Enhancing Generative Models via Quantum Correlations

Abstract

Generative modeling using samples drawn from the probability distribution constitutes a powerful approach for unsupervised machine learning. Quantum mechanical systems can produce probability distributions that exhibit quantum correlations which are difficult to capture using classical models. We show theoretically that such quantum correlations provide a powerful resource for generative modeling. In particular, we provide an unconditional proof of separation in expressive power between a class of widely-used generative models, known as Bayesian networks, and its minimal quantum extension. We show that this expressivity advantage is associated with quantum nonlocality and quantum contextuality. Furthermore, we numerically test this separation on standard machine learning data sets and show that it holds for practical problems. The possibility of quantum advantage demonstrated in this work not only sheds light on the design of useful quantum machine learning protocols but also provides inspiration to draw on ideas from quantum foundations to improve purely classical algorithms.

arXiv comment25 pages, 13 figures

References in corpus (49)

• 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
• Supervised learning with quantum enhanced feature spaces
• Quantum computational advantage using photons
• Barren plateaus in quantum neural network training landscapes
• 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
• Quantum machine learning in feature Hilbert spaces
• Improved Simulation of Stabilizer Circuits
• An introduction to quantum machine learning
• Strong quantum computational advantage using a superconducting quantum processor
• Entanglement renormalization
• Cost Function Dependent Barren Plateaus in Shallow Parametrized Quantum Circuits
• Hidden Variables and the Two Theorems of John Bell
• Quantum Computational Supremacy
• Stabilizer Codes and Quantum Error Correction
• Contextuality for preparations, transformations, and unsharp measurements
• Non-locality and Communication Complexity
• Contextuality supplies the magic for quantum computation
• Renormalization algorithms for Quantum-Many Body Systems in two and higher dimensions
• Hand-waving and Interpretive Dance: An Introductory Course on Tensor Networks
• Quantum advantage with shallow circuits
• A generative modeling approach for benchmarking and training shallow quantum circuits
• Quantum Boltzmann Machine
• The Expressive Power of Parameterized Quantum Circuits
• Opportunities and challenges for quantum-assisted machine learning in near-term quantum computers
• Quantum simulation of time-dependent Hamiltonians and the convenient illusion of Hilbert space
• Unsupervised Generative Modeling Using Matrix Product States
• Computational power of correlations
• Quantum circuits with uniformly controlled one-qubit gates
• The Born Supremacy: Quantum Advantage and Training of an Ising Born Machine
• Entanglement Devised Barren Plateau Mitigation
• Contextuality as a resource for models of quantum computation on qubits
• Barren plateaus preclude learning scramblers
• Quantum Inference on Bayesian Networks
• Learning Relevant Features of Data with Multi-scale Tensor Networks
• Quantum Supremacy for Simulating A Translation-Invariant Ising Spin Model
• Quantum Circuits with Unbounded Fan-out
• On the Quantum versus Classical Learnability of Discrete Distributions
• Matrix Product Operators for Sequence to Sequence Learning
• Contextuality as a resource for measurement-based quantum computation beyond qubits
• Classical simulation of quantum computation, the Gottesman-Knill theorem, and slightly beyond
• Modeling Pauli measurements on graph states with nearest-neighbor classical communication
• Stochastic Matrix Product States
• Representing probabilistic data via ontological models
• Contextuality bounds the efficiency of classical simulation of quantum processes
• No Free Lunch for Quantum Machine Learning
• A simple demonstration of Bell's theorem involving two observers and no probabilities or inequalities

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• Generative Quantum Learning of Joint Probability Distribution Functions
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• Interpretable Quantum Advantage in Neural Sequence Learning
• A performance characterization of quantum generative models
• Learning shallow quantum circuits
• Tensor networks for interpretable and efficient quantum-inspired machine learning
• Experimental test of high-dimensional quantum contextuality based on contextuality concentration
• Towards AutoQML: A Cloud-Based Automated Circuit Architecture Search Framework
• Application-Oriented Benchmarking of Quantum Generative Learning Using QUARK
• Decoherence Effects in a Three-Level System under Gaussian Process
• Robust Quantum Reservoir Computing for Molecular Property Prediction
• Quantum delegated and federated learning via quantum homomorphic encryption
• Quantum Inception Score
• Tensor networks and efficient descriptions of classical data
• Probabilistic Graphical Models and Tensor Networks: A Hybrid Framework
• Bosonic Indistinguishability-Dependent Contextuality
• Sampling Problems on a Quantum Computer
• Probing many-body Bell correlation depth with superconducting qubits
• Contextuality of Quantum Error-Correcting Codes
• Quantum Curriculum Learning
• ORQVIZ: Visualizing High-Dimensional Landscapes in Variational Quantum Algorithms
• No-go theorem for environment-assisted invariance in non-unitary dynamics
• Demonstration of sequential processors with quantum advantage and analysis of classical performance limits
• Quantum-assisted tracer dispersion in turbulent shear flow
• Information Processing in Quantum Thermodynamic Systems: an Autonomous Hamiltonian Approach
• Quantum Machine Learning for Climate Modelling
• k-Contextuality as a Heuristic for Memory Separations in Learning