[1] J. Biamonte, P. Wittek, N. Pancotti, P. Rebentrost, N. Wiebe, S. Lloyd. Quantum machine learning. Nature, 549, 195-202(2017).
[2] V. Dunjko, H. J. Briegel. Machine learning & artificial intelligence in the quantum domain: a review of recent progress. Rep. Prog. Phys., 81, 074001(2018).
[3] V. Havlíčeka, A. D. Córcoles, K. Temme, A. W. Harrow, A. Kandala, J. M. Chow, J. M. Gambetta. Supervised learning with quantum-enhanced feature spaces. Nature, 567, 209-212(2019).
[4] I. Cong, S. Choi, M. D. Lukin. Quantum convolutional neural networks. Nat. Phys., 15, 1273-1278(2019).
[5] M. Schuld, N. Killoran. Quantum machine learning in feature Hilbert spaces. Phys. Rev. Lett., 122, 040504(2019).
[6] F. Verstraete, V. Murg, J. I. Cirac. Matrix product states, projected entangled pair states, and variational renormalization group methods for quantum spin systems. Adv. Phys., 57, 143-224(2008).
[7] J. I. Cirac, F. Verstraete. Renormalization and tensor product states in spin chains and lattices. J. Phys. A, 42, 504004(2009).
[8] J. Haegeman, F. Verstraete. Diagonalizing transfer matrices and matrix product operators: a medley of exact and computational methods. Annu. Rev. Condens. Matter Phys., 8, 355-406(2017).
[9] S.-J. Ran, E. Tirrito, C. Peng, X. Chen, L. Tagliacozzo, G. Su, M. Lewenstein. Tensor Network Contractions(2020).
[10] Z.-Z. Sun, C. Peng, D. Liu, S.-J. Ran, G. Su. Generative tensor network classification model for supervised machine learning. Phys. Rev. B, 101, 075135(2020).
[11] P. Rebentrost, M. Mohseni, S. Lloyd. Quantum support vector machine for big data classification. Phys. Rev. Lett., 113, 130503(2014).
[12] Z. Li, X. Liu, N. Xu, J. Du. Experimental realization of a quantum support vector machine. Phys. Rev. Lett., 114, 140504(2015).
[13] D. Anguita, S. Ridella, F. Rivieccio, R. Zunino. Quantum optimization for training support vector machines. Neural Netw., 16, 763-770(2003).
[14] Y.-Z. You, Z. Yang, X.-L. Qi. Machine learning spatial geometry from entanglement features. Phys. Rev. B, 97, 045153(2018).
[15] Y. Levine, O. Sharir, N. Cohen, A. Shashua. Quantum entanglement in deep learning architectures. Phys. Rev. Lett., 122, 065301(2019).
[16] D.-L. Deng, X. Li, S. Das Sarma. Quantum entanglement in neural network states. Phys. Rev. X, 7, 021021(2017).
[17] D. D. Lee, E. Stoudenmire, M. Sugiyama, D. J. Schwab, U. V. Luxburg, I. Guyon, R. Garnett. Supervised learning with tensor networks. Advances in Neural Information Processing Systems, 29, 4799-4807(2016).
[18] D. Liu, S.-J. Ran, P. Wittek, C. Peng, R. B. Garca, G. Su, M. Lewenstein. Machine learning by unitary tensor network of hierarchical tree structure. New J. Phys., 21, 073059(2019).
[19] Z.-Y. Han, J. Wang, H. Fan, L. Wang, P. Zhang. Unsupervised generative modeling using matrix product states. Phys. Rev. X, 8, 031012(2018).
[20] C. Guo, Z. Jie, W. Lu, D. Poletti. Matrix product operators for sequence-to-sequence learning. Phys. Rev. E, 98, 042114(2018).
[21] E. M. Stoudenmire. Learning relevant features of data with multi-scale tensor networks. Quantum Sci. Technol., 3, 034003(2018).
[22] S. Cheng, L. Wang, T. Xiang, P. Zhang. Tree tensor networks for generative modeling. Phys. Rev. B, 99, 155131(2019).
[23] I. Glasser, R. Sweke, N. Pancotti, J. Eisert, I. J. Cirac. Expressive power of tensor-network factorizations for probabilistic modeling. Advances in Neural Information Processing Systems, 32, 1496-1508(2019).
[24] S. Efthymiou, J. Hidary, S. Leichenauer. TensorNetwork for machine learning(2019).
[25] Y. Liu, X. Zhang, M. Lewenstein, S.-J. Ran. Entanglement-guided architectures of machine learning by quantum tensor network(2018).
[26] W. Huggins, P. Patil, B. Mitchell, K. B. Whaley, E. M. Stoudenmire. Towards quantum machine learning with tensor networks. Quantum Sci. Technol., 4, 024001(2019).
[27] L. Deng. The MNIST database of handwritten digit images for machine learning research [best of the web]. IEEE Signal Process. Mag., 29, 141-142(2012).
[28] X.-D. Cai, D. Wu, Z.-E. Su, M.-C. Chen, X.-L. Wang, L. Li, N.-L. Liu, C.-Y. Lu, J.-W. Pan. Entanglement-based machine learning on a quantum computer. Phys. Rev. Lett., 114, 110504(2015).
[29] D.-B. Zhang, S.-L. Zhu, Z. D. Wang. Protocol for implementing quantum nonparametric learning with trapped ions. Phys. Rev. Lett., 124, 010506(2020).
[30] F. Arute, K. Arya, R. Babbush, D. Bacon, J. C. Bardin, R. Barends, R. Biswas, S. Boixo, F. G. S. L. Brandao, D. A. Buell, B. Burkett, Y. Chen, Z. Chen, B. Chiaro, R. Collins, W. Courtney, A. Dunsworth, E. Farhi, B. Foxen, A. Fowler, C. Gidney, M. Giustina, R. Graff, K. Guerin, S. Habegger, M. P. Harrigan, M. J. Hartmann, A. Ho, M. Hoffmann, T. Huang, T. S. Humble, S. V. Isakov, E. Jeffrey, Z. Jiang, D. Kafri, K. Kechedzhi, J. Kelly, P. V. Klimov, S. Knysh, A. Korotkov, F. Kostritsa, D. Landhuis, M. Lindmark, E. Lucero, D. Lyakh, S. Mandrà, J. R. McClean, M. McEwen, A. Megrant, X. Mi, K. Michielsen, M. Mohseni, J. Mutus, O. Naaman, M. Neeley, C. Neill, M. Y. Niu, E. Ostby, A. Petukhov, J. C. Platt, C. Quintana, E. G. Rieffel, P. Roushan, N. C. Rubin, D. Sank, K. J. Satzinger, V. Smelyanskiy, K. J. Sung, M. D. Trevithick, A. Vainsencher, B. Villalonga, T. White, Z. J. Yao, P. Yeh, A. Zalcman, H. Neven, J. M. Martinis. Quantum supremacy using a programmable superconducting processor. Nature, 574, 505-510(2019).
[31] A. Pepper, N. Tischler, G. J. Pryde. Experimental realization of a quantum autoencoder: the compression of qutrits via machine learning. Phys. Rev. Lett., 122, 060501(2019).
[32] H.-K. Lau, R. Pooser, G. Siopsis, C. Weedbrook. Quantum machine learning over infinite dimensions. Phys. Rev. Lett., 118, 080501(2017).
[33] X. Gao, Z.-Y. Zhang, L.-M. Duan. A quantum machine learning algorithm based on generative models. Sci. Adv., 4, eaat9004(2018).
[34] D. Zhu, N. M. Linke, M. Benedetti, K. A. Landsman, N. H. Nguyen, C. H. Alderete, A. Perdomo-Ortiz, N. Korda, A. Garfoot, C. Brecque, L. Egan, O. Perdomo, C. Monroe. Training of quantum circuits on a hybrid quantum computer. Sci. Adv., 5, eaaw9918(2019).
[35] K. Bartkiewicz, C. Gneiting, A. Černoch, K. Jiráková, K. Lemr, F. Nori. Experimental kernel-based quantum machine learning in finite feature space. Sci. Rep., 10, 12356(2020).
[36] J. Gao, L.-F. Qiao, Z.-Q. Jiao, Y.-C. Ma, C.-Q. Hu, R.-J. Ren, A.-L. Yang, H. Tang, M.-H. Yung, X.-M. Jin. Experimental machine learning of quantum states. Phys. Rev. Lett., 120, 240501(2018).
[37] L. Hu, S.-H. Wu, W. Cai, Y. Ma, X. Mu, Y. Xu, H. Wang, Y. Song, D.-L. Deng, C.-L. Zou, L. Sun. Quantum generative adversarial learning in a superconducting quantum circuit. Sci. Adv., 5, eaav2761(2019).
[38] A. Hentschel, B. C. Sanders. Machine learning for precise quantum measurement. Phys. Rev. Lett., 104, 063603(2010).
[39] W. Lian, S.-T. Wang, S. Lu, Y. Huang, F. Wang, X. Yuan, W. Zhang, X. Ouyang, X. Wang, X. Huang, L. He, X. Chang, D.-L. Deng, L. Duan. Machine learning topological phases with a solid-state quantum simulator. Phys. Rev. Lett., 122, 210503(2019).
[40] P. Xue, Y.-F. Xiao. Universal quantum computation in decoherence-free subspace with neutral atoms. Phys. Rev. Lett., 97, 140501(2006).
[41] P. Xue, B. C. Sanders, D. Leibfried. Quantum walk on a line for a trapped ion. Phys. Rev. Lett., 103, 183602(2009).
[42] C. Schön, E. Solano, F. Verstraete, J. I. Cirac, M. M. Wolf. Sequential generation of entangled multiqubit states. Phys. Rev. Lett., 95, 110503(2005).
[43] K. Wang, X. Wang, X. Zhan, Z. Bian, J. Li, B. C. Sanders, P. Xue. Entanglement-enhanced quantum metrology in a noisy environment. Phys. Rev. A, 97, 042112(2018).
[44] D. Pérez-García, F. Verstraete, M. M. Wolf, J. I. Cirac. Matrix product state representations. Quantum Inf. Comput., 7, 401-430(2007).
[45] C. M. Bishop. Pattern Recognition and Machine Learning(2006).
[47] L. Xiao, X. Zhan, Z.-H. Bian, K. Wang, X. Zhang, X.-P. Wang, J. Li, K. Mochizuki, D. Kim, N. Kawakami, W. Yi, H. Obuse, B. C. Sanders, P. Xue. Observation of topological edge states in parity–time-symmetric quantum walks. Nat. Phys., 13, 1117-1123(2017).
[48] J. A. Izaac, X. Zhan, Z. Bian, K. Wang, J. Li, J. Wang, P. Xue. Centrality measure based on continuous-time quantum walks and experimental realization. Phys. Rev. A, 95, 032318(2017).
