Towards Quantum Machine Learning with Tensor Networks

Abstract

Machine learning is a promising application of quantum computing, but challenges remain as near-term devices will have a limited number of physical qubits and high error rates. Motivated by the usefulness of tensor networks for machine learning in the classical context, we propose quantum computing approaches to both discriminative and generative learning, with circuits based on tree and matrix product state tensor networks that could have benefits for near-term devices. The result is a unified framework where classical and quantum computing can benefit from the same theoretical and algorithmic developments, and the same model can be trained classically then transferred to the quantum setting for additional optimization. Tensor network circuits can also provide qubit-efficient schemes where, depending on the architecture, the number of physical qubits required scales only logarithmically with, or independently of the input or output data sizes. We demonstrate our proposals with numerical experiments, training a discriminative model to perform handwriting recognition using a optimization procedure that could be carried out on quantum hardware, and testing the noise resilience of the trained model.

arXiv comment10 pages; 14 figures; added new detailed study of noise resilience

References in corpus (19)

• Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer
• A variational eigenvalue solver on a quantum processor
• The density-matrix renormalization group in the age of matrix product states
• Efficient classical simulation of slightly entangled quantum computations
• The theory of variational hybrid quantum-classical algorithms
• A Practical Introduction to Tensor Networks: Matrix Product States and Projected Entangled Pair States
• Matrix Product States, Projected Entangled Pair States, and variational renormalization group methods for quantum spin systems
• Characterizing Quantum Supremacy in Near-Term Devices
• Thermodynamic limit of the density matrix renormalization for the spin-1 Heisenberg chain
• No Signalling and Quantum Key Distribution
• A class of quantum many-body states that can be efficiently simulated
• Detecting arbitrary quantum errors via stabilizer measurements on a sublattice of the surface code
• Tensor network states and geometry
• Simulation of two-dimensional quantum systems using a tree tensor network that exploits the entropic area law
• Unsupervised Generative Modeling Using Matrix Product States
• Information Perspective to Probabilistic Modeling: Boltzmann Machines versus Born Machines
• Learning Relevant Features of Data with Multi-scale Tensor Networks
• Preparing projected entangled pair states on a quantum computer
• Preparing topological PEPS on a quantum computer

Cited by in corpus (149)

• Quantum Convolutional Neural Networks
• Parameterized quantum circuits as machine learning models
• A high-bias, low-variance introduction to Machine Learning for physicists
• Matrix Product States and Projected Entangled Pair States: Concepts, Symmetries, and Theorems
• Quantum algorithms for quantum chemistry and quantum materials science
• Quantum Natural Gradient
• Hierarchical quantum classifiers
• The Expressive Power of Parameterized Quantum Circuits
• Experimental Quantum Generative Adversarial Networks for Image Generation
• Differentiable Programming Tensor Networks
• Quantum Computing for High-Energy Physics: State of the Art and Challenges. Summary of the QC4HEP Working Group
• Solving nonlinear differential equations with differentiable quantum circuits
• Quantum generative adversarial network for generating discrete distribution
• Hardware-efficient variational quantum algorithms for time evolution
• Quantum noise protects quantum classifiers against adversaries
• Quantum Machine Learning for Chemistry and Physics
• Variational Quantum Eigensolver with Fewer Qubits
• Encoding of Matrix Product States into Quantum Circuits of One- and Two-Qubit Gates
• Yao.jl: Extensible, Efficient Framework for Quantum Algorithm Design
• Efficient measure for the expressivity of variational quantum algorithms
• Parallel Quantum Simulation of Large Systems on Small Quantum Computers
• On barren plateaus and cost function locality in variational quantum algorithms
• Machine Learning by Unitary Tensor Network of Hierarchical Tree Structure
• Variational Quantum Reinforcement Learning via Evolutionary Optimization
• Learning and Inference on Generative Adversarial Quantum Circuits
• Holographic quantum algorithms for simulating correlated spin systems
• The Variational Power of Quantum Circuit Tensor Networks
• Learning Feynman Diagrams with Tensor Trains
• An end-to-end trainable hybrid classical-quantum classifier
• Barren plateaus in quantum tensor network optimization
• Fast quantum circuit cutting with randomized measurements
• Machine Learning Phase Transitions with a Quantum Processor
• Information Scrambling in Quantum Neural Networks
• Synergy Between Quantum Circuits and Tensor Networks: Short-cutting the Race to Practical Quantum Advantage
• Holographic dynamics simulations with a trapped ion quantum computer
• Data compression for quantum machine learning
• Experimental quantum kernel machine learning with nuclear spins in a solid
• Sequential generation of projected entangled-pair states
• Quantum enhancements for deep reinforcement learning in large spaces
• The Presence and Absence of Barren Plateaus in Tensor-network Based Machine Learning
• Generative Tensor Network Classification Model for Supervised Machine Learning
• Robust in Practice: Adversarial Attacks on Quantum Machine Learning
• Self-Correcting Quantum Many-Body Control using Reinforcement Learning with Tensor Networks
• Quantum Embedding Search for Quantum Machine Learning
• Expressivity of Quantum Neural Networks
• Multi-class quantum classifiers with tensor network circuits for quantum phase recognition
• Accurate simulation for finite projected entangled pair states in two dimensions
• Tensor networks for quantum machine learning
• Hybrid quantum-classical neural network for calculating ground state energies of molecules
• Qubit-efficient entanglement spectroscopy using qubit resets
• Scrambling Ability of Quantum Neural Networks Architectures
• Predicting toxicity by quantum machine learning
• Simulating groundstate and dynamical quantum phase transitions on a superconducting quantum computer
• Classical versus Quantum: comparing Tensor Network-based Quantum Circuits on LHC data
• Quantum algorithms for estimating quantum entropies
• Tree tensor network classifiers for machine learning: from quantum-inspired to quantum-assisted
• Gauging tensor networks with belief propagation
• Generative machine learning with tensor networks: benchmarks on near-term quantum computers
• Entanglement from tensor networks on a trapped-ion QCCD quantum computer
• End-to-End Quantum Machine Learning Implemented with Controlled Quantum Dynamics
• Tensor-based algorithms for image classification
• Probabilistic Modeling with Matrix Product States
• Cost function embedding and dataset encoding for machine learning with parameterized quantum circuits
• Entanglement-guided architectures of machine learning by quantum tensor network
• Noise robustness and experimental demonstration of a quantum generative adversarial network for continuous distributions
• Preparing quantum many-body scar states on quantum computers
• Variational quantum algorithm for unconstrained black box binary optimization: Application to feature selection
• A hybrid quantum-classical conditional generative adversarial network algorithm for human-centered paradigm in cloud
• Cyber-Physical Defense in the Quantum Era
• Experimental realization of a quantum image classifier via tensor-network-based machine learning
• Quantum Machine Learning Tensor Network States
• QSpace - An open-source tensor library for Abelian and non-Abelian symmetries
• Quantum computing quantum Monte Carlo with hybrid tensor network for electronic structure calculations
• Dequantizing quantum machine learning models using tensor networks
• Mutual Information Scaling for Tensor Network Machine Learning
• Tensor networks for quantum computing
• Quantum Compressed Sensing with Unsupervised Tensor-Network Machine Learning
• Approximate encoding of quantum states using shallow circuits
• Quantum-probabilistic Hamiltonian learning for generative modelling & anomaly detection
• Combining Matrix Product States and Noisy Quantum Computers for Quantum Simulation
• Tangent-Space Gradient Optimization of Tensor Network for Machine Learning
• Atomic Quantum Technologies for Quantum Matter and Fundamental Physics Applications
• Qibolab: an open-source hybrid quantum operating system
• Loop-Free Tensor Networks for High-Energy Physics
• Assessment of the variational quantum eigensolver: application to the Heisenberg model
• Tensor-network-assisted variational quantum algorithm
• The minimal canonical form of a tensor network
• Numerical hardware-efficient variational quantum simulation of a soliton solution
• Towards a Quantum Simulation of Nonlinear Sigma Models with a Topological Term
• Quantum-machine-learning channel discrimination
• Residual Tensor Train: A Quantum-inspired Approach for Learning Multiple Multilinear Correlations
• Efficient MPS representations and quantum circuits from the Fourier modes of classical image data
• Quantum circuits for the realization of equivalent forms of one-dimensional discrete-time quantum walks on near-term quantum hardware
• When Federated Learning Meets Quantum Computing: Survey and Research Opportunities
• Fine-Grained Tensor Network Methods
• Variational quantum state preparation via quantum data buses
• Decohering Tensor Network Quantum Machine Learning Models
• A tensor network discriminator architecture for classification of quantum data on quantum computers
• Machine learning with tree tensor networks, CP rank constraints, and tensor dropout
• On the descriptive power of Neural-Networks as constrained Tensor Networks with exponentially large bond dimension
• Probing phases of quantum matter with an ion-trap tensor-network quantum eigensolver
• Generalization Error Bound for Quantum Machine Learning in NISQ Era -- A Survey
• Approximate Quantum Compiling for Quantum Simulation: A Tensor Network based approach
• Qsun: an open-source platform towards practical quantum machine learning applications
• Variational adiabatic transport of tensor networks
• NoRA: A Tensor Network Ansatz for Volume-Law Entangled Equilibrium States of Highly Connected Hamiltonians
• The cross-sectional stock return predictions via quantum neural network and tensor network
• Convergence and Quantum Advantage of Trotterized MERA for Strongly-Correlated Systems
• A Universal Quantum Circuit Design for Periodical Functions
• Towards AutoQML: A Cloud-Based Automated Circuit Architecture Search Framework
• Framework for Learning and Control in the Classical and Quantum Domains
• Entropy, Free Energy, and Work of Restricted Boltzmann Machines
• Bosonic entanglement renormalization circuits from wavelet theory
• Optimizing Radiotherapy Plans for Cancer Treatment with Tensor Networks
• Quantum algorithm for calculation of transition amplitudes in hybrid tensor networks
• The resource theory of tensor networks
• Generation of photonic tensor network states with Circuit QED
• An example of use of Variational Methods in Quantum Machine Learning
• Non-parametric Semi-Supervised Learning in Many-body Hilbert Space with Rescaled Logarithmic Fidelity
• Tensor networks and efficient descriptions of classical data
• Image Classification by Throwing Quantum Kitchen Sinks at Tensor Networks
• Dual-VQE: A quantum algorithm to lower bound the ground-state energy
• Quantum Feasibility Labeling for NP-complete Vertex Coloring Problem
• Almost fault-tolerant quantum machine learning with drastic overhead reduction
• Quantum Technology for Military Applications
• Quantum Algorithms for Compositional Text Processing
• Tensor Decompositions and Adiabatic Quantum Computing for Discovering Practical Matrix Multiplication Algorithms
• Scaling of contraction costs for entanglement renormalization algorithms including tensor Trotterization and variational Monte Carlo
• Quantum tensor network algorithms for evaluation of spectral functions on quantum computers
• Quantum circuit-like learning: A fast and scalable classical machine-learning algorithm with similar performance to quantum circuit learning
• Detecting Entanglement Generating Circuits in Cloud-Based Quantum Computing
• Accelerating Decision Diagram-based Multi-node Quantum Simulation with Ring Communication and Automatic SWAP Insertion
• WaveTrain: A Python Package for Numerical Quantum Mechanics of Chain-Like Systems Based on Tensor Trains
• Typical Machine Learning Datasets as Low-Depth Quantum Circuits
• Generative flow-based warm start of the variational quantum eigensolver
• Harnessing Quantum Dynamics for Robust and Scalable Quantum Extreme Learning Machines
• Quantum Patch-Based Autoencoder for Anomaly Segmentation
• Quantum Magnetic Skyrmions on Kondo-type Lattices
• Vertex Representation of Hyperbolic Tensor Networks
• The Software Landscape for the Density Matrix Renormalization Group
• QAS-QTNs: Curriculum Reinforcement Learning-Driven Quantum Architecture Search for Quantum Tensor Networks
• A coherent approach to quantum-classical optimization
• Explaining Anomalies with Tensor Networks
• A quantum eigenvalue solver based on tensor networks
• Trainable Quantum Neural Network for Multiclass Image Classification with the Power of Pre-trained Tree Tensor Networks
• Time series generation for option pricing on quantum computers using tensor network
• Quantum generative classification with mixed states
• Application of Langevin Dynamics to Advance the Quantum Natural Gradient Optimization Algorithm
• Transfer entropy and O-information to detect grokking in tensor network multi-class classification problems