Fate of Entanglement for Initial Separable States in Quantum Neural Network

Abstract

This study is related to the fate of entanglement for initial separable states in a quantum neural network (QNN) model, which is in contact with the data environments locally. The duration of entanglement in quantum systems becomes extremely important when we consider it as a valuable resource. Thus, the effects of various initial states on the occurrence or decay of entanglement are investigated in the presence of information reservoirs. Especially in this study, central spin model has been examined as a quantum version of neural networks by taking inspiration from the biological models. Our model consists of a central spin system with two nodes to which the nodes are coupled to independent spin baths. Numerical results clearly show that different initial states have a profound effect on the fate of the entanglement. It also shows that the entanglement lifetime can be adjusted by regulating the reservoir states. The results can be used in realistic communication network situations to improve the performance of entanglement formation or distribution.

Keywords

• Entanglement,Information reservoir,Central spin model,Quantum neural network

References

1. [1] S. Russell, P. Norvig, Artificial Intelligence: A Modern Approach. USA: Pearson, Upper Saddle River, 2009.
2. [2] W.S. McCulloch, W. Pitts, “A logical calculus of the ideas immanent in nervous activity” The bulletin of mathematical biophysics, Vol.5, 4, 1943, pp.115-133.
3. [3] F. Rosenblatt, “The perceptron: A probabilistic model for information storage and organization in the brain” Psychological Review, Vol.65, 6, 1958, pp.386-408.
4. [4] D. O. Hebb, The Organization of Behavior: A Neuropsychological Theory, Psychology Press, Mahwah NJ, 2002.
5. [5] R. Hecht-Nielsen, Neurocomputing, Boston, MA, USA: Addison-Wesley, 1990.
6. [6] J. I. Cirac, P. Zoller, H. J. Kimble, H. Mabuchi, “Quantum state transfer and entanglement distribution among distant nodes in a quantum network” Physical Review Letters, Vol.78, 16, 1997, p. 3221.
7. [7] M. Lewenstein, M. Olko, “Quantum neural networks” Network: Computation in Neural Systems, Vol.2, 1, 1991, pp.207-230.
8. [8] S. Kak, “On quantum neural computing” Information Sciences, Vol.83, 3-4, 1995, pp.143-160.

9. [9] M. Lewenstein, “Quantum Perceptrons” Journal of Modern Optics, Vol.41, 12, 1994, pp.2491-2501.
10. [10] I. E. Lagaris, A. Likas, D. I. Fotiadis, “Artificial neural network methods in quantum mechanics” Computer Physics Communications, Vol.104, 1-3, 1997, pp.1-14.
11. [11] M. Zak, C. P. Williams, “Quantum Neural Nets” International Journal of Theoretical Physics, Vol.37, 2, 1998, pp.651-684.
12. [12] A. Narayanan, T. Menneer, “Quantum artificial neural network architectures and components” Information Sciences, 2000; Vol.128, 3-4, 2000, pp.231-255.
13. [13] D. Ventura, T. Martinez, “Quantum associative memory” Information Sciences, 2000; Vol.124, 1-4, 2000, pp.273-296.
14. [14] S. Gupta, R. K. P. Zia, “Quantum Neural Networks” Journal of Computer and System Sciences, Vol.63, 3, 2001, pp.355-383.
15. [15] M. Panella, G. Martinelli, “Neural networks with quantum architecture and quantum learning” International Journal of Circuit Theory and Applications, Vol.39, 1, 2011, pp.61-77.
16. [16] R. Zhou, H. Wang, Q. Wu, Y. Shi, “Quantum Associative Neural Network with Nonlinear Search Algorithm” International Journal of Theoretical Physics, Vol.51, 3, 2012, pp.705-723.
17. [17] M. Schuld, I. Sinayskiy, F. Petruccione, “Simulating a perceptron on a quantum computer” Physics Letters A, 2015; Vol.379, 7, 2015, pp.660-663.
18. [18] L. Banchi, N. Pancotti, S. Bose, “Quantum gate learning in qubit networks: Toffoli gate without time-dependent control” npj Quantum Information, Vol.2, 2016, p.16019.
19. [19] R. Horodecki, P. Horodecki, M. Horodecki, K. Horodecki, “Quantum entanglement” Reviews of Modern Physics, Vol.81, 2, 2009, p.865.
20. [20] L. Mazzola, S. Maniscalco, J. Piilo, K. A. Suominen, B. M. Garraway, “Sudden death and sudden birth of entanglement in common structured reservoirs” Physical Review A, Vol.79, 4, 2009, p.042302.
21. [21] D. Türkpençe, “Disentanglement Dynamics of a Data Driven Quantum Neural Network” NeuroQuantology, Vol.16, 10, 2018, pp.14-19.
22. [22] C. H. Bennett, G. Brassard, C. Crépeau, R. Jozsa, A. Peres, W. K. Wootters, “Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels” Physical Review Letters, 1993; Vol.70, 13, 1993, pp.1895-1899.
23. [23] V. Scarani, H. Bechmann-Pasquinucci, N. J. Cerf, M. Dušek, N. Lütkenhaus, M. Peev, “The security of practical quantum key distribution” Reviews of Modern Physics, Vol.81, 3, 2009, p.1301.
24. [24] A. Galindo, M. A. Martin-Delgado, “Information and computation: Classical and quantum aspects” Reviews of Modern Physics, Vol.74, 2, 2002, p.347.
25. [25] A. Al-Qasimi, D. F. V. James, “Sudden death of entanglement at finite temperature” Physical Review A, Vol.77, 1, 2008, p.012117.
26. [26] T. Yu, J. H. Eberly, “Sudden Death of Entanglement” Science, Vol.323, 5914, 2009, pp.598-601.
27. [27] J. León, C. Sabín, “Photon exchange and correlation transfer in atom-atom entanglement Dynamics” Physical Review A, Vol.79, 1, 2009, p.012301.
28. [28] M. P. Almeida, F. de Melo, M. Hor-Meyll, A. Salles, S. P. Walborn, et al., “Environment-Induced Sudden Death of Entanglement” Science Vol.316, 5824, 2007, pp.579-582.
29. [29] Z. Ficek, R. Tanaś, “Delayed sudden birth of entanglement” Physical Review A, Vol.77, 5, 2008, p.054301.
30. [30] M. Schuld, I. Sinayskiy, F. Petruccione, “The quest for a quantum neural network” Quantum Information Processing, Vol.13, 11, 2014, pp.2567-86.
31. [31] P. C. Humphreys, N. Kalb, J. P. Morits, R. N. Schouten, R. F. Vermeulen, et al., “Deterministic delivery of remote entanglement on a quantum network” Nature, Vol.558, 7709, 2018, p.268.
32. [32] M. Ziman, P. Štelmachovič, V. Bužek, M. Hillery, V. Scarani, et al., “Diluting quantum information: An analysis of information transfer in system-reservoir interactions” Physical Review A, Vol.65, 4, 2002, p.042105.
33. [33] V. Scarani, M. Ziman, P. Štelmachovič, N. Gisin, V. Bužek, “Thermalizing Quantum Machines: Dissipation and Entanglement” Physical Review Letters, Vol.88, 9, 2002, p.097905.
34. [34] M. M. Wolf, J. I. Cirac, “Dividing quantum channels” Communications in Mathematical Physics, Vol.279, 1, 2008, pp.147-68.
35. [35] W. H. Zurek, “Decoherence, einselection, and the quantum origins of the classical” Reviews of Modern Physics, Vol.75, 3, 2003, p.715.
36. [36] Q. Chen, J. Cheng, K. L. Wang, J. Du, Optimal quantum cloning via spin networks” Physical Review A, Vol.74, 3, 2006, p.034303.
37. [37] D. Türkpençe, T. C. Akıncı, S. Şeker, “Decoherence in a quantumneural network” NeuroQuantology, Vol.16, 6, 2018, pp.1-5.
38. [38] D. Türkpençe, F. Altintas, M. Paternostro, O. E. Müstecaplıoğlu, “A photonic Carnot engine powered by a spin-star network” EPL (Europhysics Letters), Vol.117, 5, 2017, p.50002.
39. [39] E. J. O’Reilly, A. Olaya-Castro, “Non-classicality of the molecular vibrations assisting exciton energy transfer at room temperature” Nature Communications, Vol.5, 3012, 2014.
40. [40] D. Türkpençe, T. C. Akıncı, S. Şeker, “A steady state quantum classifier” Physics Letters A, 2019; In Press. doi: 10.1016/j.physleta.2019.01.063
41. [41] R. Hildebranda, “Concurrence revisited” Journal of Mathematical Physics, Vol.48, 10, 2007, p.102108.
42. [42] S. Hill, W. K. Wootters, “Entanglement of a Pair of Quantum Bits” Physical Review Letters, Vol.78, 26, 1997, p.5022.
43. [43] T. Yu, J. H. Eberly, “Finite-time disentanglement via spontaneous emission” Physical Review Letters, Vol.93, 14, 2004, p.140404.