Abstract
Quantum transport is a significant phenomenon in the mesoscopic system which is widely studied in recent years. In physical experiments, the fluctuation noise can reflect the microscopic properties of the quantum transport system easier than the transport current. In theory, the quantum conditional master equation (QCME) is a very effective method for studying quantum transport process of charge qubits. But, the QCME is an infinite recursive differential equation system that is difficult to solve theoretically. So, we try to solve this problem by combining the requirements of the solution and some advantages of the machine learning algorithms. Firstly, compared the calculation diagram of QCME and recurrent neural network (RNN), the relationship between them was found. Long Short-Term Memory (LSTM) has great advantages in processing time-series data as a typical network of RNN. Secondly, the behavior of parameters transfers from time \(t\) to \(t+\Delta t\) in QCME is consistent with the behavior of parameter transfer in LSTM. Based on the above two reasons, the LSTM is used to simulate QCME. In the numerical experiment, an effective method is proposed to truncate QCME, and then the fluctuation noise spectrum data from a two-level quantum transport system is used to train the LSTM network and calculate the transition probability of electron with the parameters of LSTM.
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References
Chen, D., Shi, D.D., Pan, G.J.: Correlation between the electrical transport performance and the communicability sequence entropy in complex networks. Acta Phys. Sinica 68, 11 (2019)
Szpunar, B., Ranasinghe, J.: First-principles investigation of thermal transport of uranium mononitride. J. Phys. Chem. Solids 146, 109636 (2020)
Moussa, O., Baugh, J., et al.: Demonstration of sufficient control for two rounds of quantum error correction in a solid-state ensemble quantum information processor. Phys. Rev. Lett 107, 160501 (2011)
Blanter, Y.M., Buttiker, M.: Shot noise in mesoscopic conductors. Phys. Reports 336, 1–166 (2000)
Gurvitz, S.A.: Measurements with a noninvasive detector and dephasing mechanism. Phys. Rev. B. 56, 15215 (1997)
Mozyrsky, D., Martin, I.: Efficiency of mesoscopic detectors. Phys. Rev. Lett. 89, 200401 (2002)
Gurvitz, S.A., Fedichkin, L., Mozyrsky, D., Berman, G.P.: Relaxation and the Zeno effect in qubit measurements. Phys. Rev. Lett. 91, 066801 (2003)
Datta, S.: Electronic Transport in Mesoscopic Systems. Cambridge University Press, New York (1995)
Haug, H., Jauho, A.-P.: Quantum Kinetics in Transport and Optics of Semiconductors. Springer, Berlin (1996)
Glazman, L.I., Matveev, K.A.: JETP Lett. 48, 445 (1988). D.V. Averin and A. N. Korotkov, Sov, Phys. JETP 70, 937 s1990d; C. W. J. Beenakker, Phys. Rev. B 44, 1646 (1991)
Davies, J.H., Hershfield, S., Hyldgaard, P., Wilkins, J.W.: Phys. Rev. B 47, 4603 (1993). S. A. Gurvitz, H. J. Lipkin, and Ya. S. Prager, Mod. Phys. Lett. B 8, 1377 (1994)
Nazarov, Y.V.: Quantum interference, tunnel junctions and resonant tunneling interferometer. Physica B 189, 57 (1993)
Gurvitz, S.A., Lipkin, H.J., Ya, S.P.: Interference effects in resonant tunneling and the Pauli principle. Phys. Lett. A 212, 91 (1996)
Gurvitz, S.A., Prager, Y.S.: Microscopic derivation of rate equations for quantum transport. Phys. Rev. B 53, 15932 (1996)
Gurvitz, S.A., Prager, Y.S.: Microscopic derivation of rate equations for quantum transport. Phys. Rev. B 53, 23 (1995)
Xin-Qi, L., Jun, Y.L., Yong-Gang, Y.: Quantum master equation approach to quantum transport through mesoscopic systems. Phys. Rev. B 71, 205304 (2005)
Torlai, G., Mazzola, G., Carrasquilla, J., et al.: Neural-network quantum state tomography. Nat. Phys. 14, 447 (2018)
Zhang, Y., Kim, E.A.: Quantum loop topography for machine learning. Phys. Rev. Lett 188, 21 (2017)
Qu, Z.G., Chen, S.Y., Wang, X.J.: A secure controlled quantum image steganography algorithm. Quantum Inf. Process. 19(380), 1–25 (2020)
Qu, Z.G., Wu, S.Y., Liu, W.J., Wang, X.J.: Analysis and improvement of steganography protocol based on bell states in noise environment. Comput. Mater. Continua 59(2), 607–624 (2019)
Li, X.-Y., Zhu, Q.-S., Zhu, M.-Z., Huang, Y.-M., Hao, W., Shao-Yi, W.: Machine learning study of the relationship between the geometric and entropy discord. EPL 127, 20009 (2019)
Carleo, G., Troyer, M.: Solving the quantum many-body problem with artificial neural networks. Science 355(6325), 602–605 (2017)
Yan, Y.J.: Quantum Fokker-Planck theory in a non-Gaussian-Markovian medium. Phys. Rev. A 58, 2721 (1998)
Clark, L.A., Huang, W., Barlow, T.M., Beige, A.: Hidden quantum Markov models and open quantum systems with instantaneous feedback,arXiv:1406.5847v2 [quant-ph], 5 July 2014
Gers, F.A., Schmidhuber, J., Cummins, F.: Learning to forget: Continual prediction with LSTM. Neural Comput. 12(10), 2451–2471 (2000)
Graves, A., Schmidhuber, J.: Offline handwriting recognition with multidimensional recurrent neural networks. In: Koller, D., Schuurmans, D., Bengio, Y., Bottou, L. (eds.) NIPS 2008, pp. 545–552 (2009)
Graves, A.: Generating sequences with recurrent neural networks, Technical report, arXiv: 1308.0850
Graves, A., Jaitly, N.: Towards end-to-end speech recognition with recurrent neural networks. In: ICML (2014)
Kiros, R., Salakhutdinov, R., Zemel, R.: Unifying visual-semantic embeddings with multimodal neural language models, arXiv: 1411.2539 (2014)
Vinyals, O., Kaiser, L., Koo, T., Petrov, S., Sutskever, I., Hinton, G.: Grammar as a foreign language, arXiv: 1411.4555 (2014)
Xu, K., Ba, J.L., Kiros, R., Cho, K., Courville, A., et al.: Show, attend and tell: Neural image caption generation with visual attention, arXiv: 1502.03044 (2015)
Sutskever, I., Vinyals, O., Le, Q.V.: Sequence to sequence learning with neural networks, arXiv: 1409.3215 (2014)
Luchnikov, I.A., Vintskevich, S.V., Grigoriev, D.A., Filippov, S.N.: Machine learning non-Markovian quantum dynamics. Phys. Rev. Lett 124, 140502 (2020)
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Project supported by the National Key R&D Program of China, Grant No. 2018YFĂ703.
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Hu, Y., Li, XY., Zhu, QS. (2021). Study the Quantum Transport Process: Machine Learning Simulates Quantum Conditional Master Equation. In: Sun, X., Zhang, X., Xia, Z., Bertino, E. (eds) Artificial Intelligence and Security. ICAIS 2021. Lecture Notes in Computer Science(), vol 12736. Springer, Cham. https://doi.org/10.1007/978-3-030-78609-0_12
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