Matrix Product Operators for Sequence to Sequence Learning

Abstract

The method of choice to study one-dimensional strongly interacting many body quantum systems is based on matrix product states and operators. Such method allows to explore the most relevant, and numerically manageable, portion of an exponentially large space. It also allows to describe accurately correlations between distant parts of a system, an important ingredient to account for the context in machine learning tasks. Here we introduce a machine learning model in which matrix product operators are trained to implement sequence to sequence prediction, i.e. given a sequence at a time step, it allows one to predict the next sequence. We then apply our algorithm to cellular automata (for which we show exact analytical solutions in terms of matrix product operators), and to nonlinear coupled maps. We show advantages of the proposed algorithm when compared to conditional random fields and bidirectional long short-term memory neural network. To highlight the flexibility of the algorithm, we also show that it can readily perform classification tasks.

arXiv comment9+4 pages, 6+2 figures

References in corpus (39)

• Quantum Machine Learning
• The density-matrix renormalization group in the age of matrix product states
• The density-matrix renormalization group
• Solving the Quantum Many-Body Problem with Artificial Neural Networks
• Efficient simulation of one-dimensional quantum many-body systems
• Machine learning phases of matter
• Real time evolution using the density matrix renormalization group
• An introduction to quantum machine learning
• Time-dependent density-matrix renormalization-group using adaptive effective Hilbert spaces
• Matrix Product Density Operators: Simulation of finite-T and dissipative systems
• Quantum trajectories and open many-body quantum systems
• Learning phase transitions by confusion
• Discovering Phase Transitions with Unsupervised Learning
• From density-matrix renormalization group to matrix product states
• Quantum Entanglement in Neural Network States
• Why does deep and cheap learning work so well?
• Machine learning quantum phases of matter beyond the fermion sign problem
• Quantum Boltzmann Machine
• Restricted-Boltzmann-Machine Learning for Solving Strongly Correlated Quantum Systems
• Quantum Loop Topography for Machine Learning
• Machine Learning Topological Invariants with Neural Networks
• Unsupervised Generative Modeling Using Matrix Product States
• Learning Thermodynamics with Boltzmann Machines
• Machine Learning Phases of Strongly Correlated Fermions
• Self-Learning Monte Carlo Method
• Accelerate Monte Carlo Simulations with Restricted Boltzmann Machines
• Equivalence of restricted Boltzmann machines and tensor network states
• Unsupervised machine learning account of magnetic transitions in the Hubbard model
• Machine learning for many-body physics: The case of the Anderson impurity model
• Matrix Product Unitaries: Structure, Symmetries, and Topological Invariants
• Learning Relevant Features of Data with Multi-scale Tensor Networks
• Quenches near Ising quantum criticality as a challenge for artificial neural networks
• Matrix Product Eigenstates for One-Dimensional Stochastic Models and Quantum Spin Chains
• Dynamical simulations of classical stochastic systems using matrix product states
• Exact matrix product decay modes of a boundary driven cellular automaton
• Restricted Boltzmann Machines for the Long Range Ising Models
• Machine learning for many-body physics: efficient solution of dynamical mean-field theory
• Capturing exponential variance using polynomial resources: applying tensor networks to non-equilibrium stochastic processes
• Language as a matrix product state

Cited by in corpus (32)

• Machine learning and the physical sciences
• Lecture Notes of Tensor Network Contractions
• Machine Learning for Quantum Matter
• Enhancing Generative Models via Quantum Correlations
• Supervised Learning with Projected Entangled Pair States
• Tensor network based machine learning of non-Markovian quantum processes
• The Presence and Absence of Barren Plateaus in Tensor-network Based Machine Learning
• Generative Tensor Network Classification Model for Supervised Machine Learning
• Automatic Differentiation for Second Renormalization of Tensor Networks
• Tree tensor network classifiers for machine learning: from quantum-inspired to quantum-assisted
• Generative machine learning with tensor networks: benchmarks on near-term quantum computers
• Compressing deep neural networks by matrix product operators
• Matrix Product States for Quantum Stochastic Modelling
• Modeling Sequences with Quantum States: A Look Under the Hood
• Experimental realization of a quantum image classifier via tensor-network-based machine learning
• Quantum Compressed Sensing with Unsupervised Tensor-Network Machine Learning
• Tangent-Space Gradient Optimization of Tensor Network for Machine Learning
• Quantifying Non-Markovianity in Open Quantum Dynamics
• Explainable Natural Language Processing with Matrix Product States
• Measures of distinguishability between stochastic processes
• Reconstructing Non-Markovian Open Quantum Evolution From Multi-time Measurements
• Stack operation of tensor networks
• Randomised benchmarking for characterizing and forecasting correlated processes
• Language Modeling with Reduced Densities
• Network-Initialized Monte Carlo Based on Generative Neural Networks
• Density Matrix Renormalization Group Algorithm For Mixed Quantum States
• Deep tensor networks with matrix product operators
• Bayesian Tensor Network with Polynomial Complexity for Probabilistic Machine Learning
• Quantum Tensor Networks, Stochastic Processes, and Weighted Automata
• Effective classical correspondence of the Mott transition
• Tensor-Networks-based Learning of Probabilistic Cellular Automata Dynamics
• Quantum tensor network algorithms for evaluation of spectral functions on quantum computers