2018

Continuous-variable quantum neural networks

Killoran, Nathan, Bromley, Thomas R., Arrazola, Juan Miguel et al.

Understand

We introduce a general method for building neural networks on quantum computers.

The quantum neural network is a variational quantum circuit built in the continuous-variable (CV) architecture, which encodes quantum information in continuous degrees of freedom such as the amplitudes of the electromagnetic field.
This circuit contains a layered structure of continuously parameterized gates which is universal for CV quantum computation.
Affine transformations and nonlinear activation functions, two key elements in neural networks, are enacted in the quantum network using Gaussian and non-Gaussian gates, respectively.

Built on

Invariante Variationsprobleme
E Noether · 1918
Earlier work this paper cites.
Quantisierung als Eigenwertproblem
Erwin Schrödinger · 1926
Earlier work this paper cites.
An undulatory theory of the mechanics of atoms and molecules
Erwin Schrödinger · 1926
Earlier work this paper cites.
Quantenmechanik und Gruppentheorie
Hermann Weyl · 1927
Earlier work this paper cites.
Über die Quantenmechanik der Elektronen in Kristallgittern
Felix Bloch · 1929
Earlier work this paper cites.
On the quantum correction for thermodynamic equilibrium
Eugene Wigner · 1932
Earlier work this paper cites.
On the principles of elementary quantum mechanics
Hilbrand Johannes Groenewold · 1946
Earlier work this paper cites.
Quantum mechanics as a statistical theory
José E Moyal · 1949
Earlier work this paper cites.
Learning representations by back-propagating errors
David E Rumelhart, Geoffrey E Hinton, and Ronald J Williams · 1986
Earlier work this paper cites.
Backpropagation applied to handwritten zip code recognition
Yann LeCun, Bernhard Boser, John S Denker, Donnie Henderson, Richard E Howard, Wayne Hubbard, and Lawrence D Jackel · 1989
Earlier work this paper cites.
Multilayer feedforward networks are universal approximators
Kurt Hornik, Maxwell Stinchcombe, and Halbert White · 1989
Earlier work this paper cites.
Approximation by superpositions of a sigmoidal function
George Cybenko · 1989
Earlier work this paper cites.
Neuromorphic electronic systems
Carver Mead · 1990
Earlier work this paper cites.
Multilayer feedforward networks with a nonpolynomial activation function can approximate any function
Moshe Leshno, Vladimir Ya Lin, Allan Pinkus, and Shimon Schocken · 1993
Earlier work this paper cites.
A comparison of the computational power of sigmoid and boolean threshold circuits
Wolfgang Maass, Georg Schnitger, and Eduardo D Sontag · 1994
Earlier work this paper cites.
Generation of nonclassical motional states of a trapped atom
DM Meekhof, C Monroe, BE King, Wayne M Itano, and David J Wineland · 1996
Earlier work this paper cites.
A “schrödinger cat” superposition state of an atom
Ch Monroe, DM Meekhof, BE King, and David J Wineland · 1996
Earlier work this paper cites.
Online learning and stochastic approximations
Léon Bottou · 1998
Earlier work this paper cites.
Quantum computation over continuous variables
Seth Lloyd and Samuel L Braunstein · 1999
Earlier work this paper cites.
Encoding a qubit in an oscillator
Daniel Gottesman, Alexei Kitaev, and John Preskill · 2001
Earlier work this paper cites.
A scheme for efficient quantum computation with linear optics
Emanuel Knill, Raymond Laflamme, and Gerald J Milburn · 2001
Earlier work this paper cites.
Methods in theoretical quantum optics
Stephen M Barnett and Paul M Radmore · 2002
Earlier work this paper cites.
Gaussian states in continuous variable quantum information
Alessandro Ferraro, Stefano Olivares, and Matteo GA Paris · 2005
Earlier work this paper cites.
Theory of microwave parametric down-conversion and squeezing using circuit QED
K Moon and SM Girvin · 2005
Earlier work this paper cites.
Theano: A CPU and GPU math compiler in Python
James Bergstra, Olivier Breuleux, Frédéric Bastien, Pascal Lamblin, Razvan Pascanu, Guillaume Desjardins, Joseph Turian, David Warde-Farley, and Yoshua Bengio · 2010
Earlier work this paper cites.
Introduction to optical quantum information processing
Pieter Kok and Brendon W Lovett · 2010
Earlier work this paper cites.
Neuromorphic silicon neurons and large-scale neural networks: challenges and opportunities
Chi-Sang Poon and Kuan Zhou · 2011
Earlier work this paper cites.
Information processing using a single dynamical node as complex system
Lennert Appeltant, Miguel Cornelles Soriano, Guy Van der Sande, Jan Danckaert, Serge Massar, Joni Dambre, Benjamin Schrauwen, Claudio R Mirasso, and Ingo Fischer · 2011
Earlier work this paper cites.
Quantum algorithm for data fitting
Nathan Wiebe, Daniel Braun, and Seth Lloyd · 2012
Earlier work this paper cites.
Gaussian quantum information
Christian Weedbrook, Stefano Pirandola, Raúl García-Patrón, Nicolas J Cerf, Timothy C Ralph, Jeffrey H Shapiro, and Seth Lloyd · 2012
Earlier work this paper cites.
Supervised sequence labelling with recurrent neural networks
Alex Graves · 2012
Earlier work this paper cites.
Auto-encoding variational Bayes
Original
Diederik P Kingma and Max Welling · 2013
Earlier work this paper cites.
Mixing nonclassical pure states in a linear-optical network almost always generates modal entanglement
Zhang Jiang, Matthias D Lang, and Carlton M Caves · 2013
Earlier work this paper cites.

Similar

Quantum machine learning: what quantum computing means to data mining
Peter Wittek · 2014
Cited alongside, same era.
Quantum principal component analysis
Seth Lloyd, Masoud Mohseni, and Patrick Rebentrost · 2014
Cited alongside, same era.
Quantum inference on bayesian networks
Guang Hao Low, Theodore J Yoder, and Isaac L Chuang · 2014
Cited alongside, same era.
Quantum support vector machine for big data classification
Patrick Rebentrost, Masoud Mohseni, and Seth Lloyd · 2014
Cited alongside, same era.
Caffe: Convolutional architecture for fast feature embedding
Yangqing Jia, Evan Shelhamer, Jeff Donahue, Sergey Karayev, Jonathan Long, Ross Girshick, Sergio Guadarrama, and Trevor Darrell · 2014
Cited alongside, same era.
cudnn: Efficient primitives for deep learning
Original
Sharan Chetlur, Cliff Woolley, Philippe Vandermersch, Jonathan Cohen, John Tran, Bryan Catanzaro, and Evan Shelhamer · 2014
Cited alongside, same era.
Broadcast and weight: an integrated network for scalable photonic spike processing
Alexander N Tait, Mitchell A Nahmias, Bhavin J Shastri, and Paul R Prucnal · 2014
Cited alongside, same era.
Neuromorphic computing gets ready for the (really) big time
Don Monroe · 2014
Cited alongside, same era.
Photonic neuromorphic signal processing and computing
Alexander N Tait, Mitchell A Nahmias, Yue Tian, Bhavin J Shastri, and Paul R Prucnal · 2014
Cited alongside, same era.
Experimental demonstration of reservoir computing on a silicon photonics chip
Kristof Vandoorne, Pauline Mechet, Thomas Van Vaerenbergh, Martin Fiers, Geert Morthier, David Verstraeten, Benjamin Schrauwen, Joni Dambre, and Peter Bienstman · 2014
Cited alongside, same era.
Continuous variable quantum information: Gaussian states and beyond
Gerardo Adesso, Sammy Ragy, and Antony R Lee · 2014
Cited alongside, same era.
Multiple object recognition with visual attention
Original
Jimmy Ba, Volodymyr Mnih, and Koray Kavukcuoglu · 2014
Cited alongside, same era.

Then

Automatic differentiation in PyTorch
Adam Paszke, Sam Gross, Soumith Chintala, Gregory Chanan, Edward Yang, Zachary DeVito, Zeming Lin, Alban Desmaison, Luca Antiga, and Adam Lerer · 2017
Later among the works it cites.
In-datacenter performance analysis of a tensor processing unit
Norman P Jouppi, Cliff Young, Nishant Patil, David Patterson, Gaurav Agrawal, Raminder Bajwa, Sarah Bates, Suresh Bhatia, Nan Boden, Al Borchers, et al · 2017
Later among the works it cites.
Deep learning with coherent nanophotonic circuits
Yichen Shen, Nicholas C Harris, Scott Skirlo, Mihika Prabhu, Tom Baehr-Jones, Michael Hochberg, Xin Sun, Shijie Zhao, Hugo Larochelle, Dirk Englund, et al · 2017
Later among the works it cites.
Quantum autoencoders for efficient compression of quantum data
Jonathan Romero, Jonathan P Olson, and Alan Aspuru-Guzik · 2017
Later among the works it cites.
Quantum generalisation of feedforward neural networks
Kwok Ho Wan, Oscar Dahlsten, Hlér Kristjánsson, Robert Gardner, and MS Kim · 2017
Later among the works it cites.
A quantum algorithm to train neural networks using low-depth circuits
Original
Guillaume Verdon, Michael Broughton, and Jacob Biamonte · 2017
Later among the works it cites.
Opportunities and challenges for quantum-assisted machine learning in near-term quantum computers
Original
Alejandro Perdomo-Ortiz, Marcello Benedetti, John Realpe-Gómez, and Rupak Biswas · 2017
Later among the works it cites.
Quantum machine learning over infinite dimensions
Hoi-Kwan Lau, Raphael Pooser, George Siopsis, and Christian Weedbrook · 2017
Later among the works it cites.
Quantum Continuous Variables: A Primer of Theoretical Methods
Alessio Serafini · 2017
Later among the works it cites.
Why does deep and cheap learning work so well?
Henry W Lin, Max Tegmark, and David Rolnick · 2017
Later among the works it cites.
Quantum neuron: an elementary building block for machine learning on quantum computers
Original
Yudong Cao, Gian Giacomo Guerreschi, and Alán Aspuru-Guzik · 2017
Later among the works it cites.
Quantum generalisation of feedforward neural networks
Kwok Ho Wan, Oscar Dahlsten, Hlér Kristjánsson, Robert Gardner, and MS Kim · 2017
Later among the works it cites.
Schrodinger cat states in circuit qed
Original
SM Girvin · 2017
Later among the works it cites.
Quantum optimization using variational algorithms on near-term quantum devices
Original
Nikolaj Moll, Panagiotis Barkoutsos, Lev S Bishop, Jerry M Chow, Andrew Cross, Daniel J Egger, Stefan Filipp, Andreas Fuhrer, Jay M Gambetta, Marc Ganzhorn, et al · 2017
Later among the works it cites.
Continuous-variable instantaneous quantum computing is hard to sample
T. Douce, D. Markham, E. Kashefi, E. Diamanti, T. Coudreau, P. Milman, P. van Loock, and G. Ferrini · 2017
Later among the works it cites.
Quantum supremacy and high-dimensional integration
Original
J. M. Arrazola, P. Rebentrost, and C. Weedbrook · 2017
Later among the works it cites.
Quantum machine learning in feature Hilbert spaces
Original
Maria Schuld and Nathan Killoran · 2018
Closest in time.
Quantum Boltzmann machine
Mohammad H Amin, Evgeny Andriyash, Jason Rolfe, Bohdan Kulchytskyy, and Roger Melko · 2018
Closest in time.
Classification with quantum neural networks on near term processors
Original
Edward Farhi and Hartmut Neven · 2018
Closest in time.
Quantum circuit learning
Original
Kosuke Mitarai, Makoto Negoro, Masahiro Kitagawa, and Keisuke Fujii · 2018
Closest in time.
Circuit-centric quantum classifiers
Original
Maria Schuld, Alex Bocharov, Krysta Svore, and Nathan Wiebe · 2018
Closest in time.
Hierarchical quantum classifiers
Original
Edward Grant, Marcello Benedetti, Shuxiang Cao, Andrew Hallam, Joshua Lockhart, Vid Stojevic, Andrew G Green, and Simone Severini · 2018
Closest in time.
Universal discriminative quantum neural networks
Original
Hongxiang Chen, Leonard Wossnig, Simone Severini, Hartmut Neven, and Masoud Mohseni · 2018
Closest in time.
Quantum-assisted Helmholtz machines: A quantum-classical deep learning framework for industrial datasets in near-term devices
Marcello Benedetti, John Realpe Gómez, and Alejandro Perdomo-Ortiz · 2018
Closest in time.
Continuous-variable quantum Gaussian process regression and quantum singular value decomposition of nonsparse low-rank matrices
Siddhartha Das, George Siopsis, and Christian Weedbrook · 2018
Closest in time.
Universal quantum perceptron as efficient unitary approximators
Original
E Torrontegui and JJ Garcia-Ripoll · 2018
Closest in time.
Circuit-centric quantum classifiers
Original
Krysta Svore Nathan Wiebe Maria Schuld, Alex Bocharov · 2018
Closest in time.
Classification with quantum neural networks on near term processors
Original
Edward Farhi and Hartmut Neven · 2018
Closest in time.
Quantum generative adversarial networks
Original
Pierre-Luc Dallaire-Demers and Nathan Killoran · 2018
Closest in time.
Adversarial quantum circuit learning for pure state approximation
Original
Marcello Benedetti, Edward Grant, Leonard Wossnig, and Simone Severini · 2018
Closest in time.
Supervised learning with quantum enhanced feature spaces
Original
Vojtech Havlicek, Antonio D Córcoles, Kristan Temme, Aram W Harrow, Jerry M Chow, and Jay M Gambetta · 2018
Closest in time.
Strawberry Fields online documentation: Controlled-X gate
Xanadu Quantum Technologies · 2018
Closest in time.
Strawberry Fields: A software platform for photonic quantum computing
Original
Nathan Killoran, Josh Izaac, Nicolás Quesada, Ville Bergholm, Matthew Amy, and Christian Weedbrook · 2018
Closest in time.

Beyond the bibliography

alphaXiv searches the wider corpus for related work and actual follow-ups.

Open on alphaXiv

alphaXiv is searching for related work…

Reading the bibliography…