Classical models may be a better explanation of the Jiuzhang 1.0 Gaussian Boson Sampler than its targeted squeezed light model

Javier Martínez-Cifuentes1, K. M. Fonseca-Romero2, and Nicolás Quesada1

1Department of Engineering Physics, École Polytechnique de Montréal, Montréal, QC, H3T 1JK, Canada
2Departamento de Física, Universidad Nacional de Colombia - Sede Bogotá, Facultad de Ciencias, Grupo de Óptica e Información Cuántica, Carrera 30 Calle 45-03, C.P. 111321, Bogotá, Colombia

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

Abstract

Recently, Zhong et al. [1, 2] performed landmark Gaussian boson sampling experiments with up to 144 modes using threshold detectors. The authors claim to have achieved quantum computational advantage with the implementation of these experiments, named Jiuzhang 1.0 and Jiuzhang 2.0. Their experimental results are validated against several classical hypotheses and adversaries using tests such as the comparison of statistical correlations between modes, Bayesian hypothesis testing and the Heavy Output Generation (HOG) test. In this work we propose an alternative classical hypothesis for the validation of these experiments. We use the probability distribution of mixtures of coherent states sent into a lossy interferometer; these input mixed states, which we term $\textit{squashed states}$, have vacuum fluctuations in one quadrature and excess fluctuations in the other. We find that for configurations in the high photon number density regime, the comparison of statistical correlations does not tell apart the ground truth of the experiment (two-mode squeezed states sent into an interferometer) from our alternative hypothesis. On the other hand, the Bayesian test indicates that, for all configurations excepting Jiuzhang 1.0, the ground truth is a more likely explanation of the experimental data than our alternative hypothesis. A similar result is obtained for the HOG test: for all configurations of Jiuzhang 2.0, the test indicates that the experimental samples have higher ground truth probability than the samples obtained from our alternative distribution; for Jiuzhang 1.0 the test is inconclusive. Our results provide a new hypothesis that should be considered in the validation of future GBS experiments, and shed light into the need to identify proper metrics to verify quantum advantage in the context of threshold GBS. Additionally, they indicate that a classical explanation of the Jiuzhang 1.0 experiment, lacking any quantum features, has not been ruled out.

► BibTeX data

► References

[1] Han-Sen Zhong, Hui Wang, Yu-Hao Deng, Ming-Cheng Chen, Li-Chao Peng, Yi-Han Luo, Jian Qin, Dian Wu, Xing Ding, Yi Hu, Peng Hu, Xiao-Yan Yang, Wei-Jun Zhang, Hao Li, Yuxuan Li, Xiao Jiang, Lin Gan, Guangwen Yang, Lixing You, Zhen Wang, Li Li, Nai-Le Liu, Chao-Yang Lu, and Jian-Wei Pan. Quantum computational advantage using photons. Science, 370 (6523): 1460–1463, 2020a. https:/​/​doi.org/​10.1126/​science.abe8770.
https:/​/​doi.org/​10.1126/​science.abe8770

[2] Han-Sen Zhong, Yu-Hao Deng, Jian Qin, Hui Wang, Ming-Cheng Chen, Li-Chao Peng, Yi-Han Luo, Dian Wu, Si-Qiu Gong, Hao Su, Yi Hu, Peng Hu, Xiao-Yan Yang, Wei-Jun Zhang, Hao Li, Yuxuan Li, Xiao Jiang, Lin Gan, Guangwen Yang, Lixing You, Zhen Wang, Li Li, Nai-Le Liu, Jelmer J. Renema, Chao-Yang Lu, and Jian-Wei Pan. Phase-programmable gaussian boson sampling using stimulated squeezed light. Phys. Rev. Lett., 127: 180502, 10 2021a. 10.1103/​PhysRevLett.127.180502. URL https:/​/​link.aps.org/​doi/​10.1103/​PhysRevLett.127.180502.
https:/​/​doi.org/​10.1103/​PhysRevLett.127.180502

[3] Aram W Harrow and Ashley Montanaro. Quantum computational supremacy. Nature, 549 (7671): 203–209, 2017. https:/​/​doi.org/​10.1038/​nature23458.
https:/​/​doi.org/​10.1038/​nature23458

[4] Dominik Hangleiter and Jens Eisert. Computational advantage of quantum random sampling. arXiv preprint arXiv:2206.04079, 2022. https:/​/​doi.org/​10.48550/​arXiv.2206.04079.
https:/​/​doi.org/​10.48550/​arXiv.2206.04079
arXiv:2206.04079

[5] 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/​10.1038/​s41586-019-1666-5.
https:/​/​doi.org/​10.1038/​s41586-019-1666-5

[6] Yulin Wu, Wan-Su Bao, Sirui Cao, Fusheng Chen, Ming-Cheng Chen, Xiawei Chen, Tung-Hsun Chung, Hui Deng, Yajie Du, Daojin Fan, Ming Gong, Cheng Guo, Chu Guo, Shaojun Guo, Lianchen Han, Linyin Hong, He-Liang Huang, Yong-Heng Huo, Liping Li, Na Li, Shaowei Li, Yuan Li, Futian Liang, Chun Lin, Jin Lin, Haoran Qian, Dan Qiao, Hao Rong, Hong Su, Lihua Sun, Liangyuan Wang, Shiyu Wang, Dachao Wu, Yu Xu, Kai Yan, Weifeng Yang, Yang Yang, Yangsen Ye, Jianghan Yin, Chong Ying, Jiale Yu, Chen Zha, Cha Zhang, Haibin Zhang, Kaili Zhang, Yiming Zhang, Han Zhao, Youwei Zhao, Liang Zhou, Qingling Zhu, Chao-Yang Lu, Cheng-Zhi Peng, Xiaobo Zhu, and Jian-Wei Pan. Strong quantum computational advantage using a superconducting quantum processor. Phys. Rev. Lett., 127: 180501, Oct 2021. 10.1103/​PhysRevLett.127.180501. URL https:/​/​link.aps.org/​doi/​10.1103/​PhysRevLett.127.180501.
https:/​/​doi.org/​10.1103/​PhysRevLett.127.180501

[7] Lars S Madsen, Fabian Laudenbach, Mohsen Falamarzi Askarani, Fabien Rortais, Trevor Vincent, Jacob FF Bulmer, Filippo M Miatto, Leonhard Neuhaus, Lukas G Helt, Matthew J Collins, et al. Quantum computational advantage with a programmable photonic processor. Nature, 606 (7912): 75–81, 2022. https:/​/​doi.org/​10.1038/​s41586-022-04725-x.
https:/​/​doi.org/​10.1038/​s41586-022-04725-x

[8] Sergio Boixo, Sergei V Isakov, Vadim N Smelyanskiy, Ryan Babbush, Nan Ding, Zhang Jiang, Michael J Bremner, John M Martinis, and Hartmut Neven. Characterizing quantum supremacy in near-term devices. Nature Physics, 14 (6): 595–600, 2018. https:/​/​doi.org/​10.1038/​s41567-018-0124-x.
https:/​/​doi.org/​10.1038/​s41567-018-0124-x

[9] Adam Bouland, Bill Fefferman, Chinmay Nirkhe, and Umesh Vazirani. On the complexity and verification of quantum random circuit sampling. Nature Physics, 15 (2): 159–163, 2019. https:/​/​doi.org/​10.1038/​s41567-018-0318-2.
https:/​/​doi.org/​10.1038/​s41567-018-0318-2

[10] Craig S. Hamilton, Regina Kruse, Linda Sansoni, Sonja Barkhofen, Christine Silberhorn, and Igor Jex. Gaussian boson sampling. Phys. Rev. Lett., 119: 170501, Oct 2017. 10.1103/​PhysRevLett.119.170501. URL https:/​/​link.aps.org/​doi/​10.1103/​PhysRevLett.119.170501.
https:/​/​doi.org/​10.1103/​PhysRevLett.119.170501

[11] Regina Kruse, Craig S Hamilton, Linda Sansoni, Sonja Barkhofen, Christine Silberhorn, and Igor Jex. Detailed study of gaussian boson sampling. Phys. Rev. A, 100 (3): 032326, 2019. 10.1103/​PhysRevA.100.032326. URL https:/​/​link.aps.org/​doi/​10.1103/​PhysRevA.100.032326.
https:/​/​doi.org/​10.1103/​PhysRevA.100.032326

[12] Abhinav Deshpande, Arthur Mehta, Trevor Vincent, Nicolás Quesada, Marcel Hinsche, Marios Ioannou, Lars Madsen, Jonathan Lavoie, Haoyu Qi, Jens Eisert, et al. Quantum computational advantage via high-dimensional gaussian boson sampling. Science advances, 8 (1): eabi7894, 2022. https:/​/​doi.org/​10.1126/​sciadv.abi7894.
https:/​/​doi.org/​10.1126/​sciadv.abi7894

[13] Daniel Grier, Daniel J. Brod, Juan Miguel Arrazola, Marcos Benicio de Andrade Alonso, and Nicolás Quesada. The Complexity of Bipartite Gaussian Boson Sampling. Quantum, 6: 863, November 2022. ISSN 2521-327X. 10.22331/​q-2022-11-28-863. URL https:/​/​doi.org/​10.22331/​q-2022-11-28-863.
https:/​/​doi.org/​10.22331/​q-2022-11-28-863

[14] Nicolás Quesada, Juan Miguel Arrazola, and Nathan Killoran. Gaussian boson sampling using threshold detectors. Phys. Rev. A, 98: 062322, 12 2018. 10.1103/​PhysRevA.98.062322. URL https:/​/​link.aps.org/​doi/​10.1103/​PhysRevA.98.062322.
https:/​/​doi.org/​10.1103/​PhysRevA.98.062322

[15] Jacob FF Bulmer, Bryn A Bell, Rachel S Chadwick, Alex E Jones, Diana Moise, Alessandro Rigazzi, Jan Thorbecke, Utz-Uwe Haus, Thomas Van Vaerenbergh, Raj B Patel, et al. The boundary for quantum advantage in gaussian boson sampling. Science advances, 8 (4): eabl9236, 2022a. https:/​/​doi.org/​10.1126/​sciadv.abl9236.
https:/​/​doi.org/​10.1126/​sciadv.abl9236

[16] Nicolás Quesada, Rachel S. Chadwick, Bryn A. Bell, Juan Miguel Arrazola, Trevor Vincent, Haoyu Qi, and Raúl García-Patrón. Quadratic speed-up for simulating gaussian boson sampling. PRX Quantum, 3: 010306, Jan 2022. 10.1103/​PRXQuantum.3.010306. URL https:/​/​link.aps.org/​doi/​10.1103/​PRXQuantum.3.010306.
https:/​/​doi.org/​10.1103/​PRXQuantum.3.010306

[17] Nicolás Quesada and Juan Miguel Arrazola. Exact simulation of gaussian boson sampling in polynomial space and exponential time. Phys. Rev. Res., 2: 023005, Apr 2020. 10.1103/​PhysRevResearch.2.023005. URL https:/​/​link.aps.org/​doi/​10.1103/​PhysRevResearch.2.023005.
https:/​/​doi.org/​10.1103/​PhysRevResearch.2.023005

[18] Brajesh Gupt, Juan Miguel Arrazola, Nicolás Quesada, and Thomas R Bromley. Classical benchmarking of gaussian boson sampling on the titan supercomputer. Quantum Information Processing, 19 (8): 1–14, 2020. https:/​/​doi.org/​10.1007/​s11128-020-02713-6.
https:/​/​doi.org/​10.1007/​s11128-020-02713-6

[19] J. Eli Bourassa, Nicolás Quesada, Ilan Tzitrin, Antal Száva, Theodor Isacsson, Josh Izaac, Krishna Kumar Sabapathy, Guillaume Dauphinais, and Ish Dhand. Fast simulation of bosonic qubits via gaussian functions in phase space. PRX Quantum, 2: 040315, Oct 2021. 10.1103/​PRXQuantum.2.040315. URL https:/​/​link.aps.org/​doi/​10.1103/​PRXQuantum.2.040315.
https:/​/​doi.org/​10.1103/​PRXQuantum.2.040315

[20] Ulysse Chabaud and Mattia Walschaers. Resources for bosonic quantum computational advantage. Phys. Rev. Lett., 130: 090602, Mar 2023. 10.1103/​PhysRevLett.130.090602. URL https:/​/​link.aps.org/​doi/​10.1103/​PhysRevLett.130.090602.
https:/​/​doi.org/​10.1103/​PhysRevLett.130.090602

[21] Benjamin Villalonga, Murphy Yuezhen Niu, Li Li, Hartmut Neven, John C Platt, Vadim N Smelyanskiy, and Sergio Boixo. Efficient approximation of experimental gaussian boson sampling. arXiv preprint arXiv:2109.11525, 2021. https:/​/​doi.org/​10.48550/​arXiv.2109.11525.
https:/​/​doi.org/​10.48550/​arXiv.2109.11525
arXiv:2109.11525

[22] Haoyu Qi, Daniel J. Brod, Nicolás Quesada, and Raúl García-Patrón. Regimes of classical simulability for noisy gaussian boson sampling. Phys. Rev. Lett., 124: 100502, 3 2020. 10.1103/​PhysRevLett.124.100502. URL https:/​/​link.aps.org/​doi/​10.1103/​PhysRevLett.124.100502.
https:/​/​doi.org/​10.1103/​PhysRevLett.124.100502

[23] Soran Jahangiri, Juan Miguel Arrazola, Nicolás Quesada, and Nathan Killoran. Point processes with gaussian boson sampling. Phys. Rev. E, 101: 022134, Feb 2020. 10.1103/​PhysRevE.101.022134. URL https:/​/​link.aps.org/​doi/​10.1103/​PhysRevE.101.022134.
https:/​/​doi.org/​10.1103/​PhysRevE.101.022134

[24] M. D. Reid and D. F. Walls. Violations of classical inequalities in quantum optics. Phys. Rev. A, 34: 1260–1276, Aug 1986. 10.1103/​PhysRevA.34.1260. URL https:/​/​link.aps.org/​doi/​10.1103/​PhysRevA.34.1260.
https:/​/​doi.org/​10.1103/​PhysRevA.34.1260

[25] Peter D Drummond and Mark Hillery. The quantum theory of nonlinear optics. Cambridge University Press, 2014.

[26] Saleh Rahimi-Keshari, Timothy C. Ralph, and Carlton M. Caves. Sufficient conditions for efficient classical simulation of quantum optics. Phys. Rev. X, 6: 021039, Jun 2016. 10.1103/​PhysRevX.6.021039. URL https:/​/​link.aps.org/​doi/​10.1103/​PhysRevX.6.021039.
https:/​/​doi.org/​10.1103/​PhysRevX.6.021039

[27] Saleh Rahimi-Keshari, Austin P. Lund, and Timothy C. Ralph. What can quantum optics say about computational complexity theory? Phys. Rev. Lett., 114: 060501, 2 2015. 10.1103/​PhysRevLett.114.060501. URL https:/​/​link.aps.org/​doi/​10.1103/​PhysRevLett.114.060501.
https:/​/​doi.org/​10.1103/​PhysRevLett.114.060501

[28] Brajesh Gupt, Josh Izaac, and Nicolás Quesada. The walrus: a library for the calculation of hafnians, hermite polynomials and gaussian boson sampling. Journal of Open Source Software, 4 (44): 1705, 2019. 10.21105/​joss.01705. URL https:/​/​doi.org/​10.21105/​joss.01705.
https:/​/​doi.org/​10.21105/​joss.01705

[29] Peter D. Drummond, Bogdan Opanchuk, A. Dellios, and M. D. Reid. Simulating complex networks in phase space: Gaussian boson sampling. Phys. Rev. A, 105: 012427, 1 2022. 10.1103/​PhysRevA.105.012427. URL https:/​/​link.aps.org/​doi/​10.1103/​PhysRevA.105.012427.
https:/​/​doi.org/​10.1103/​PhysRevA.105.012427

[30] Martin Houde and Nicolás Quesada. Waveguided sources of consistent, single-temporal-mode squeezed light: The good, the bad, and the ugly. AVS Quantum Science, 5 (1), 02 2023. ISSN 2639-0213. https:/​/​doi.org/​10.1116/​5.0133009. 011404.
https:/​/​doi.org/​10.1116/​5.0133009

[31] Alessio Serafini. Quantum continuous variables: a primer of theoretical methods. CRC press, 2017.

[32] Stephen Barnett and Paul M Radmore. Methods in theoretical quantum optics, volume 15. Oxford University Press, 2002.

[33] Han-Sen Zhong, Hui Wang, Yu-Hao Deng, Ming-Cheng Chen, Li-Chao Peng, Yi-Han Luo, Jian Qin, Dian Wu, Xing Ding, Yi Hu, Peng Hu, Xiao-Yan Yang, Wei-Jun Zhang, Hao Li, Yuxuan Li, Xiao Jiang, Lin Gan, Guangwen Yang, Lixing You, Zhen Wang, Li Li, Nai-Le Liu, Chao-Yang Lu, and Jian-Wei Pan. Experimental raw data of "quantum computational advantage using photons". https:/​/​quantum.ustc.edu.cn/​web/​en/​node/​915, 12 2020b.
https:/​/​quantum.ustc.edu.cn/​web/​en/​node/​915

[34] Han-Sen Zhong, Yu-Hao Deng, Jian Qin, Hui Wang, Ming-Cheng Chen, Li-Chao Peng, Yi-Han Luo, Dian Wu, Si-Qiu Gong, Hao Su, Yi Hu, Peng Hu, Xiao-Yan Yang, Wei-Jun Zhang, Hao Li, Yuxuan Li, Xiao Jiang, Lin Gan, Guangwen Yang, Lixing You, Zhen Wang, Li Li, Nai-Le Liu, Jelmer J. Renema, Chao-Yang Lu, and Jian-Wei Pan. Raw data of jiuzhang 2.0 for sharing. https:/​/​quantum.ustc.edu.cn/​web/​en/​node/​951, 4 2021b.
https:/​/​quantum.ustc.edu.cn/​web/​en/​node/​951

[35] G.S. Thekkadath, S. Sempere-Llagostera, B.A. Bell, R.B. Patel, M.S. Kim, and I.A. Walmsley. Experimental demonstration of gaussian boson sampling with displacement. PRX Quantum, 3: 020336, May 2022. 10.1103/​PRXQuantum.3.020336. URL https:/​/​link.aps.org/​doi/​10.1103/​PRXQuantum.3.020336.
https:/​/​doi.org/​10.1103/​PRXQuantum.3.020336

[36] J. F. F. Bulmer, S. Paesani, R. S. Chadwick, and N. Quesada. Threshold detection statistics of bosonic states. Phys. Rev. A, 106: 043712, Oct 2022b. 10.1103/​PhysRevA.106.043712. URL https:/​/​link.aps.org/​doi/​10.1103/​PhysRevA.106.043712.
https:/​/​doi.org/​10.1103/​PhysRevA.106.043712

[37] D. S. Phillips, M. Walschaers, J. J. Renema, I. A. Walmsley, N. Treps, and J. Sperling. Benchmarking of gaussian boson sampling using two-point correlators. Phys. Rev. A, 99: 023836, Feb 2019. 10.1103/​PhysRevA.99.023836. URL https:/​/​link.aps.org/​doi/​10.1103/​PhysRevA.99.023836.
https:/​/​doi.org/​10.1103/​PhysRevA.99.023836

[38] R. A. Fisher and J. Wishart. The Derivation of the Pattern Formulae of Two-Way Partitions from those of Simpler Patterns. Proceedings of the London Mathematical Society, s2-33 (1): 195–208, 1932. https:/​/​doi.org/​10.1112/​plms/​s2-33.1.195.
https:/​/​doi.org/​10.1112/​plms/​s2-33.1.195

[39] Yanic Cardin and Nicolás Quesada. Photon-number moments and cumulants of gaussian states. arXiv preprint arXiv:2212.06067, 2022. https:/​/​doi.org/​10.48550/​arXiv.2212.06067.
https:/​/​doi.org/​10.48550/​arXiv.2212.06067
arXiv:2212.06067

[40] H. D. Ursell. The evaluation of gibbs' phase-integral for imperfect gases. Mathematical Proceedings of the Cambridge Philosophical Society, 23 (6): 685–697, 1927. 10.1017/​S0305004100011191.
https:/​/​doi.org/​10.1017/​S0305004100011191

[41] M Duneau, Daniel Iagolnitzer, and B Souillard. Decrease properties of truncated correlation functions and analyticity properties for classical lattices and continuous systems. Communications in Mathematical Physics, 31 (3): 191–208, 1973. https:/​/​doi.org/​10.1007/​BF01646265.
https:/​/​doi.org/​10.1007/​BF01646265

[42] R Core Team. R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria, 2013. URL http:/​/​www.R-project.org/​. ISBN 3-900051-07-0.
http:/​/​www.R-project.org/​

[43] Pauli Virtanen, Ralf Gommers, Travis E. Oliphant, Matt Haberland, Tyler Reddy, David Cournapeau, Evgeni Burovski, Pearu Peterson, Warren Weckesser, Jonathan Bright, Stéfan J. van der Walt, Matthew Brett, Joshua Wilson, K. Jarrod Millman, Nikolay Mayorov, Andrew R. J. Nelson, Eric Jones, Robert Kern, Eric Larson, C J Carey, İlhan Polat, Yu Feng, Eric W. Moore, Jake VanderPlas, Denis Laxalde, Josef Perktold, Robert Cimrman, Ian Henriksen, E. A. Quintero, Charles R. Harris, Anne M. Archibald, Antônio H. Ribeiro, Fabian Pedregosa, Paul van Mulbregt, and SciPy 1.0 Contributors. SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods, 17: 261–272, 2020. 10.1038/​s41592-019-0686-2.
https:/​/​doi.org/​10.1038/​s41592-019-0686-2

[44] Ágoston Kaposi, Zoltán Kolarovszki, Tamás Kozsik, Zoltán Zimborás, and Péter Rakyta. Polynomial speedup in torontonian calculation by a scalable recursive algorithm. arXiv preprint arXiv:2109.04528, 2021. https:/​/​doi.org/​10.48550/​arXiv.2109.04528.
https:/​/​doi.org/​10.48550/​arXiv.2109.04528
arXiv:2109.04528

[45] Marco Bentivegna, Nicolò Spagnolo, Chiara Vitelli, Daniel J. Brod, Andrea Crespi, Fulvio Flamini, Roberta Ramponi, Paolo Mataloni, Roberto Osellame, Ernesto F. Galvão, and Fabio Sciarrino. Bayesian approach to boson sampling validation. International Journal of Quantum Information, 12 (07n08): 1560028, 2014. https:/​/​doi.org/​10.1142/​S021974991560028X.
https:/​/​doi.org/​10.1142/​S021974991560028X

[46] Javier Martínez-Cifuentes and Nicolás Quesada. torontonian-julia. https:/​/​github.com/​polyquantique/​torontonian-julia, 09 2022.
https:/​/​github.com/​polyquantique/​torontonian-julia

[47] Jeffrey Sarnoff and JuliaMath. DoubleFloats, 6 2022. URL https:/​/​github.com/​JuliaMath/​DoubleFloats.jl.
https:/​/​github.com/​JuliaMath/​DoubleFloats.jl

[48] Jeff Bezanson, Alan Edelman, Stefan Karpinski, and Viral B Shah. Julia: A fresh approach to numerical computing. SIAM review, 59 (1): 65–98, 2017. https:/​/​doi.org/​10.1137/​141000671.
https:/​/​doi.org/​10.1137/​141000671

[49] Yuan Yao, Filippo Miatto, and Nicolás Quesada. The recursive representation of gaussian quantum mechanics. arXiv preprint arXiv:2209.06069, 2022. https:/​/​doi.org/​10.48550/​arXiv.2209.06069.
https:/​/​doi.org/​10.48550/​arXiv.2209.06069
arXiv:2209.06069

[50] N Quesada, LG Helt, J Izaac, JM Arrazola, R Shahrokhshahi, CR Myers, and KK Sabapathy. Simulating realistic non-gaussian state preparation. Physical Review A, 100 (2): 022341, 2019. https:/​/​doi.org/​10.1103/​PhysRevA.100.022341.
https:/​/​doi.org/​10.1103/​PhysRevA.100.022341

Cited by

[1] Tian-Yu Yang and Xiang-Bin Wang, "Speeding up the classical simulation of Gaussian boson sampling with limited connectivity", Scientific Reports 14 1, 7680 (2024).

[2] Naomi R. Solomons, Oliver F. Thomas, and Dara P. S. McCutcheon, "Effect of photonic errors on quantum enhanced dense-subgraph finding", Physical Review Applied 20 5, 054043 (2023).

[3] Yu-Hao Deng, Yi-Chao Gu, Hua-Liang Liu, Si-Qiu Gong, Hao Su, Zhi-Jiong Zhang, Hao-Yang Tang, Meng-Hao Jia, Jia-Min Xu, Ming-Cheng Chen, Jian Qin, Li-Chao Peng, Jiarong Yan, Yi Hu, Jia Huang, Hao Li, Yuxuan Li, Yaojian Chen, Xiao Jiang, Lin Gan, Guangwen Yang, Lixing You, Li Li, Han-Sen Zhong, Hui Wang, Nai-Le Liu, Jelmer J. Renema, Chao-Yang Lu, and Jian-Wei Pan, "Gaussian Boson Sampling with Pseudo-Photon-Number-Resolving Detectors and Quantum Computational Advantage", Physical Review Letters 131 15, 150601 (2023).

[4] Alexander S. Dellios, Margaret D. Reid, and Peter D. Drummond, "Simulating Gaussian boson sampling quantum computers", AAPPS Bulletin 33 1, 31 (2023).

[5] Minzhao Liu, Changhun Oh, Junyu Liu, Liang Jiang, and Yuri Alexeev, "Simulating lossy Gaussian boson sampling with matrix-product operators", Physical Review A 108 5, 052604 (2023).

[6] Dominik Hangleiter and Jens Eisert, "Computational advantage of quantum random sampling", Reviews of Modern Physics 95 3, 035001 (2023).

[7] Changhun Oh, Liang Jiang, and Bill Fefferman, "Spoofing Cross-Entropy Measure in Boson Sampling", Physical Review Letters 131 1, 010401 (2023).

[8] Tian-Yu Yang, Yi-Xin Shen, Zhou-Kai Cao, and Xiang-Bin Wang, "Post-selection in noisy Gaussian boson sampling: part is better than whole", Quantum Science and Technology 8 4, 045020 (2023).

[9] Martin Houde and Nicolás Quesada, "Waveguided sources of consistent, single-temporal-mode squeezed light: The good, the bad, and the ugly", AVS Quantum Science 5 1, 011404 (2023).

[10] Alexander S. Dellios, Bogdan Opanchuk, Margaret D. Reid, and Peter D. Drummond, "Validation tests of GBS quantum computers give evidence for quantum advantage with a decoherent target", arXiv:2211.03480, (2022).

[11] Gabriele Bressanini, Benoit Seron, Leonardo Novo, Nicolas J. Cerf, and M. S. Kim, "Gaussian boson sampling validation via detector binning", arXiv:2310.18113, (2023).

[12] Naomi R. Solomons, Oliver F. Thomas, and Dara P. S. McCutcheon, "Gaussian-boson-sampling-enhanced dense subgraph finding shows limited advantage over efficient classical algorithms", arXiv:2301.13217, (2023).

[13] Denis Stanev, Taira Giordani, Nicolò Spagnolo, and Fabio Sciarrino, "Testing of on-cloud Gaussian Boson Sampler "Borealis'' via graph theory", arXiv:2306.12120, (2023).

The above citations are from Crossref's cited-by service (last updated successfully 2024-04-15 01:37:25) and SAO/NASA ADS (last updated successfully 2024-04-15 01:37:26). The list may be incomplete as not all publishers provide suitable and complete citation data.