Tree tensor network classifiers for machine learning: from quantum-inspired to quantum-assisted

Abstract

We describe a quantum-assisted machine learning (QAML) method in which multivariate data is encoded into quantum states in a Hilbert space whose dimension is exponentially large in the length of the data vector. Learning in this space occurs through applying a low-depth quantum circuit with a tree tensor network (TTN) topology, which acts as an unsupervised feature extractor to identify the most relevant quantum states in a data-driven fashion. This unsupervised feature extractor then feeds a supervised linear classifier and encodes the output in a small-dimensional quantum register. In contrast to previous work on \emph{quantum-inspired} TTN classifiers, in which the embedding map and class decision weights did not map the data to well-defined quantum states, we present an approach that can be implemented on gate-based quantum computing devices. In particular, we identify an embedding map with accuracy similar to exponential machines (Novikov \emph{et al.}, arXiv:1605.03795), but which produces valid quantum states from classical data vectors, and utilize manifold-based gradient optimization schemes to produce isometric operations mapping quantum states to a register of qubits defining a class decision. We detail methods for efficiently obtaining one- and two-point correlation functions of the decision boundary vectors of the quantum model, which can be used for model interpretability, as well as methods for obtaining classifications from partial data vectors. Further, we show that the use of isometric tensors can significantly aid in the human interpretability of the correlation functions extracted from the decision weights, and may produce models that are less susceptible to adversarial perturbations. We demonstrate our methodologies in applications utilizing the MNIST handwritten digit dataset and a multivariate timeseries dataset of human activity recognition.

arXiv comment20 pages, 15 figures. Abstract slightly shortened to fit arXiv requirements

References in corpus (62)

• Scikit-learn: Machine Learning in Python
• Quantum Computing in the NISQ era and beyond
• Supplementary information for "Quantum supremacy using a programmable superconducting processor"
• Quantum Machine Learning
• The density-matrix renormalization group in the age of matrix product states
• Barren plateaus in quantum neural network training landscapes
• A Practical Introduction to Tensor Networks: Matrix Product States and Projected Entangled Pair States
• Simulated Quantum Computation of Molecular Energies
• Cost Function Dependent Barren Plateaus in Shallow Parametrized Quantum Circuits
• Evaluating analytic gradients on quantum hardware
• Circuit-centric quantum classifiers
• A class of quantum many-body states that can be efficiently simulated
• Quantum algorithms for quantum chemistry and quantum materials science
• The effect of data encoding on the expressive power of variational quantum machine learning models
• Hartree-Fock on a superconducting qubit quantum computer
• Area laws in quantum systems: mutual information and correlations
• How to factor 2048 bit RSA integers in 8 hours using 20 million noisy qubits
• Roads towards fault-tolerant universal quantum computation
• Classical simulation of quantum many-body systems with a tree tensor network
• Tensor networks for complex quantum systems
• Demonstration of the trapped-ion quantum-CCD computer architecture
• Quantum machine learning: a classical perspective
• Adversarial Attacks and Defences: A Survey
• ProjectQ: An Open Source Software Framework for Quantum Computing
• An initialization strategy for addressing barren plateaus in parametrized quantum circuits
• Sequential generation of entangled multi-qubit states
• Robust data encodings for quantum classifiers
• Reconstructing quantum states with generative models
• Hierarchical quantum classifiers
• Towards Quantum Machine Learning with Tensor Networks
• Opportunities and challenges for quantum-assisted machine learning in near-term quantum computers
• Unsupervised Generative Modeling Using Matrix Product States
• Concrete Categorical Model of a Quantum Circuit Description Language with Measurement
• Tensor Networks for Dimensionality Reduction and Large-Scale Optimizations. Part 2 Applications and Future Perspectives
• Stochastic gradient descent for hybrid quantum-classical optimization
• A Software Methodology for Compiling Quantum Programs
• The Born Supremacy: Quantum Advantage and Training of an Ising Born Machine
• Quantum Adversarial Machine Learning
• Overview and Comparison of Gate Level Quantum Software Platforms
• Sequential Generation of Matrix-Product States in Cavity QED
• Tree Tensor Networks for Generative Modeling
• Machine Learning by Unitary Tensor Network of Hierarchical Tree Structure
• Learning Relevant Features of Data with Multi-scale Tensor Networks
• On the Quantum versus Classical Learnability of Discrete Distributions
• Vulnerability of quantum classification to adversarial perturbations
• TensorNetwork: A Library for Physics and Machine Learning
• Machine Learning Phase Transitions with a Quantum Processor
• Riemannian optimization of isometric tensor networks
• TensorNetwork for Machine Learning
• Matrix Product Operators for Sequence to Sequence Learning
• Riemannian geometry and automatic differentiation for optimization problems of quantum physics and quantum technologies
• Expressibility and trainability of parameterized analog quantum systems for machine learning applications
• Generative machine learning with tensor networks: benchmarks on near-term quantum computers
• Tensor-based algorithms for image classification
• Correlation density matrix: an unbiased analysis of exact diagonalizations
• Expressive power of tensor-network factorizations for probabilistic modeling, with applications from hidden Markov models to quantum machine learning
• Modeling Sequences with Quantum States: A Look Under the Hood
• Quantum Machine Learning Tensor Network States
• Anomaly Detection with Tensor Networks
• Correlation density matrices for 1- dimensional quantum chains based on the density matrix renormalization group
• Deep convolutional tensor network
• Number-State Preserving Tensor Networks as Classifiers for Supervised Learning

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