A Conditional Generative Model Based on Quantum Circuit and Classical Optimization

Generative model is an important branch of unsupervised learning techniques in machine learning. Current research shows that quantum circuits can be used to implement simple generative models. In this paper, we train a quantum conditional generator, which can generate different probability distributions according to different input labels, i.e., different initial quantum states. The model is evaluated with different datasets including chessboard images, and bars and stripes (BAS) images of 2 × 2 and 3 × 3 pixels. We also improve the performance of the model by introducing a controlled-NOT (CNOT) layer. The simulation results show that the CNOT layer can improve the performance, especially for the generative model with chain-connected entangling layers.

[1]  Alejandro Perdomo-Ortiz,et al.  Quantum-assisted Helmholtz machines: A quantum–classical deep learning framework for industrial datasets in near-term devices , 2017, ArXiv.

[2]  Max Welling,et al.  Auto-Encoding Variational Bayes , 2013, ICLR.

[3]  José David Martín-Guerrero,et al.  Quantum autoencoders via quantum adders with genetic algorithms , 2017, Quantum Science and Technology.

[4]  Geoffrey E. Hinton,et al.  A Learning Algorithm for Boltzmann Machines , 1985, Cogn. Sci..

[5]  M. Benedetti,et al.  Estimation of effective temperatures in quantum annealers for sampling applications: A case study with possible applications in deep learning , 2015, 1510.07611.

[6]  Songfeng Lu,et al.  Quantum decision tree classifier , 2014, Quantum Inf. Process..

[7]  Lingli Wang,et al.  A quantum-implementable neural network model , 2017, Quantum Inf. Process..

[8]  Ying Liu,et al.  Quantum algorithm for support matrix machines , 2017 .

[9]  Masoud Mohseni,et al.  Quantum support vector machine for big feature and big data classification , 2013, Physical review letters.

[10]  Ting Yu,et al.  Generalized coherent states, reproducing kernels, and quantum support vector machines , 2016, Quantum Inf. Comput..

[11]  Alán Aspuru-Guzik,et al.  Quantum autoencoders for efficient compression of quantum data , 2016, 1612.02806.

[12]  Ashish Kapoor,et al.  Quantum deep learning , 2014, Quantum Inf. Comput..

[13]  Soumith Chintala,et al.  Unsupervised Representation Learning with Deep Convolutional Generative Adversarial Networks , 2015, ICLR.

[14]  Seth Lloyd,et al.  Quantum Generative Adversarial Learning. , 2018, Physical review letters.

[15]  Alejandro Perdomo-Ortiz,et al.  A generative modeling approach for benchmarking and training shallow quantum circuits , 2018, npj Quantum Information.

[16]  Blake R. Johnson,et al.  Unsupervised Machine Learning on a Hybrid Quantum Computer , 2017, 1712.05771.

[17]  Steven H. Adachi,et al.  Application of Quantum Annealing to Training of Deep Neural Networks , 2015, ArXiv.

[18]  Ajit Narayanan,et al.  Quantum artificial neural network architectures and components , 2000, Inf. Sci..

[19]  Lucas Lamata,et al.  Basic protocols in quantum reinforcement learning with superconducting circuits , 2017, Scientific Reports.

[20]  Yoshua Bengio,et al.  Generative Adversarial Nets , 2014, NIPS.

[21]  Roger Melko,et al.  Quantum Boltzmann Machine , 2016, 1601.02036.

[22]  S. Eddy Hidden Markov models. , 1996, Current opinion in structural biology.

[23]  Peter Wittek,et al.  Quantum Enhanced Inference in Markov Logic Networks , 2016, Scientific Reports.

[24]  E. Farhi,et al.  A Quantum Approximate Optimization Algorithm , 2014, 1411.4028.

[25]  Zhengyu Zhang,et al.  An efficient quantum algorithm for generative machine learning , 2017, ArXiv.

[26]  Chao-Hua Yu,et al.  Quantum algorithm for association rules mining , 2015, 1512.02420.

[27]  Jacob biamonte,et al.  Quantum machine learning , 2016, Nature.

[28]  Tzyh Jong Tarn,et al.  Quantum Reinforcement Learning , 2005, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[29]  Rupak Biswas,et al.  From the Quantum Approximate Optimization Algorithm to a Quantum Alternating Operator Ansatz , 2017, Algorithms.

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

[31]  Zhiming Huang,et al.  Quantum-enhanced feature selection with forward selection and backward elimination , 2018, Quantum Inf. Process..