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Generative Modelling has become a promising use case for near term quantum computers.
Gradients of parameterized quantum gates using the parameter-shift rule and gate decomposition
Gavin E. Crooks · 1905
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Quantum Hamiltonian-Based Models and the Variational Quantum Thermalizer Algorithm
Guillaume Verdon, Jacob Marks, Sasha Nanda, Stefan Leichenauer, and Jack Hidary · 1910
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On the Quantum Correction For Thermodynamic Equilibrium
E. Wigner · 1932
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Quantum mechanics as a statistical theory
J. E. Moyal · 1949
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Probability Inequalities for Sums of Bounded Random Variables
Wassily Hoeffding · 1963
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Principles of Risk Minimization for Learning Theory
V. Vapnik · 1992
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Quantum Computation over Continuous Variables
Seth Lloyd and Samuel L. Braunstein · 1999
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Classical Mechanics, 3rd ed
Herbert Goldstein, Charles Poole, and John Safko · 2002
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Quantum information with continuous variables
Samuel L. Braunstein and Peter van Loock · 2005
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Measuring Analytic Gradients of General Quantum Evolution with the Stochastic Parameter Shift Rule
Leonardo Banchi and Gavin E. Crooks · 2005
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On the learnability of quantum neural networks
Yuxuan Du, Min-Hsiu Hsieh, Tongliang Liu, Shan You, and Dacheng Tao · 2007
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On the Quantum versus Classical Learnability of Discrete Distributions
Ryan Sweke, Jean-Pierre Seifert, Dominik Hangleiter, and Jens Eisert · 2007
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A Kernel Method for the Two-Sample-Problem
Arthur Gretton, Karsten M. Borgwardt, Malte Rasch, Bernhard Schölkopf, and Alex J. Smola · 2007
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The effect of data encoding on the expressive power of variational quantum machine learning models
Maria Schuld, Ryan Sweke, and Johannes Jakob Meyer · 2008
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Kernel methods in machine learning
Thomas Hofmann, Bernhard Schölkopf, and Alexander J. Smola · 2008
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On integral probability metrics, \phi-divergences and binary classification
Bharath K. Sriperumbudur, Kenji Fukumizu, Arthur Gretton, Bernhard Schölkopf, and Gert R. G. Lanckriet · 2009
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Optimal quantum-programmable projective measurements with coherent states
Niraj Kumar, Ulysse Chabaud, Elham Kashefi, Damian Markham, and Eleni Diamanti · 2009
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Quantum Mechanics in Phase Space
Thomas L Curtright and Cosmas K Zachos · 2011
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Quantum Computation and Quantum Information: 10th Anniversary Edition
Michael A. Nielsen and Isaac L. Chuang · 2011
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Gaussian quantum information
Christian Weedbrook, Stefano Pirandola, Raúl García-Patrón, Nicolas J. Cerf, Timothy C. Ralph, Jeffrey H. Shapiro, and Seth Lloyd · 2012
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A Kernel Two-Sample Test
Arthur Gretton, Karsten M. Borgwardt, Malte J. Rasch, Bernhard Schölkopf, and Alexander Smola · 2012
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A variational eigenvalue solver on a photonic quantum processor
Alberto Peruzzo, Jarrod McClean, Peter Shadbolt, Man-Hong Yung, Xiao-Qi Zhou, Peter J. Love, Alán Aspuru-Guzik, and Jeremy L. O’Brien · 2014
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Adam: A Method for Stochastic Optimization
Diederik P. Kingma and Jimmy Ba · 2015
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A Practical Quantum Instruction Set Architecture
Robert S. Smith, Michael J. Curtis, and William J. Zeng · 2016
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A quantum algorithm to train neural networks using low-depth circuits
Guillaume Verdon, Michael Broughton, and Jacob Biamonte · 2017
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Quantum autoencoders for efficient compression of quantum data
Jonathan Romero, Jonathan P. Olson, and Alan Aspuru-Guzik · 2017
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An overview of gradient descent optimization algorithms
Sebastian Ruder · 2017
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Quantum Machine Learning in Feature Hilbert Spaces
Maria Schuld and Nathan Killoran · 2019
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Supervised learning with quantum-enhanced feature spaces
Vojtěch Havlíček, Antonio D. Córcoles, Kristan Temme, Aram W. Harrow, Abhinav Kandala, Jerry M. Chow, and Jay M. Gambetta · 2019
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A generative modeling approach for benchmarking and training shallow quantum circuits
Marcello Benedetti, Delfina Garcia-Pintos, Oscar Perdomo, Vicente Leyton-Ortega, Yunseong Nam, and Alejandro Perdomo-Ortiz · 2019
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Jonathan Romero and Alan Aspuru-Guzik · 2019
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Quantum Generative Adversarial Networks for learning and loading random distributions
Christa Zoufal, Aurélien Lucchi, and Stefan Woerner · 2019
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Aude Genevay, Gabriel Peyré, and Marco Cuturi · 2017
Cited alongside, same era.
Quantum Computing in the NISQ era and beyond
John Preskill · 2018
Cited alongside, same era.
Classification with Quantum Neural Networks on Near Term Processors
Edward Farhi and Hartmut Neven · 2018
Cited alongside, same era.
Circuit-centric quantum classifiers
Maria Schuld, Alex Bocharov, Krysta Svore, and Nathan Wiebe · 2018
Cited alongside, same era.
Differentiable learning of quantum circuit Born machines
Jin-Guo Liu and Lei Wang · 2018
Cited alongside, same era.
Variational learning of Grover’s quantum search algorithm
Mauro E. S. Morales, Timur Tlyachev, and Jacob Biamonte · 2018
Cited alongside, same era.
Learning the quantum algorithm for state overlap
Lukasz Cincio, Yiğit Subaşı, Andrew T. Sornborger, and Patrick J. Coles · 2018
Cited alongside, same era.
Quantum-assisted quantum compiling
Sumeet Khatri, Ryan LaRose, Alexander Poremba, Lukasz Cincio, Andrew T. Sornborger, and Patrick J. Coles · 2019
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Variational quantum state diagonalization
Ryan LaRose, Arkin Tikku, Étude O’Neel-Judy, Lukasz Cincio, and Patrick J. Coles · 2019
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Product spectrum ansatz and the simplicity of thermal states
John Martyn · 2019
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Continuous-variable quantum neural networks
Nathan Killoran, Thomas R. Bromley, Juan Miguel Arrazola, Maria Schuld, Nicolás Quesada, and Seth Lloyd · 2019
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Quantum mean embedding of probability distributions
Jonas M. Kübler, Krikamol Muandet, and Bernhard Schölkopf · 2019
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Evaluating analytic gradients on quantum hardware
Maria Schuld, Ville Bergholm, Christian Gogolin, Josh Izaac, and Nathan Killoran · 2019
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The market generator
Alexei Kondratyev and Christian Schwarz · 2019
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Robust data encodings for quantum classifiers
Ryan LaRose and Brian Coyle · 2020
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Variational Quantum Fidelity Estimation
Marco Cerezo, Alexander Poremba, Lukasz Cincio, and Patrick J. Coles · 2020
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Input Redundancy for Parameterized Quantum Circuits
Francisco Javier Gil Vidal and Dirk Oliver Theis · 2020
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The Born supremacy: quantum advantage and training of an Ising Born machine
Brian Coyle, Daniel Mills, Vincent Danos, and Elham Kashefi · 2020
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The Capacity of Quantum Neural Networks
Logan G. Wright, Logan G. Wright, Peter L. McMahon, and Peter L. McMahon · 2020
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Solving quantum statistical mechanics with variational autoregressive networks and quantum circuits
JinGuo Liu, Liang Mao, Pan Zhang, and Lei Wang · 2020
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Expressive power of parametrized quantum circuits
Yuxuan Du, Min-Hsiu Hsieh, Tongliang Liu, and Dacheng Tao · 2020
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Classical versus quantum models in machine learning: insights from a finance application
Javier Alcazar, Vicente Leyton-Ortega, and Alejandro Perdomo-Ortiz · 2020
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Experimental demonstration of a quantum generative adversarial network for continuous distributions
Abhinav Anand, Jonathan Romero, Matthias Degroote, and Alán Aspuru-Guzik · 2020
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