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[Crossref]

F. Nogrette, H. Labuhn, S. Ravets, D. Barredo, L. Beguin, A. Vernier, T. Lahaye, and A. Browaeys, “Single-atom trapping in holographic 2D arrays of microtraps with arbitrary geometries,” Phys. Rev. X 4, 021034 (2014).

[Crossref]

P. Raccuglia, K. C. Elbert, P. D. Adler, C. Falk, M. B. Wenny, A. Mollo, M. Zeller, S. A. Friedler, J. Schrier, and A. J. Norquist, “Machine-learning-assisted materials discovery using failed experiments,” Nature 533, 73–76 (2016).

[Crossref]

X. Lin, Y. Rivenson, N. T. Yardimci, M. Veli, Y. Luo, M. Jarrahi, and A. Ozcan, “All-optical machine learning using diffractive deep neural networks,” Science 361, 1004–1008 (2018).

[Crossref]

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[Crossref]

M. Miscuglio, A. Mehrabian, Z. Hu, S. I. Azzam, J. George, A. V. Kildishev, M. Pelton, and V. J. Sorger, “All-optical nonlinear activation function for photonic neural networks,” Opt. Mater. Express 8, 3851–3863 (2018).

[Crossref]

J. Feldmann, N. Youngblood, C. D. Wright, H. Bhaskaran, and W. H. P. Pernice, “All-optical spiking neurosynaptic networks with self-learning capabilities,” Nature 569, 208–214 (2019).

[Crossref]

L. Larger, M. C. Soriano, D. Brunner, L. Appeltant, J. M. Gutiérrez, L. Pesquera, C. R. Mirasso, and I. Fischer, “Photonic information processing beyond Turing: an optoelectronic implementation of reservoir computing,” Opt. Express 20, 3241–3249 (2012).

[Crossref]

Y. Shen, N. C. Harris, S. Skirlo, M. Prabhu, T. Baehr-Jones, M. Hochberg, X. Sun, S. Zhao, H. Larochelle, D. Englund, and M. Soljačić, “Deep learning with coherent nanophotonic circuits,” Nat. Photonics 11, 441–446 (2017).

[Crossref]

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[Crossref]

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[Crossref]

J. George, R. Amin, A. Mehrabian, J. Khurgin, T. El-Ghazawi, P. R. Prucnal, and V. J. Sorger, “Electrooptic nonlinear activation functions for vector matrix multiplications in optical neural networks,” in Signal Processing in Photonic Communications (Optical Society of America, 2018), paper SpW4G-3.

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[Crossref]

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[Crossref]

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[Crossref]

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[Crossref]

P. Raccuglia, K. C. Elbert, P. D. Adler, C. Falk, M. B. Wenny, A. Mollo, M. Zeller, S. A. Friedler, J. Schrier, and A. J. Norquist, “Machine-learning-assisted materials discovery using failed experiments,” Nature 533, 73–76 (2016).

[Crossref]

F. Nogrette, H. Labuhn, S. Ravets, D. Barredo, L. Beguin, A. Vernier, T. Lahaye, and A. Browaeys, “Single-atom trapping in holographic 2D arrays of microtraps with arbitrary geometries,” Phys. Rev. X 4, 021034 (2014).

[Crossref]

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[Crossref]

X. Lin, Y. Rivenson, N. T. Yardimci, M. Veli, Y. Luo, M. Jarrahi, and A. Ozcan, “All-optical machine learning using diffractive deep neural networks,” Science 361, 1004–1008 (2018).

[Crossref]

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[Crossref]

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[Crossref]

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[Crossref]

S. Du, M. B. Squires, Y. Imai, L. Czaia, R. A. Saravanan, V. Bright, J. Reichel, T. W. Hansch, and D. Z. Anderson, “Atom-chip Bose-Einstein condensation in a portable vacuum cell,” Phys. Rev. A 70, 053606 (2004).

[Crossref]

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[Crossref]

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[Crossref]

B. Wu, J. F. Hulbert, E. J. Lunt, K. Hurd, A. R. Hawkins, and H. Schmidt, “Slow light on a chip via atomic quantum state control,” Nat. Photonics 4, 776–779 (2010).

[Crossref]

Y. Paquot, F. Duport, A. Smerieri, J. Dambre, B. Schrauwen, M. Haelterman, and S. Massar, “Optoelectronic reservoir computing,” Sci. Rep. 2, 287 (2012).

[Crossref]

P. Raccuglia, K. C. Elbert, P. D. Adler, C. Falk, M. B. Wenny, A. Mollo, M. Zeller, S. A. Friedler, J. Schrier, and A. J. Norquist, “Machine-learning-assisted materials discovery using failed experiments,” Nature 533, 73–76 (2016).

[Crossref]

D. M. Farkas, K. M. Hudek, E. A. Salim, S. R. Segal, M. B. Squires, and D. Z. Anderson, “A compact, transportable, microchip-based system for high repetition rate production of Bose-Einstein condensates,” Appl. Phys. Lett. 96, 093102 (2010).

[Crossref]

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[Crossref]

Y. Shen, N. C. Harris, S. Skirlo, M. Prabhu, T. Baehr-Jones, M. Hochberg, X. Sun, S. Zhao, H. Larochelle, D. Englund, and M. Soljačić, “Deep learning with coherent nanophotonic circuits,” Nat. Photonics 11, 441–446 (2017).

[Crossref]

Y. Shen, N. C. Harris, S. Skirlo, M. Prabhu, T. Baehr-Jones, M. Hochberg, X. Sun, S. Zhao, H. Larochelle, D. Englund, and M. Soljačić, “Deep learning with coherent nanophotonic circuits,” Nat. Photonics 11, 441–446 (2017).

[Crossref]

Y. Paquot, F. Duport, A. Smerieri, J. Dambre, B. Schrauwen, M. Haelterman, and S. Massar, “Optoelectronic reservoir computing,” Sci. Rep. 2, 287 (2012).

[Crossref]

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[Crossref]

Y. Shen, N. C. Harris, S. Skirlo, M. Prabhu, T. Baehr-Jones, M. Hochberg, X. Sun, S. Zhao, H. Larochelle, D. Englund, and M. Soljačić, “Deep learning with coherent nanophotonic circuits,” Nat. Photonics 11, 441–446 (2017).

[Crossref]

M. Miscuglio, A. Mehrabian, Z. Hu, S. I. Azzam, J. George, A. V. Kildishev, M. Pelton, and V. J. Sorger, “All-optical nonlinear activation function for photonic neural networks,” Opt. Mater. Express 8, 3851–3863 (2018).

[Crossref]

J. George, R. Amin, A. Mehrabian, J. Khurgin, T. El-Ghazawi, P. R. Prucnal, and V. J. Sorger, “Electrooptic nonlinear activation functions for vector matrix multiplications in optical neural networks,” in Signal Processing in Photonic Communications (Optical Society of America, 2018), paper SpW4G-3.

L. Larger, M. C. Soriano, D. Brunner, L. Appeltant, J. M. Gutiérrez, L. Pesquera, C. R. Mirasso, and I. Fischer, “Photonic information processing beyond Turing: an optoelectronic implementation of reservoir computing,” Opt. Express 20, 3241–3249 (2012).

[Crossref]

D. M. Farkas, K. M. Hudek, E. A. Salim, S. R. Segal, M. B. Squires, and D. Z. Anderson, “A compact, transportable, microchip-based system for high repetition rate production of Bose-Einstein condensates,” Appl. Phys. Lett. 96, 093102 (2010).

[Crossref]

S. Du, M. B. Squires, Y. Imai, L. Czaia, R. A. Saravanan, V. Bright, J. Reichel, T. W. Hansch, and D. Z. Anderson, “Atom-chip Bose-Einstein condensation in a portable vacuum cell,” Phys. Rev. A 70, 053606 (2004).

[Crossref]

Y. Wang, J. Li, S. Zhang, K. Su, Y. Zhou, K. Liao, S. Du, H. Yan, and S.-L. Zhu, “Efficient quantum memory for single-photon polarization qubits,” Nat. Photonics 13, 346–351 (2019).

[Crossref]

Y. Shen, N. C. Harris, S. Skirlo, M. Prabhu, T. Baehr-Jones, M. Hochberg, X. Sun, S. Zhao, H. Larochelle, D. Englund, and M. Soljačić, “Deep learning with coherent nanophotonic circuits,” Nat. Photonics 11, 441–446 (2017).

[Crossref]

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[Crossref]

H. J. Metcalf and P. van der Straten, Laser Cooling and Trapping (Springer-Verlag, 1999).

X. Lin, Y. Rivenson, N. T. Yardimci, M. Veli, Y. Luo, M. Jarrahi, and A. Ozcan, “All-optical machine learning using diffractive deep neural networks,” Science 361, 1004–1008 (2018).

[Crossref]

F. Nogrette, H. Labuhn, S. Ravets, D. Barredo, L. Beguin, A. Vernier, T. Lahaye, and A. Browaeys, “Single-atom trapping in holographic 2D arrays of microtraps with arbitrary geometries,” Phys. Rev. X 4, 021034 (2014).

[Crossref]

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[Crossref]

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[Crossref]

Y. Wang, J. Li, S. Zhang, K. Su, Y. Zhou, K. Liao, S. Du, H. Yan, and S.-L. Zhu, “Efficient quantum memory for single-photon polarization qubits,” Nat. Photonics 13, 346–351 (2019).

[Crossref]

P. Raccuglia, K. C. Elbert, P. D. Adler, C. Falk, M. B. Wenny, A. Mollo, M. Zeller, S. A. Friedler, J. Schrier, and A. J. Norquist, “Machine-learning-assisted materials discovery using failed experiments,” Nature 533, 73–76 (2016).

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[Crossref]

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[Crossref]

J. Feldmann, N. Youngblood, C. D. Wright, H. Bhaskaran, and W. H. P. Pernice, “All-optical spiking neurosynaptic networks with self-learning capabilities,” Nature 569, 208–214 (2019).

[Crossref]

B. Wu, J. F. Hulbert, E. J. Lunt, K. Hurd, A. R. Hawkins, and H. Schmidt, “Slow light on a chip via atomic quantum state control,” Nat. Photonics 4, 776–779 (2010).

[Crossref]

Y. Wang, J. Li, S. Zhang, K. Su, Y. Zhou, K. Liao, S. Du, H. Yan, and S.-L. Zhu, “Efficient quantum memory for single-photon polarization qubits,” Nat. Photonics 13, 346–351 (2019).

[Crossref]

X. Lin, Y. Rivenson, N. T. Yardimci, M. Veli, Y. Luo, M. Jarrahi, and A. Ozcan, “All-optical machine learning using diffractive deep neural networks,” Science 361, 1004–1008 (2018).

[Crossref]

J. Feldmann, N. Youngblood, C. D. Wright, H. Bhaskaran, and W. H. P. Pernice, “All-optical spiking neurosynaptic networks with self-learning capabilities,” Nature 569, 208–214 (2019).

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[Crossref]

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[Crossref]

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[Crossref]

Y. Shen, N. C. Harris, S. Skirlo, M. Prabhu, T. Baehr-Jones, M. Hochberg, X. Sun, S. Zhao, H. Larochelle, D. Englund, and M. Soljačić, “Deep learning with coherent nanophotonic circuits,” Nat. Photonics 11, 441–446 (2017).

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[Crossref]

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[Crossref]

B. Wu, J. F. Hulbert, E. J. Lunt, K. Hurd, A. R. Hawkins, and H. Schmidt, “Slow light on a chip via atomic quantum state control,” Nat. Photonics 4, 776–779 (2010).

[Crossref]

Y. Shen, N. C. Harris, S. Skirlo, M. Prabhu, T. Baehr-Jones, M. Hochberg, X. Sun, S. Zhao, H. Larochelle, D. Englund, and M. Soljačić, “Deep learning with coherent nanophotonic circuits,” Nat. Photonics 11, 441–446 (2017).

[Crossref]

Y. Wang, J. Li, S. Zhang, K. Su, Y. Zhou, K. Liao, S. Du, H. Yan, and S.-L. Zhu, “Efficient quantum memory for single-photon polarization qubits,” Nat. Photonics 13, 346–351 (2019).

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P. Raccuglia, K. C. Elbert, P. D. Adler, C. Falk, M. B. Wenny, A. Mollo, M. Zeller, S. A. Friedler, J. Schrier, and A. J. Norquist, “Machine-learning-assisted materials discovery using failed experiments,” Nature 533, 73–76 (2016).

[Crossref]

K. T. Butler, D. W. Davies, H. Cartwright, O. Isayev, and A. Walsh, “Machine learning for molecular and materials science,” Nature 559, 547–555 (2018).

[Crossref]

J. Feldmann, N. Youngblood, C. D. Wright, H. Bhaskaran, and W. H. P. Pernice, “All-optical spiking neurosynaptic networks with self-learning capabilities,” Nature 569, 208–214 (2019).

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L. Larger, M. C. Soriano, D. Brunner, L. Appeltant, J. M. Gutiérrez, L. Pesquera, C. R. Mirasso, and I. Fischer, “Photonic information processing beyond Turing: an optoelectronic implementation of reservoir computing,” Opt. Express 20, 3241–3249 (2012).

[Crossref]

F. Duport, B. Schneider, A. Smerieri, M. Haelterman, and S. Massar, “All-optical reservoir computing,” Opt. Express 20, 22783–22795(2012).

[Crossref]

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[Crossref]

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[Crossref]

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[Crossref]

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[Crossref]

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[Crossref]

D.-L. Deng, X. Li, and S. D. Sarma, “Machine learning topological states,” Phys. Rev. B 96, 195145 (2017).

[Crossref]

J. Liu, H. Shen, Y. Qi, Z. Y. Meng, and L. Fu, “Self-learning Monte Carlo method and cumulative update in fermion systems,” Phys. Rev. B 95, 241104 (2017).

[Crossref]

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[Crossref]

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[Crossref]

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[Crossref]

Y. Abu-Mostafa and D. Psaltis, “Optical neural computers,” Sci. Am. 256, 88–95 (1987).

[Crossref]

Y. Paquot, F. Duport, A. Smerieri, J. Dambre, B. Schrauwen, M. Haelterman, and S. Massar, “Optoelectronic reservoir computing,” Sci. Rep. 2, 287 (2012).

[Crossref]

X. Lin, Y. Rivenson, N. T. Yardimci, M. Veli, Y. Luo, M. Jarrahi, and A. Ozcan, “All-optical machine learning using diffractive deep neural networks,” Science 361, 1004–1008 (2018).

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J. George, R. Amin, A. Mehrabian, J. Khurgin, T. El-Ghazawi, P. R. Prucnal, and V. J. Sorger, “Electrooptic nonlinear activation functions for vector matrix multiplications in optical neural networks,” in Signal Processing in Photonic Communications (Optical Society of America, 2018), paper SpW4G-3.

See the supplemental material and Refs. [33–39] for (S1) the technical information of SLM; (S2) the Gerchberg–Saxton algorithm and feedback iteration process; (S3) the principle of linear optical power summation; (S4) the two matrices used for testing the linear operation; (S5) the operation of 2D MOT; (S6) the two-layer AONN implementation; (S7) the training of two-layer AONN; and (S8) Ising model related data processing.

H. J. Metcalf and P. van der Straten, Laser Cooling and Trapping (Springer-Verlag, 1999).

Y. Zuo, B. Li, Y. Zhao, Y. Jiang, Y.-C. Chen, P. Chen, G.-B. Jo, J. Liu, and S. Du, “All optical neural network with nonlinear activation functions,” arXiv: 1904.10819 (2019).