2469-9934. 10.1103/physreva.103.042605. URL http://dx.doi.org/10.1103/PhysRevA.103.042605.
https://doi.org/10.1103/physreva.103.042605

[16] Michael R Geller and Mingyu Sun. Toward efficient correction of multiqubit measurement errors: pair correlation method. Quantum Science and Technology, 6 (2): 025009, feb 2021. 10.1088/2058-9565/abd5c9. URL https://doi.org/10.1088/2058-9565/abd5c9.
https://doi.org/10.1088/2058-9565/abd5c9

[17] Michael R Geller. Rigorous measurement error correction. Quantum Science and Technology, 5 (3): 03LT01, Jun 2020. ISSN 2058-9565. 10.1088/2058-9565/ab9591. URL http://dx.doi.org/10.1088/2058-9565/ab9591.
https://doi.org/10.1088/2058-9565/ab9591

[18] Benjamin Nachman, Miroslav Urbanek, Wibe A. de Jong, and Christian W. Bauer. Unfolding quantum computer readout noise. npj Quantum Information, 6 (1): 84, Sep 2020. ISSN 2056-6387. 10.1038/s41534-020-00309-7. URL https://doi.org/10.1038/s41534-020-00309-7.
https://doi.org/10.1038/s41534-020-00309-7

[19] Hyeokjea Kwon and Joonwoo Bae. A hybrid quantum-classical approach to mitigating measurement errors in quantum algorithms. IEEE Transactions on Computers, page 1–1, 2020. ISSN 2326-3814. 10.1109/tc.2020.3009664. URL http://dx.doi.org/10.1109/TC.2020.3009664.
https://doi.org/10.1109/tc.2020.3009664

[20] Kathleen E. Hamilton, Tyler Kharazi, Titus Morris, Alexander J. McCaskey, Ryan S. Bennink, and Raphael C. Pooser. Scalable quantum processor noise characterization. In 2020 IEEE International Conference on Quantum Computing and Engineering (QCE), pages 430–440, 2020. 10.1109/QCE49297.2020.00060. URL https://arxiv.org/abs/2006.01805.
https://doi.org/10.1109/QCE49297.2020.00060
arXiv:2006.01805

[21] Megan L. Dahlhauser and Travis S. Humble. Modeling noisy quantum circuits using experimental characterization. Phys. Rev. A, 103: 042603, Apr 2021. 10.1103/PhysRevA.103.042603.
https://doi.org/10.1103/PhysRevA.103.042603

[22] Lena Funcke, Tobias Hartung, Karl Jansen, Stefan Kühn, Paolo Stornati, and Xiaoyang Wang. Measurement error mitigation in quantum computers through classical bit-flip correction. 2020. URL https://arxiv.org/abs/2007.03663.
arXiv:2007.03663

[23] Muqing Zheng, Ang Li, Tamás Terlaky, and Xiu Yang. A bayesian approach for characterizing and mitigating gate and measurement errors. 2020. URL https://arxiv.org/abs/2010.09188.
arXiv:2010.09188

[24] Edward Farhi, Jeffrey Goldstone, and Sam Gutmann. A quantum approximate optimization algorithm. 2014. URL https://arxiv.org/abs/1411.4028.
arXiv:1411.4028

[25] M Cerezo, Andrew Arrasmith, Ryan Babbush, Simon C Benjamin, Suguru Endo, Keisuke Fujii, Jarrod R McClean, Kosuke Mitarai, Xiao Yuan, Lukasz Cincio, and P. J. Coles. Variational quantum algorithms. 2020. URL https://arxiv.org/abs/2012.09265.
arXiv:2012.09265

[26] Stuart Hadfield, Zhihui Wang, Bryan O’Gorman, Eleanor Rieffel, Davide Venturelli, and Rupak Biswas. From the quantum approximate optimization algorithm to a quantum alternating operator ansatz. Algorithms, 12 (2): 34, Feb 2019. ISSN 1999-4893. 10.3390/a12020034. URL http://dx.doi.org/10.3390/a12020034.
https://doi.org/10.3390/a12020034

[27] Seth Lloyd. Quantum approximate optimization is computationally universal. 2018. URL https://arxiv.org/abs/1812.11075.
arXiv:1812.11075

[28] M. E. S. Morales, J. D. Biamonte, and Z. Zimborás. On the universality of the quantum approximate optimization algorithm. Quantum Information Processing, 19 (9): 291, Aug 2020. ISSN 1573-1332. 10.1007/s11128-020-02748-9. URL https://doi.org/10.1007/s11128-020-02748-9.
https://doi.org/10.1007/s11128-020-02748-9

[29] Pierre Hansen and Brigitte Jaumard. Algorithms for the maximum satisfiability problem. Computing, 44 (4): 279–303, Dec 1990. ISSN 1436-5057. 10.1007/BF02241270. URL https://doi.org/10.1007/BF02241270.
https://doi.org/10.1007/BF02241270

[30] G. G. Guerreschi and A. Y. Matsuura. Qaoa for max-cut requires hundreds of qubits for quantum speed-up. Scientific Reports, 9 (1): 6903, May 2019. ISSN 2045-2322. 10.1038/s41598-019-43176-9. URL https://doi.org/10.1038/s41598-019-43176-9.
https://doi.org/10.1038/s41598-019-43176-9

[31] Dmitry Panchenko. The sherrington-kirkpatrick model: An overview. Journal of Statistical Physics, 149 (2): 362–383, Sep 2012. ISSN 1572-9613. 10.1007/s10955-012-0586-7. URL http://dx.doi.org/10.1007/s10955-012-0586-7.
https://doi.org/10.1007/s10955-012-0586-7

[32] Edward Farhi, Jeffrey Goldstone, Sam Gutmann, and Leo Zhou. The quantum approximate optimization algorithm and the sherrington-kirkpatrick model at infinite size. 2019. URL https://arxiv.org/abs/1910.08187.
arXiv:1910.08187

[33] Jordan Cotler and Frank Wilczek. Quantum overlapping tomography. Physical Review Letters, 124 (10), Mar 2020. ISSN 1079-7114. 10.1103/physrevlett.124.100401. URL http://dx.doi.org/10.1103/PhysRevLett.124.100401.
https://doi.org/10.1103/physrevlett.124.100401

[34] Jens Koch, Terri M. Yu, Jay Gambetta, A. A. Houck, D. I. Schuster, J. Majer, Alexandre Blais, M. H. Devoret, S. M. Girvin, and R. J. Schoelkopf. Charge-insensitive qubit design derived from the cooper pair box. Phys. Rev. A, 76: 042319, Oct 2007. 10.1103/PhysRevA.76.042319.
https://doi.org/10.1103/PhysRevA.76.042319

[35] Cheng Xue, Zhao-Yun Chen, Yu-Chun Wu, and Guo-Ping Guo. Effects of quantum noise on quantum approximate optimization algorithm. Chinese Physics Letters, 38 (3): 030302, mar 2021. 10.1088/0256-307x/38/3/030302. URL https://doi.org/10.1088/0256-307x/38/3/030302.
https://doi.org/10.1088/0256-307x/38/3/030302

[36] Jeffrey Marshall, Filip Wudarski, Stuart Hadfield, and Tad Hogg. Characterizing local noise in qaoa circuits. IOP SciNotes, 1 (2): 025208, Aug 2020. ISSN 2633-1357. 10.1088/2633-1357/abb0d7. URL http://dx.doi.org/10.1088/2633-1357/abb0d7.
https://doi.org/10.1088/2633-1357/abb0d7

[37] Mahabubul Alam, Abdullah Ash-Saki, and Swaroop Ghosh. Analysis of quantum approximate optimization algorithm under realistic noise in superconducting qubits. 2019. URL https://arxiv.org/abs/1907.09631.
arXiv:1907.09631

[38] Matthew P. Harrigan et al. Quantum approximate optimization of non-planar graph problems on a planar superconducting processor. Nature Physics, 17 (3): 332–336, Mar 2021. ISSN 1745-2481. 10.1038/s41567-020-01105-y. URL https://doi.org/10.1038/s41567-020-01105-y.
https://doi.org/10.1038/s41567-020-01105-y

[39] Ashley Montanaro and Stasja Stanisic. Compressed variational quantum eigensolver for the fermi-hubbard model. 2020. URL https://arxiv.org/abs/2006.01179.
arXiv:2006.01179

[40] Pranav Gokhale, Ali Javadi-Abhari, Nathan Earnest, Yunong Shi, and Frederic T. Chong. Optimized quantum compilation for near-term algorithms with openpulse. 2020. URL https://arxiv.org/abs/2004.11205.
arXiv:2004.11205

[41] Asher Peres. Quantum theory: Concepts and methods, volume 57. Springer Science & Business Media, 2006. https://doi.org/10.1007/0-306-47120-5.
https://doi.org/10.1007/0-306-47120-5

[42] J. S. Lundeen, A. Feito, H. Coldenstrodt-Ronge, K. L. Pregnell, Ch. Silberhorn, T. C. Ralph, J. Eisert, M. B. Plenio, and I. A. Walmsley. Tomography of quantum detectors. Nature Physics, 5: 27, November 2008. URL http://dx.doi.org/10.1038/nphys1133.
https://doi.org/10.1038/nphys1133

[43] Zdeněk Hradil, Jaroslav Řeháček, Jaromír Fiurášek, and Miroslav Ježek. 3 Maximum-Likelihood Methodsin Quantum Mechanics, pages 59–112. Springer Berlin Heidelberg, Berlin, Heidelberg, 2004. ISBN 978-3-540-44481-7. 10.1007/978-3-540-44481-7_3. URL https://doi.org/10.1007/978-3-540-44481-7_3.
https://doi.org/10.1007/978-3-540-44481-7_3

[44] Jaromír Fiurášek. Maximum-likelihood estimation of quantum measurement. Physical Review A, 64: 024102, August 2001. 10.1103/PhysRevA.64.024102.
https://doi.org/10.1103/PhysRevA.64.024102

[45] I. Gianani, Y.S. Teo, V. Cimini, H. Jeong, G. Leuchs, M. Barbieri, and L.L. Sánchez-Soto. Compressively certifying quantum measurements. PRX Quantum, 1 (2), Oct 2020. ISSN 2691-3399. 10.1103/prxquantum.1.020307. URL http://dx.doi.org/10.1103/PRXQuantum.1.020307.
https://doi.org/10.1103/prxquantum.1.020307

[46] Tim J. Evans, Robin Harper, and Steven T. Flammia. Scalable bayesian hamiltonian learning. 2019. URL https://arxiv.org/abs/1912.07636.
arXiv:1912.07636

[47] Nengkun Yu. Sample efficient tomography via Pauli measurements. 2020. URL https://arxiv.org/abs/2009.04610.
arXiv:2009.04610

[48] B. S. Majewski, N. C. Wormald, G. Havas, and Z. J. Czech. A Family of Perfect Hashing Methods. The Computer Journal, 39 (6): 547–554, 01 1996. ISSN 0010-4620. 10.1093/comjnl/39.6.547. URL https://doi.org/10.1093/comjnl/39.6.547.
https://doi.org/10.1093/comjnl/39.6.547

[49] D. R. Stinson, R. Wei, and L. Zhu. New constructions for perfect hash families and related structures using combinatorial designs and codes. Journal of Combinatorial Designs, 8 (3): 189–200, 2000. https://doi.org/10.1002/(SICI)1520-6610(2000)8:3<189::AID-JCD4>3.0.CO;2-A.
[50] Simon R. Blackburn. Perfect hash families: Probabilistic methods and explicit constructions. Journal of Combinatorial Theory, Series A, 92 (1): 54 – 60, 2000. ISSN 0097-3165. https://doi.org/10.1006/jcta.1999.3050. URL https://www.sciencedirect.com/science/article/pii/S0097316599930509.
https://doi.org/10.1006/jcta.1999.3050
https://www.sciencedirect.com/science/article/pii/S0097316599930509

[51] Noga Alon and Shai Gutner. Balanced Families of Perfect Hash Functions and Their Applications. May 2008. URL https://arxiv.org/abs/0805.4300.
arXiv:0805.4300

[52] Siddhartha Santra, Gregory Quiroz, Greg Ver Steeg, and Daniel A Lidar. Max 2-SAT with up to 108 qubits. New Journal of Physics, 16 (4): 045006, apr 2014. 10.1088/1367-2630/16/4/045006. URL https://doi.org/10.1088/1367-2630/16/4/045006.
https://doi.org/10.1088/1367-2630/16/4/045006

[53] Kenneth Rudinger, Timothy Proctor, Dylan Langharst, Mohan Sarovar, Kevin Young, and Robin Blume-Kohout. Probing context-dependent errors in quantum processors. Physical Review X, 9 (2), Jun 2019. ISSN 2160-3308. 10.1103/physrevx.9.021045. URL http://dx.doi.org/10.1103/PhysRevX.9.021045.
https://doi.org/10.1103/physrevx.9.021045

[54] Edward Farhi, David Gamarnik, and Sam Gutmann. The quantum approximate optimization algorithm needs to see the whole graph: A typical case. 2020. URL https://arxiv.org/abs/2004.09002.
arXiv:2004.09002

[55] Sandu Popescu, Anthony J. Short, and Andreas Winter. Entanglement and the foundations of statistical mechanics. Nature Physics, 2 (11): 754–758, November 2006. 10.1038/nphys444.
https://doi.org/10.1038/nphys444

[56] M. Oszmaniec, R. Augusiak, C. Gogolin, J. Kołodyński, A. Acín, and M. Lewenstein. Random bosonic states for robust quantum metrology. Phys. Rev. X, 6: 041044, Dec 2016. 10.1103/PhysRevX.6.041044.
https://doi.org/10.1103/PhysRevX.6.041044

[57] Fernando G. S. L. Brandão, Aram W. Harrow, and Michał Horodecki. Local Random Quantum Circuits are Approximate Polynomial-Designs. Communications in Mathematical Physics, 346 (2): 397–434, September 2016. 10.1007/s00220-016-2706-8.
https://doi.org/10.1007/s00220-016-2706-8

[58] Jordan Cotler, Nicholas Hunter-Jones, and Daniel Ranard. Fluctuations of subsystem entropies at late times. October 2020. URL https://arxiv.org/abs/2010.11922.
arXiv:2010.11922

[59] J. Spall. An overview of the simultaneous perturbation method for efficient optimization. Johns Hopkins Apl Technical Digest, 19: 482–492, 1998. URL https://www.jhuapl.edu/Content/techdigest/pdf/V19-N04/19-04-Spall.pdf.
https://www.jhuapl.edu/Content/techdigest/pdf/V19-N04/19-04-Spall.pdf

[60] Chris Cade, Lana Mineh, Ashley Montanaro, and Stasja Stanisic. Strategies for solving the fermi-hubbard model on near-term quantum computers. Phys. Rev. B, 102: 235122, Dec 2020. 10.1103/PhysRevB.102.235122.
https://doi.org/10.1103/PhysRevB.102.235122

[61] Abhinav Kandala, Antonio Mezzacapo, Kristan Temme, Maika Takita, Markus Brink, Jerry M. Chow, and Jay M. Gambetta. Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. nat, 549: 242–246, Sep 2017. 10.1038/nature23879.
https://doi.org/10.1038/nature23879

[62] William J. Huggins, Jarrod R. McClean, Nicholas C. Rubin, Zhang Jiang, Nathan Wiebe, K. Birgitta Whaley, and Ryan Babbush. Efficient and noise resilient measurements for quantum chemistry on near-term quantum computers. npj Quantum Information, 7 (1): 23, Feb 2021. ISSN 2056-6387. 10.1038/s41534-020-00341-7. URL https://doi.org/10.1038/s41534-020-00341-7.
https://doi.org/10.1038/s41534-020-00341-7

[63] George S. Barron and Christopher J. Wood. Measurement error mitigation for variational quantum algorithms. 2020. URL https://arxiv.org/abs/2010.08520.
arXiv:2010.08520

[64] Timothy Proctor, Melissa Revelle, Erik Nielsen, Kenneth Rudinger, Daniel Lobser, Peter Maunz, Robin Blume-Kohout, and Kevin Young. Detecting and tracking drift in quantum information processors. Nature Communications, 11 (1): 5396, Oct 2020. ISSN 2041-1723. 10.1038/s41467-020-19074-4. URL https://doi.org/10.1038/s41467-020-19074-4.
https://doi.org/10.1038/s41467-020-19074-4

[65] Samudra Dasgupta and Travis S. Humble. Characterizing the stability of nisq devices. In 2020 IEEE International Conference on Quantum Computing and Engineering (QCE), pages 419–429, 2020. 10.1109/QCE49297.2020.00059.
https://doi.org/10.1109/QCE49297.2020.00059

[66] L. C. G. Govia, G. J. Ribeill, D. Ristè, M. Ware, and H. Krovi. Bootstrapping quantum process tomography via a perturbative ansatz. Nature Communications, 11 (1): 1084, Feb 2020. ISSN 2041-1723. 10.1038/s41467-020-14873-1. URL https://doi.org/10.1038/s41467-020-14873-1.
https://doi.org/10.1038/s41467-020-14873-1

[67] Steven T. Flammia and Joel J. Wallman. Efficient estimation of Pauli channels. ACM Transactions on Quantum Computing, 1 (1): 1–32, Dec 2020. ISSN 2643-6817. 10.1145/3408039. URL http://dx.doi.org/10.1145/3408039.
https://doi.org/10.1145/3408039

[68] Robin Harper, Steven T. Flammia, and Joel J. Wallman. Efficient learning of quantum noise. Nature Physics, 16 (12): 1184–1188, Aug 2020. ISSN 1745-2481. 10.1038/s41567-020-0992-8. URL http://dx.doi.org/10.1038/s41567-020-0992-8.
https://doi.org/10.1038/s41567-020-0992-8

[69] Hsin-Yuan Huang, Richard Kueng, and John Preskill. Predicting many properties of a quantum system from very few measurements. Nature Physics, 16 (10): 1050–1057, Jun 2020. ISSN 1745-2481. 10.1038/s41567-020-0932-7. URL http://dx.doi.org/10.1038/s41567-020-0932-7.
https://doi.org/10.1038/s41567-020-0932-7

[70] Senrui Chen, Wenjun Yu, Pei Zeng, and Steven T. Flammia. Robust shadow estimation. 2020. URL https://arxiv.org/abs/2011.09636.
arXiv:2011.09636

[71] Kelly Boothby, Paul Bunyk, Jack Raymond, and Aidan Roy. Next-generation topology of d-wave quantum processors. 2020. URL https://arxiv.org/abs/2003.00133.
arXiv:2003.00133

[72] Colin D. Bruzewicz, John Chiaverini, Robert McConnell, and Jeremy M. Sage. Trapped-ion quantum computing: Progress and challenges. Applied Physics Reviews, 6 (2): 021314, Jun 2019. ISSN 1931-9401. 10.1063/1.5088164. URL http://dx.doi.org/10.1063/1.5088164.
https://doi.org/10.1063/1.5088164

[73] Jianwei Wang, Fabio Sciarrino, Anthony Laing, and Mark G. Thompson. Integrated photonic quantum technologies. Nature Photonics, 14 (5): 273–284, Oct 2019. ISSN 1749-4893. 10.1038/s41566-019-0532-1. URL http://dx.doi.org/10.1038/s41566-019-0532-1.
https://doi.org/10.1038/s41566-019-0532-1

[74] Héctor Abraham et al. Qiskit: An open-source framework for quantum computing, 2019. URL https://qiskit.org/documentation/.
https://qiskit.org/documentation/

[75] F. B. Maciejewski, T. Rybotycki, and M. Oszmaniec. Quantum readout errors mitigation (qrem) – open source github repository, 2020b. URL https://github.com/fbm2718/QREM.
https://github.com/fbm2718/QREM

[76] Tsachy Weissman, Erik Ordentlich, Gadiel Seroussi, Sergio Verdu1, and Marcelo J. Weinberger. Inequalities for the l1 deviation of the empirical distribution. Technical Report HPL-2003-97R1, Hewlett-Packard Labs, 08 2003. URL https://www.hpl.hp.com/techreports/2003/HPL-2003-97R1.pdf?origin=publicationDetail.
https://www.hpl.hp.com/techreports/2003/HPL-2003-97R1.pdf?origin=publicationDetail.

[77] Zbigniew Puchała, Łukasz Pawela, Aleksandra Krawiec, and Ryszard Kukulski. Strategies for optimal single-shot discrimination of quantum measurements. Physical Review A, 98 (4), Oct 2018. ISSN 2469-9934. 10.1103/physreva.98.042103. URL http://dx.doi.org/10.1103/PhysRevA.98.042103.
https://doi.org/10.1103/physreva.98.042103

[78] Michael A. Nielsen and Isaac L. Chuang. Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press, 2010. 10.1017/CBO9780511976667.
https://doi.org/10.1017/CBO9780511976667

[79] V. Akshay, H. Philathong, M. E. S. Morales, and J. D. Biamonte. Reachability deficits in quantum approximate optimization. Phys. Rev. Lett., 124: 090504, Mar 2020. 10.1103/PhysRevLett.124.090504.
https://doi.org/10.1103/PhysRevLett.124.090504

Cited by

[1] Ellen Derbyshire, Rawad Mezher, Theodoros Kapourniotis, and Elham Kashefi, “Randomized Benchmarking with Stabilizer Verification and Gate Synthesis”, arXiv:2102.13044.

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

[3] Benjamin Nachman and Michael R. Geller, “Categorizing Readout Error Correlations on Near Term Quantum Computers”, arXiv:2104.04607.

[4] Tanmay Singal, Filip B. Maciejewski, and Michał Oszmaniec, “Implementation of quantum measurements using classical resources and only a single ancillary qubit”, arXiv:2104.05612.

[5] Kerstin Beer, Daniel List, Gabriel Müller, Tobias J. Osborne, and Christian Struckmann, “Training Quantum Neural Networks on NISQ Devices”, arXiv:2104.06081.

The above citations are from SAO/NASA ADS (last updated successfully 2021-06-01 16:38:57). The list may be incomplete as not all publishers provide suitable and complete citation data.

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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.

Generative Data Intelligence

Modeling and mitigation of cross-talk effects in readout noise with applications to the Quantum Approximate Optimization Algorithm

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