Shadows of quantum machine learning

Abstract

Quantum machine learning is often highlighted as one of the most promising practical applications for which quantum computers could provide a computational advantage. However, a major obstacle to the widespread use of quantum machine learning models in practice is that these models, even once trained, still require access to a quantum computer in order to be evaluated on new data. To solve this issue, we introduce a new class of quantum models where quantum resources are only required during training, while the deployment of the trained model is classical. Specifically, the training phase of our models ends with the generation of a 'shadow model' from which the classical deployment becomes possible. We prove that: i) this class of models is universal for classically-deployed quantum machine learning; ii) it does have restricted learning capacities compared to 'fully quantum' models, but nonetheless iii) it achieves a provable learning advantage over fully classical learners, contingent on widely-believed assumptions in complexity theory. These results provide compelling evidence that quantum machine learning can confer learning advantages across a substantially broader range of scenarios, where quantum computers are exclusively employed during the training phase. By enabling classical deployment, our approach facilitates the implementation of quantum machine learning models in various practical contexts.

7 + 16 pages, 5 figures; changes in the main text, added content in the appendix

References in corpus (22)

• Quantum Machine Learning
• Variational Quantum Algorithms
• Supervised learning with quantum enhanced feature spaces
• Noisy intermediate-scale quantum (NISQ) algorithms
• Quantum machine learning in feature Hilbert spaces
• Predicting Many Properties of a Quantum System from Very Few Measurements
• Parameterized quantum circuits as machine learning models
• Circuit-centric quantum classifiers
• The effect of data encoding on the expressive power of variational quantum machine learning models
• Efficient quantum state tomography
• A rigorous and robust quantum speed-up in supervised machine learning
• Differentiable Learning of Quantum Circuit Born Machine
• Training of Quantum Circuits on a Hybrid Quantum Computer
• Quantum machine learning beyond kernel methods
• Quantum agents in the Gym: a variational quantum algorithm for deep Q-learning
• Classical Shadow Tomography with Locally Scrambled Quantum Dynamics
• On the Quantum versus Classical Learnability of Discrete Distributions
• Matchgate Shadows for Fermionic Quantum Simulation
• Quantum machine learning of large datasets using randomized measurements
• Classical surrogates for quantum learning models
• Structural risk minimization for quantum linear classifiers
• Multidimensional Fourier series with quantum circuits

Cited by in corpus (23)

• Barren Plateaus in Variational Quantum Computing
• Does provable absence of barren plateaus imply classical simulability?
• Demonstration of Robust and Efficient Quantum Property Learning with Shallow Shadows
• Quantum Convolutional Neural Networks are Effectively Classically Simulable
• Lie-algebraic classical simulations for quantum computing
• Training robust and generalizable quantum models
• Potential and limitations of random Fourier features for dequantizing quantum machine learning
• Opportunities and challenges of quantum computing for climate modelling
• Constrained and Vanishing Expressivity of Quantum Fourier Models
• Quantum Supervised Learning
• Observing Schrödinger's Cat with Artificial Intelligence: Emergent Classicality from Information Bottleneck
• Quantum delegated and federated learning via quantum homomorphic encryption
• Efficient quantum-enhanced classical simulation for patches of quantum landscapes
• Learning unitaries with quantum statistical queries
• Quantum Neural Networks in Practice: A Comparative Study with Classical Models from Standard Data Sets to Industrial Images
• Learning Fourier series with parametrized quantum circuits
• Learning Density Functionals from Noisy Quantum Data
• Holographic Classical Shadow Tomography
• i-QLS: Quantum-supported Algorithm for Least Squares Optimization in Non-Linear Regression
• When Quantum and Classical Models Disagree: Learning Beyond Minimum Norm Least Square
• Quantum Machine Learning for Climate Modelling
• Learning complexity gradually in quantum machine learning models
• Classical Shadows with Improved Median-of-Means Estimation