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Variational learning the SDC quantum protocol with gradient-based optimization

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Abstract

Recently, a variational learning approach is adopted to discover quantum communication protocols (Wan et al. in npj Quantum Inf 3:36, 2017). Because designing quantum protocols manually is a delicate and difficult work, this variational learning approach is well worth further study. In this paper, we use the same approach to learn the simultaneous dense coding (SDC) protocols with two or three receivers. The gradient-based optimization is used to learn the parameters of the locking operator of the SDC protocol. Two different designs of the loss function are considered. Numerical experiment results show the effectiveness of this variational learning approach.

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References

  1. Biamonte, J., Wittek, P., Pancotti, N., Rebentrost, P., Wiebe, N., Lloyd, S.: Quantum machine learning. Nature 549, 195 (2017)

    Article  ADS  Google Scholar 

  2. Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information. Cambridge University Press, Cambridge (2000)

    MATH  Google Scholar 

  3. Bishop, C.M.: Pattern Recognition and Machine Learning. Springer, Berlin (2006)

    MATH  Google Scholar 

  4. Wan, K.H., Dahlsten, O., Kristjánsson, H., Gardner, R., Kim, M.S.: Quantum generalisation of feedforward neural networks. npj Quantum Inf. 3, 36 (2017)

    Article  ADS  Google Scholar 

  5. Cincio, L., Subasi, Y., Sornborger, A.T., Coles, R.J.: Learning the quantum algorithm for state overlap. New J. Phys. 20, 113022 (2018)

    Article  ADS  Google Scholar 

  6. Morales, M.E.S., Tlyachev, T., Biamonte, J.: Variational learning of Grovers quantum search algorithm. Phys. Rev. A 98, 062333 (2018)

    Article  ADS  Google Scholar 

  7. Situ, H.Z., Qiu, D.W.: Simultaneous dense coding. J. Phys. A Math. Theor. 43, 055301 (2010)

    Article  ADS  MathSciNet  Google Scholar 

  8. Situ, H.Z.: Controlled simultaneous teleportation and dense coding. Int. J. Theor. Phys. 53, 1003 (2014)

    Article  Google Scholar 

  9. Situ, H.Z., Qiu, D.W., Mateus, P., Paunkovic, N.: Secure N-dimensional simultaneous dense coding and applications. Int. J. Quantum Inf. 13, 1550051 (2015)

    Article  MathSciNet  Google Scholar 

  10. Zhang, C., Situ, H.Z., Li, Q., He, G.P.: Efficient simultaneous dense coding and teleportation with two-photon four-qubit cluster states. Int. J. Quantum Inf. 14, 1650023 (2016)

    Article  MathSciNet  Google Scholar 

  11. Yang, X., Bai, M.Q., Zuo, Z.C., Mo, Z.W.: Secure simultaneous dense coding using \(\chi \)-type entangled state. Quantum Inf. Process. 17, 261 (2018)

    Article  ADS  MathSciNet  Google Scholar 

  12. Huang, Z.M., Zhang, C., Situ, H.Z.: Performance analysis of simultaneous dense coding protocol under decoherence. Quantum Inf. Process. 16, 227 (2017)

    Article  ADS  MathSciNet  Google Scholar 

  13. Huang, Z.M., Ye, Y.Y., Luo, D.R.: Simultaneous dense coding affected by fluctuating massless scalar field. Quantum Inf. Process. 17, 101 (2018)

    Article  ADS  MathSciNet  Google Scholar 

  14. Kingma, D.P., Ba, J.: Adam: a method for stochastic optimization. arXiv: 1412.6980

  15. Duchi, J., Hazan, E., Singer, Y.: Adaptive subgradient methods for online learning and stochastic optimization. J. Mach. Learn. Res. 12, 2121 (2011)

    MathSciNet  MATH  Google Scholar 

  16. Tieleman, T., Hinton, G.: Lecture 6.5—RMSProp, COURSERA: neural networks for machine learning. Technical report (2012)

Download references

Acknowledgements

We are very grateful to the reviewers and the editors for their invaluable comments and detailed suggestions that helped to improve the quality of the present paper. This work is supported by the National Natural Science Foundation of China (Nos. 61772565, 61602532, 61871205), the Innovation Project of Department of Education of Guangdong Province of China (No. 2017KTSCX180), the Jiangmen Science and Technology Plan Project for Basic and Theoretical Research (No. 2018JC01010) and the Science and Technology Project of Jiangmen City of China (No. 2018JC01019).

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Authors and Affiliations

  1. College of Mathematics and Informatics, South China Agricultural University, Guangzhou, 510642, China

    Haozhen Situ

  2. Center for Quantum Computing, Peng Cheng Laboratory, Shenzhen, 518055, China

    Haozhen Situ, Xiangfu Zou & Shenggen Zheng

  3. School of Economics and Management, Wuyi University, Jiangmen, 529020, China

    Zhiming Huang

  4. Institute for Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen, 518055, China

    Shenggen Zheng

  5. School of Mathematics and Computational Science, Wuyi University, Jiangmen, 529020, China

    Xiangfu Zou

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  1. Haozhen Situ
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  2. Zhiming Huang
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  3. Xiangfu Zou
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  4. Shenggen Zheng
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Correspondence to Zhiming Huang.

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Appendix

Appendix

This “Appendix” gives the solutions for SDC2R and SDC3R found by our methods. Because our method is inherently stochastic, different runs of the experiment give different optimal solutions. Here, we list one optimal solution for SDC2R and one optimal solution for SDC3R, respectively.

$$\begin{aligned} U_2&= \left( \begin{array}{c@{\quad }c@{\quad }c@{\quad }c} -0.0393+0.7878\mathrm {i} &{} -0.1875+0.4444\mathrm {i} &{} -0.1661+0.3331\mathrm {i} &{} -0.0470+0.0664\mathrm {i} \\ -0.3271+0.1792\mathrm {i} &{} -0.0690+0.0344\mathrm {i} &{} 0.8352-0.0342\mathrm {i} &{} 0.2516-0.3049\mathrm {i} \\ -0.4302+0.2283\mathrm {i} &{} 0.8346-0.1481\mathrm {i} &{} -0.0469+0.0035\mathrm {i} &{} -0.0995+0.1794\mathrm {i} \\ -0.0371-0.0115\mathrm {i} &{} -0.1982+0.0601\mathrm {i} &{} 0.3466-0.2011\mathrm {i} &{} -0.2396+0.8589\mathrm {i} \\ \end{array} \right) , \end{aligned}$$
(12)
$$\begin{aligned} U_3&= \left( \begin{array}{c@{\quad }c@{\quad }c@{\quad }c@{\quad }c@{\quad }c@{\quad }c@{\quad }c} 0.1225 &{} 0.0103 &{} -\,0.3390 &{} -\,0.1423 &{} -\,0.1179 &{} 0.1186 &{} -\,0.1449 &{} -\,0.1298 \\ -\,0.4212 &{} 0.0371 &{} -\,0.0202 &{} -\,0.5556 &{} -\,0.1380 &{} -\,0.2497 &{} 0.2013 &{} 0.0684 \\ -\,0.5623 &{} -\,0.4511 &{} 0.3432 &{} -\,0.0888 &{} -\,0.2240 &{} 0.1570 &{} -\,0.1438 &{} -\,0.2143 \\ 0.1207 &{} -\,0.0993 &{} 0.3640 &{} 0.3322 &{} -\,0.2098 &{} -\,0.3190 &{} -\,0.4001 &{} 0.0796 \\ 0.4173 &{} -\,0.1945 &{} 0.2179 &{} -\,0.3981 &{} 0.1161 &{} -\,0.2262 &{} -\,0.1019 &{} -\,0.3981 \\ 0.0677 &{} -\,0.1777 &{} -\,0.0841 &{} -\,0.1454 &{} -\,0.0134 &{} 0.2191 &{} 0.2885 &{} 0.4974 \\ 0.2113 &{} 0.0094 &{} 0.2078 &{} -\,0.4535 &{} -\,0.1338 &{} 0.1132 &{} -\,0.1770 &{} 0.4125 \\ -\,0.0302 &{} 0.3255 &{} 0.0905 &{} -\,0.0081 &{} -\,0.4659 &{} -\,0.1066 &{} -\,0.2799 &{} 0.3438 \\ \end{array} \right) \nonumber \\&+\mathrm {i}\left( \begin{array}{c@{\quad }c@{\quad }c@{\quad }c@{\quad }c@{\quad }c@{\quad }c@{\quad }c} 0.0729 &{} -\,0.1310 &{} 0.0849 &{} 0.0888 &{} -\,0.1087 &{} -\,0.7016 &{} 0.4813 &{} 0.1032 \\ 0.0961 &{} 0.1796 &{} -\,0.3401 &{} -\,0.0640 &{} -\,0.4289 &{} -\,0.0927 &{} -\,0.0548 &{} -\,0.1693 \\ 0.0320 &{} -\,0.0355 &{} 0.0879 &{} 0.1977 &{} 0.2519 &{} 0.0032 &{} 0.1044 &{} 0.2996 \\ 0.1804 &{} -\,0.3197 &{} -\,0.2770 &{} 0.0217 &{} -\,0.3671 &{} 0.0686 &{} 0.2294 &{} -\,0.1283 \\ 0.2255 &{} -\,0.1263 &{} -\,0.1262 &{} -\,0.2689 &{} 0.2459 &{} -\,0.1643 &{} -\,0.3169 &{} 0.0752 \\ 0.0613 &{} -\,0.6424 &{} -\,0.1938 &{} 0.0704 &{} 0.0080 &{} -\,0.0004 &{} -\,0.1700 &{} 0.2626 \\ 0.2238 &{} 0.1253 &{} 0.4775 &{} -\,0.1429 &{} 0.0168 &{} 0.2567 &{} 0.2942 &{} -\,0.0852 \\ -\,0.3158 &{} 0.1119 &{} -\,0.1989 &{} -\,0.1350 &{} 0.4117 &{} -\,0.2747 &{} -\,0.2011 &{} 0.0677 \\ \end{array} \right) . \end{aligned}$$
(13)

The known unlocking operators for SDC2R in the previous literature include quantum Fourier transform [7], double controlled-NOT [9] and SWAP [9] operators. The quantum circuits for these three unlocking operators are already known. In contrast, the optimal solutions found by our method need to be compiled into quantum circuits or implemented by special quantum devices. However, our method is quite useful for constructing unlocking operators for SDC protocols with more than two receivers.

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Situ, H., Huang, Z., Zou, X. et al. Variational learning the SDC quantum protocol with gradient-based optimization. Quantum Inf Process 18, 230 (2019). https://doi.org/10.1007/s11128-019-2348-9

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