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Quantum Information Processing

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01-10-2023

Quantum machine learning based on continuous variable single-photon states: an elementary foundation for quantum neural networks

Authors: Ebrahim Ghasemian, Abolhassan Razminia, Habib Rostami

Published in: Quantum Information Processing | Issue 10/2023

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Abstract

Photonic quantum computing is a leading approach toward universal quantum computation. Here, we propose a realistic model for the implementation of neural networks on photonic quantum computers. Specially, we design a quantum circuit built in the continuous-variable (CV) architecture that encodes information in the spectral amplitude functions of single-photons. This circuit consisting of some electro-optical modulators and XOR boxes that, respectively, adjust and combine their entries to provide a weighted sum of input signals. We show that our model can reproduce classical neural network models while maintaining some quantum phenomena such as superposition and entanglement. In particular, we utilize the circuit as a quantum classifier and validate the CV quantum neural network architecture through doing some machine learning modeling experiments. Such a quantum circuit can be implemented on the CV photonic quantum computers that promise exponential speed-up over the classical computers for specific tasks.

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Killoran, N., Bromley, T.R., Arrazola, J.M., Schuld, M., Quesada, N., Lloyd, S.: Continuous-variable quantum neural networks. Phys. Rev. Res. 1, 033063 (2019)CrossRef

Phillipson, F.: tQANSWER, pp. 51–56 (2020)

Perdomo-Ortiz, A., Benedetti, M., Realpe-Gómez, J., Biswas, R.: Opportunities and challenges for quantum-assisted machine learning in near-term quantum computers. Quantum Sci. Technol. 3, 030502 (2018)ADSCrossRef

Benedetti, M., Realpe-Gómez, J., Perdomo-Ortiz, A.: Quantum-assisted Helmholtz machines: a quantum-classical deep learning framework for industrial datasets in near-term devices. Quantum Sci. Technol. 3, 034007 (2018)ADSCrossRef

Gottesman, D., Kitaev, A., Preskill, J.: Encoding a qubit in an oscillator. Phys. Rev. A 64, 012310 (2001)ADSCrossRef

Giovannetti, V., Lloyd, S., Maccone, L.: Quantum random access memory. Phys. Rev. Lett. 100, 160501 (2008)ADSMathSciNetCrossRefMATH

Barenco, A., Bennett, C.H., Cleve, R., DiVincenzo, D.P., Margolus, N., Shor, P., Sleator, T., Smolin, J.A., Weinfurter, H.: Elementary gates for quantum computation. Phys. Rev. A 52, 3457 (1995)ADSCrossRef

Plesch, M., Brukner, Č: Quantum-state preparation with universal gate decompositions. Phys. Rev. A 83, 032302 (2011)ADSCrossRef

Kumar, P.: Direct implementation of an N-qubit controlled-unitary gate in a single step. Quantum Inf. Process. 12, 1201 (2013)ADSMathSciNetCrossRefMATH

10.

Knill, E., Laflamme, R., Milburn, G.J.: A scheme for efficient quantum computation with linear optics. Nature 409, 46 (2001)ADSCrossRef

11.

Kok, P., Lovett, B.W.: Introduction to Optical Quantum Information Processing. Cambridge University Press, Cambridge (2010)CrossRefMATH

12.

Rohde, P.P., Fitzsimons, J.F., Gilchrist, A.: Information capacity of a single photon. Phys. Rev. A 88, 022310 (2013)ADSCrossRef

13.

Menicucci, N.C., Van Loock, P., Gu, M., Weedbrook, C., Ralph, T.C., Nielsen, M.A.: Universal quantum computation with continuous-variable cluster states. Phys. Rev. Lett. 97, 110501 (2006)ADSCrossRef

14.

Wang, X.-B., Hiroshima, T., Tomita, A., Hayashi, M.: Quantum information with Gaussian states. Phys. Rep. 448, 1 (2007)ADSMathSciNetCrossRef

15.

Jozsa, R., Linden, N.: On the role of entanglement in quantum-computational speed-up. Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 459, 2011 (2003)ADSMathSciNetCrossRefMATH

16.

Lloyd, S., Mohseni, M., Rebentrost, P. (2013). arXiv preprint arXiv:1307.0411

17.

Cai, X.-D., Wu, D., Su, Z.-E., Chen, M.-C., Wang, X.-L., Li, L., Liu, N.-L., Lu, C.-Y., Pan, J.-W.: Entanglement-based machine learning on a quantum computer. Phys. Rev. Lett. 114, 110504 (2015)ADSCrossRef

18.

Cao, Y., Guerreschi, G.G., Aspuru-Guzik, A. (2017). arXiv preprint arXiv:1711.11240

19.

Schuld, M., Bocharov, A., Svore, K.M., Wiebe, N.: Circuit-centric quantum classifiers. Phys. Rev. A 101, 032308 (2020)ADSMathSciNetCrossRef

20.

Benedetti, M., Grant, E., Wossnig, L., Severini, S.: Adversarial quantum circuit learning for pure state approximation. New J. Phys. 21, 043023 (2019)ADSMathSciNetCrossRef

21.

Preskill, J.: Quantum computing in the NISQ era and beyond. Quantum 2, 79 (2018)CrossRef

22.

Hur, T., Kim, L., Park, D.K.: Quantum convolutional neural network for classical data classification. Quantum Mach. Intell. 4, 1 (2022)CrossRef

23.

Belsley, D.A., Kuh, E., Welsch, R.E.: Regression Diagnostics: Identifying Influential Data and Sources of Collinearity, vol. 571. Wiley, Hoboken (2005)MATH

24.

Schuld, M., Killoran, N.: Quantum machine learning in feature Hilbert spaces. Phys. Rev. Lett. 122, 040504 (2019)ADSCrossRef

25.

Havlíček, V., Córcoles, A.D., Temme, K., Harrow, A.W., Kandala, A., Chow, J.M., Gambetta, J.M.: Supervised learning with quantum-enhanced feature spaces. Nature 567, 209 (2019)ADSCrossRef

26.

Liu, H.-L., Yu, C.-H., Wu, Y.-S., Pan, S.-J., Qin, S.-J., Gao, F., Wen, Q.-Y. (2019). arXiv preprint arXiv:1906.03834

27.

Harrison, D., Jr., Rubinfeld, D.L.: Hedonic housing prices and the demand for clean air. J. Environ. Econ. Manag. 5, 81 (1978)CrossRefMATH

28.

Shadbolt, P.J., Verde, M.R., Peruzzo, A., Politi, A., Laing, A., Lobino, M., Matthews, J.C., Thompson, M.G., O’Brien, J.L.: Generating, manipulating and measuring entanglement and mixture with a reconfigurable photonic circuit. Nat. Photon. 6, 45 (2012)ADSCrossRef

29.

McGuinness, H.J., Raymer, M.G., McKinstrie, C.J., Radic, S.: Quantum frequency translation of single-photon states in a photonic crystal fiber. Phys. Rev. Lett. 105, 093604 (2010)ADSCrossRef

30.

Sinclair, N., Saglamyurek, E., Mallahzadeh, H., Slater, J.A., George, M., Ricken, R., Hedges, M.P., Oblak, D., Simon, C., Sohler, W., et al.: Spectral multiplexing for scalable quantum photonics using an atomic frequency comb quantum memory and feed-forward control. Phys. Rev. Lett. 113, 053603 (2014)ADSCrossRef

31.

Wright, L.J., Karpiński, M., Söller, C., Smith, B.J.: Spectral shearing of quantum light pulses by electro-optic phase modulation. Phys. Rev. Lett. 118, 023601 (2017)ADSCrossRef

32.

Fan, L., Zou, C.-L., Poot, M., Cheng, R., Guo, X., Han, X., Tang, H.X. (2016). arXiv preprint arXiv:1607.01823

33.

Braunstein, S.L.: Quantum Information with Continuous Variables, pp. 19–29. Springer, Berlin (1998)CrossRef

34.

Yoshikawa, J.-I., Miwa, Y., Huck, A., Andersen, U.L., Van Loock, P., Furusawa, A.: Demonstration of a quantum nondemolition sum gate. Phys. Rev. Lett. 101, 250501 (2008)ADSMathSciNetCrossRefMATH

35.

McCulloch, W.S., Pitts, W.: A logical calculus of the ideas immanent in nervous activity. Bull. Math. Biophys. 5, 115 (1943)MathSciNetCrossRefMATH

36.

Rabinovich, M.I., Varona, P., Selverston, A.I., Abarbanel, H.D.: Dynamical principles in neuroscience. Rev. Mod. Phys. 78, 1213 (2006)ADSCrossRef

37.

MacKay, D.J., Mac Kay, D.J. (2003)

38.

Glatzel, T., Sadewasser, S., Lux-Steiner, M.C.: Amplitude or frequency modulation-detection in Kelvin probe force microscopy. Appl. Surf. Sci. 210, 84 (2003)ADSCrossRef

39.

Horowitz, P., Hill, W., Robinson, I.: The Art of Electronics, vol. 2. Cambridge University Press, Cambridge (1989)

40.

Ghahderijani, M.M., Castilla, M., Momeneh, A., Miret, J.T., de Vicuna, L.G.: Frequency-modulation control of a DC/DC current-source parallel-resonant converter. IEEE Trans. Ind. Electron. 64, 5392 (2017)CrossRef

41.

Zippilli, S., Di Giuseppe, G., Vitali, D.: Entanglement and squeezing of continuous-wave stationary light. New J. Phys. 17, 043025 (2015)ADSCrossRefMATH

42.

Rohde, P.P., Mauerer, W., Silberhorn, C.: Spectral structure and decompositions of optical states, and their applications. New J. Phys. 9, 91 (2007)ADSCrossRef

43.

Branning, D., Grice, W., Erdmann, R., Walmsley, I.: Interferometric technique for engineering indistinguishability and entanglement of photon pairs. Phys. Rev. A 62, 013814 (2000)ADSCrossRef

44.

Grice, W.P., U’Ren, A.B., Walmsley, I.A.: Eliminating frequency and space–time correlations in multiphoton states. Phys. Rev. A 64, 063815 (2001)ADSCrossRef

45.

Wang, J., Sciarrino, F., Laing, A., Thompson, M.G.: Integrated photonic quantum technologies. Nat. Photon. 14, 273 (2020)ADSCrossRef

46.

Pati, A.K., Braunstein, S.L.: Quantum Information with Continuous Variables, pp. 31–36. Springer, Berlin (2003)CrossRefMATH

Title: Quantum machine learning based on continuous variable single-photon states: an elementary foundation for quantum neural networks
Authors: Ebrahim Ghasemian
Abolhassan Razminia
Habib Rostami
Publication date: 01-10-2023
Publisher: Springer US
Published in: Quantum Information Processing / Issue 10/2023
Print ISSN: 1570-0755
Electronic ISSN: 1573-1332
DOI: https://doi.org/10.1007/s11128-023-04137-4

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