Gaussian states of continuous-variable quantum systems provide universal and versatile reservoir computing

Abstract

We establish the potential of continuous-variable Gaussian states of linear dynamical systems for machine learning tasks. Specifically, we consider reservoir computing, an efficient framework for online time series processing. As a reservoir we consider a quantum harmonic network modeling e.g. linear quantum optical systems. We prove that unlike universal quantum computing, universal reservoir computing can be achieved without non-Gaussian resources. We find that encoding the input time series into Gaussian states is both a source and a means to tune the nonlinearity of the overall input-output map. We further show that the full potential of the proposed model can be reached by encoding to quantum fluctuations, such as squeezed vacuum, instead of classical intense fields or thermal fluctuations. Our results introduce a new research paradigm for reservoir computing harnessing the dynamics of a quantum system and the engineering of Gaussian quantum states, pushing both fields into a new direction.

arXiv comment14 pages, 4 figures. Supplementary material is 10 pages. This is a preprint of an article published in Communications Physics. The final authenticated version is available online at: https://doi.org/10.1038/s42005-021-00556-w

References in corpus (40)

• Quantum Computing in the NISQ era and beyond
• Quantum Machine Learning
• Gaussian Quantum Information
• Recent Advances in Physical Reservoir Computing: A Review
• Encoding a qubit in an oscillator
• Universal Quantum Computation with Continuous-Variable Cluster States
• Continuous variable quantum information: Gaussian states and beyond
• Efficient Learning for Deep Quantum Neural Networks
• The quest for a Quantum Neural Network
• Gaussian Boson Sampling
• All-optical Reservoir Computing
• Experimental realization of multipartite entanglement of 60 modes of a quantum optical frequency comb
• Time-Domain Multiplexed 2-Dimensional Cluster State: Universal Quantum Computing Platform
• Continuous-variable quantum neural networks
• Programmable quantum gate arrays
• Quantum Computing with Continuous-Variable Clusters
• Harnessing disordered quantum dynamics for machine learning
• Hyperbolic Lattices in Circuit Quantum Electrodynamics
• Resource theory of quantum non-Gaussianity and Wigner negativity
• Convex resource theory of non-Gaussianity
• Quantum reservoir processing
• Boosting computational power through spatial multiplexing in quantum reservoir computing
• Continuous variable entanglement on a chip
• Optical Reservoir Computing using multiple light scattering for chaotic systems prediction
• Quantum reservoir computing with a single nonlinear oscillator
• Temporal Information Processing on Noisy Quantum Computers
• Gaussian quantum resource theories
• Unitary quantum perceptron as efficient universal approximator
• Rapid Time Series Prediction with a Hardware-Based Reservoir Computer
• Generation and characterization of resource state for nonlinear cubic phase gate
• Supervised learning with a quantum classifier using a multi-level system
• On-demand photonic entanglement synthesizer
• Information Processing Capacity of Spin-Based Quantum Reservoir Computing Systems
• Generating Multimode Entangled Microwaves with a Superconducting Parametric Cavity
• Reconfigurable optical implementation of quantum complex networks
• ON states as resource units for universal quantum computation with photonic architectures
• Polynomial approximation of non-Gaussian unitaries by counting one photon at a time
• Learning Nonlinear Input-Output Maps with Dissipative Quantum Systems
• Production and applications of non-Gaussian quantum states of light
• Non-Markovianity over ensemble averages in quantum complex networks

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