Continuous-variable quantum neural networks

Abstract

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. The non-Gaussian gates provide both the nonlinearity and the universality of the model. Due to the structure of the CV model, the CV quantum neural network can encode highly nonlinear transformations while remaining completely unitary. We show how a classical network can be embedded into the quantum formalism and propose quantum versions of various specialized model such as convolutional, recurrent, and residual networks. Finally, we present numerous modeling experiments built with the Strawberry Fields software library. These experiments, including a classifier for fraud detection, a network which generates Tetris images, and a hybrid classical-quantum autoencoder, demonstrate the capability and adaptability of CV quantum neural networks.

References in corpus (54)

• Deep Learning in Neural Networks: An Overview
• Quantum Machine Learning
• A variational eigenvalue solver on a quantum processor
• Gaussian Quantum Information
• Deep Learning with Coherent Nanophotonic Circuits
• Supervised learning with quantum enhanced feature spaces
• The theory of variational hybrid quantum-classical algorithms
• Quantum support vector machine for big data classification
• Quantum machine learning in feature Hilbert spaces
• Quantum Circuit Learning
• Encoding a qubit in an oscillator
• Quantum principal component analysis
• Quantum computation over continuous variables
• Evaluating analytic gradients on quantum hardware
• Continuous variable quantum information: Gaussian states and beyond
• The quest for a Quantum Neural Network
• Quantum optimization using variational algorithms on near-term quantum devices
• Quantum Data Fitting
• Quantum generative adversarial networks
• Gaussian Boson Sampling
• Quantum autoencoders for efficient compression of quantum data
• Hybrid quantum information processing
• Why does deep and cheap learning work so well?
• Quantum Boltzmann Machine
• Quantum speedup of Monte Carlo methods
• Strawberry Fields: A Software Platform for Photonic Quantum Computing
• Hierarchical quantum classifiers
• Boson Sampling from Gaussian States
• Quantum generalisation of feedforward neural networks
• Opportunities and challenges for quantum-assisted machine learning in near-term quantum computers
• Generation of one-million-mode continuous-variable cluster state by unlimited time-domain multiplexing
• A detailed study of Gaussian Boson Sampling
• Tomography and Generative Data Modeling via Quantum Boltzmann Training
• Simulating a perceptron on a quantum computer
• Machine learning method for state preparation and gate synthesis on photonic quantum computers
• Implementation of a quantum cubic gate by adaptive non-Gaussian measurement
• Quantum machine learning over infinite dimensions
• Quantum Inference on Bayesian Networks
• Theory of Microwave Parametric Down Conversion and Squeezing Using Circuit QED
• Deterministic implementation of weak quantum cubic nonlinearity
• Quantum-assisted Helmholtz machines: A quantum-classical deep learning framework for industrial datasets in near-term devices
• Unitary quantum perceptron as efficient universal approximator
• Scalable Implementation of Boson Sampling with Trapped Ions
• Adversarial quantum circuit learning for pure state approximation
• Repeat-until-success cubic phase gate for universal continuous-variable quantum computation
• Continuous-Variable Instantaneous Quantum Computing is hard to sample
• Variationally Learning Grover's Quantum Search Algorithm
• General implementation of arbitrary nonlinear quadrature phase gates
• Microwave Boson Sampling
• A proposal for a scalable universal bosonic simulator using individually trapped ions
• Open quantum generalisation of Hopfield neural networks
• Mixing nonclassical pure states in a linear-optical network almost always generates modal entanglement
• Perceptrons with Hebbian learning based on wave ensembles in plastic potentials
• Continuous-variable quantum Gaussian process regression and quantum singular value decomposition of non-sparse low rank matrices

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