Quantum image classifier with single photons.

Machine learning, with promising applications in quantum computation, has been introduced to a variety of quantum mechanical platforms, where its interplay with quantum physics offers exciting prospects toward quantum advantages. A central difficulty, however, lies in the access and control of the large Hilbert space required by quantum machine learning protocols, through the limited number of noisy qubits available to near-term quantum devices. Whereas it is recognized that a viable solution lies in the design of quantum algorithms that incorporates quantum entanglement and interference, a demonstration of quantum machine learning protocols capable of solving practical tasks is still lacking. Here we report the classification of real-life, hand-drawn images on a quantum mechanical platform of single photons. Adopting a tensor-network-based machine learning algorithm with an entanglement-guided optimization, we achieve an efficient representation of the quantum feature space using matrix product states. This allows us to demonstrate image classification with a high success rate using single-photon interferometry networks. Our experiment establishes a general and scalable framework for quantum machine learning, which is readily accessible on other physical platforms.

[1]  Xiao Zhang,et al.  Entanglement-Based Feature Extraction by Tensor Network Machine Learning , 2018, Frontiers in Applied Mathematics and Statistics.

[2]  Franco Nori,et al.  Experimental kernel-based quantum machine learning in finite feature space , 2019, Scientific Reports.

[3]  Maria Schuld,et al.  Quantum Machine Learning in Feature Hilbert Spaces. , 2018, Physical review letters.

[4]  Li He,et al.  Machine Learning Topological Phases with a Solid-State Quantum Simulator. , 2019, Physical review letters.

[5]  D Zhu,et al.  Training of quantum circuits on a hybrid quantum computer , 2018, Science Advances.

[6]  Hans-J. Briegel,et al.  Machine learning \& artificial intelligence in the quantum domain , 2017, ArXiv.

[7]  F. Verstraete,et al.  Renormalization and tensor product states in spin chains and lattices , 2009, 0910.1130.

[8]  F. Verstraete,et al.  Matrix product states, projected entangled pair states, and variational renormalization group methods for quantum spin systems , 2008, 0907.2796.

[9]  Barry C. Sanders,et al.  Observation of topological edge states in parity–time-symmetric quantum walks , 2017, Nature Physics.

[10]  Kunkun Wang,et al.  Centrality measure based on continuous-time quantum walks and experimental realization , 2017, 1702.03493.

[11]  Soonwon Choi,et al.  Quantum convolutional neural networks , 2018, Nature Physics.

[12]  Zhao Yang,et al.  Machine Learning Spatial Geometry from Entanglement Features , 2017, 1709.01223.

[13]  Amnon Shashua,et al.  Quantum Entanglement in Deep Learning Architectures. , 2018, Physical review letters.

[14]  D. Deng,et al.  Quantum Entanglement in Neural Network States , 2017, 1701.04844.

[15]  E. Miles Stoudenmire,et al.  Learning relevant features of data with multi-scale tensor networks , 2017, ArXiv.

[16]  Chu Guo,et al.  Matrix product operators for sequence-to-sequence learning , 2018, Physical Review E.

[17]  Cheng Peng,et al.  Tensor Network Contractions: Methods and Applications to Quantum Many-Body Systems , 2020 .

[18]  C. Weedbrook,et al.  Quantum Machine Learning over Infinite Dimensions. , 2016, Physical review letters.

[19]  Gang Su,et al.  Machine learning by unitary tensor network of hierarchical tree structure , 2017, New Journal of Physics.

[20]  Geoff J Pryde,et al.  Experimental Realization of a Quantum Autoencoder: The Compression of Qutrits via Machine Learning. , 2018, Physical review letters.

[21]  Jun Wang,et al.  Unsupervised Generative Modeling Using Matrix Product States , 2017, Physical Review X.

[22]  Ievgeniia Oshurko.  Quantum Machine Learning , 2020, Quantum Computing.

[23]  Frank Verstraete,et al.  Matrix product state representations , 2006, Quantum Inf. Comput..

[24]  David J. Schwab,et al.  Supervised Learning with Tensor Networks , 2016, NIPS.

[25]  K. Birgitta Whaley,et al.  Towards quantum machine learning with tensor networks , 2018, Quantum Science and Technology.

[26]  Frank Verstraete,et al.  Diagonalizing transfer matrices and matrix product operators: a medley of exact and computational methods , 2016, 1611.08519.

[27]  Alexander Hentschel,et al.  Machine learning for precise quantum measurement. , 2009, Physical review letters.

[28]  Dan-Bo Zhang,et al.  Protocol for implementing quantum nonparametric learning with trapped ions , 2020 .

[29]  Christopher M. Bishop,et al.  Pattern Recognition and Machine Learning (Information Science and Statistics) , 2006 .

[30]  Davide Anguita,et al.  Quantum optimization for training support vector machines , 2003, Neural Networks.

[31]  Travis S. Humble,et al.  Quantum supremacy using a programmable superconducting processor , 2019, Nature.

[32]  C-Y Lu,et al.  Entanglement-based machine learning on a quantum computer. , 2015, Physical review letters.

[33]  F. Verstraete,et al.  Sequential generation of entangled multiqubit states. , 2005, Physical review letters.

[34]  Jiangfeng Du,et al.  Experimental realization of a quantum support vector machine. , 2015, Physical review letters.

[35]  L-M Duan,et al.  A quantum machine learning algorithm based on generative models , 2018, Science Advances.

[36]  Barry C. Sanders,et al.  Entanglement-enhanced quantum metrology in a noisy environment , 2017, 1707.08790.

[37]  Gang Su,et al.  Generative Tensor Network Classification Model for Supervised Machine Learning , 2019, Physical Review B.

[38]  Shu-Hao Wu,et al.  Quantum generative adversarial learning in a superconducting quantum circuit , 2018, Science Advances.

[39]  Lei Wang,et al.  Tree Tensor Networks for Generative Modeling , 2019, Physical Review B.

[40]  L. Deng,et al.  The MNIST Database of Handwritten Digit Images for Machine Learning Research [Best of the Web] , 2012, IEEE Signal Processing Magazine.

[41]  Jun Gao,et al.  Experimental Machine Learning of Quantum States. , 2017, Physical review letters.

[42]  Jens Eisert,et al.  Expressive power of tensor-network factorizations for probabilistic modeling, with applications from hidden Markov models to quantum machine learning , 2019, NeurIPS.