Survey on Hybrid Classical-Quantum Machine Learning Models

Optimizing for a classification problem with a 0–1 loss function is an NP-hard problem [1] even for a simple binary classification task. As Preskill stated “We don't expect a quantum computer to solve worst case instances of NP-hard problems, but it might find better approximate solution or find it faster” [2]. Hybrid Quantum Classical Platforms harness the full capacity of Near-Term Quantum Computers. In this study, a focus is given on the variational circuits based approach accomplishing various machine learning tasks. We will survey a variety of experimental demonstrations conducted on actual quantum hardware and actively developing simulation software, anticipated to have a broad range of real-world applications in this increasingly growing field.

[1]  Thierry Paul,et al.  Quantum computation and quantum information , 2007, Mathematical Structures in Computer Science.

[2]  H. Neven,et al.  Characterizing quantum supremacy in near-term devices , 2016, Nature Physics.

[3]  I. Ekeland.  On the variational principle , 1974 .

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

[5]  Alan Aspuru-Guzik,et al.  Variational Quantum Generators: Generative Adversarial Quantum Machine Learning for Continuous Distributions , 2019, Advanced Quantum Technologies.

[6]  Masoud Mohseni,et al.  TensorFlow Quantum: A Software Framework for Quantum Machine Learning , 2020, ArXiv.

[7]  R. Feynman.  Simulating physics with computers , 1999 .

[8]  Subhash C. Kak,et al.  On Quantum Neural Computing , 1995, Inf. Sci..

[9]  Catherine D. Schuman,et al.  A Classical-Quantum Hybrid Approach for Unsupervised Probabilistic Machine Learning , 2019, Lecture Notes in Networks and Systems.

[10]  John Preskill,et al.  Quantum Computing in the NISQ era and beyond , 2018, Quantum.

[11]  Alán Aspuru-Guzik,et al.  Quantum Chemistry in the Age of Quantum Computing. , 2018, Chemical reviews.

[12]  Giacomo Nannicini,et al.  Improving Variational Quantum Optimization using CVaR , 2019, Quantum.

[13]  Margaret Martonosi,et al.  Next Steps in Quantum Computing: Computer Science's Role , 2019, ArXiv.

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

[15]  H. Neven,et al.  Quantum simulation of chemistry with sublinear scaling in basis size , 2018, npj Quantum Information.

[16]  D. Deutsch.  Quantum theory, the Church–Turing principle and the universal quantum computer , 1985, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

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

[18]  R. Schumann.  Quantum Information Theory , 2000, quant-ph/0010060.

[19]  Nathan Killoran,et al.  PennyLane: Automatic differentiation of hybrid quantum-classical computations , 2018, ArXiv.

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

[21]  M. Hastings,et al.  Progress towards practical quantum variational algorithms , 2015, 1507.08969.

[22]  Dacheng Tao,et al.  The Expressive Power of Parameterized Quantum Circuits , 2018, ArXiv.

[23]  Prasad Raghavendra,et al.  Agnostic Learning of Monomials by Halfspaces Is Hard , 2009, 2009 50th Annual IEEE Symposium on Foundations of Computer Science.

[24]  Lov K. Grover.  A fast quantum mechanical algorithm for database search , 1996, STOC '96.

[25]  Peter Wittek,et al.  Quantum Machine Learning: What Quantum Computing Means to Data Mining , 2014 .

[26]  Peter J. Love,et al.  A variational eigenvalue solver on a quantum processor , 2018 .

[27]  Peter W. Shor,et al.  Algorithms for quantum computation: discrete logarithms and factoring , 1994, Proceedings 35th Annual Symposium on Foundations of Computer Science.