Classical surrogates for quantum learning models

Abstract

The advent of noisy intermediate-scale quantum computers has put the search for possible applications to the forefront of quantum information science. One area where hopes for an advantage through near-term quantum computers are high is quantum machine learning, where variational quantum learning models based on parametrized quantum circuits are discussed. In this work, we introduce the concept of a classical surrogate, a classical model which can be efficiently obtained from a trained quantum learning model and reproduces its input-output relations. As inference can be performed classically, the existence of a classical surrogate greatly enhances the applicability of a quantum learning strategy. However, the classical surrogate also challenges possible advantages of quantum schemes. As it is possible to directly optimize the ansatz of the classical surrogate, they create a natural benchmark the quantum model has to outperform. We show that large classes of well-analyzed re-uploading models have a classical surrogate. We conducted numerical experiments and found that these quantum models show no advantage in performance or trainability in the problems we analyze. This leaves only generalization capability as possible point of quantum advantage and emphasizes the dire need for a better understanding of inductive biases of quantum learning models.

4 pages, 3 figures

References in corpus (8)

• Noisy intermediate-scale quantum (NISQ) algorithms
• An introduction to quantum machine learning
• Cost Function Dependent Barren Plateaus in Shallow Parametrized Quantum Circuits
• The effect of data encoding on the expressive power of variational quantum machine learning models
• A rigorous and robust quantum speed-up in supervised machine learning
• Exploring entanglement and optimization within the Hamiltonian Variational Ansatz
• On the Quantum versus Classical Learnability of Discrete Distributions
• Completely Quantum Neural Networks

Cited by in corpus (31)

• Does provable absence of barren plateaus imply classical simulability?
• Shadows of quantum machine learning
• Quantum machine learning of large datasets using randomized measurements
• Quantum Machine Learning for Digital Health? A Systematic Review
• Quantum Deep Reinforcement Learning for Robot Navigation Tasks
• On fundamental aspects of quantum extreme learning machines
• Quantum Convolutional Neural Networks are Effectively Classically Simulable
• Dequantizing quantum machine learning models using tensor networks
• Lie-algebraic classical simulations for quantum computing
• Potential and limitations of random Fourier features for dequantizing quantum machine learning
• On the expressivity of embedding quantum kernels
• Opportunities and challenges of quantum computing for climate modelling
• Constrained and Vanishing Expressivity of Quantum Fourier Models
• Barren plateaus are swamped with traps
• Quantum continual learning on a programmable superconducting processor
• Gradients and frequency profiles of quantum re-uploading models
• Efficient Learning for Linear Properties of Bounded-Gate Quantum Circuits
• Quantum computing for genomics: conceptual challenges and practical perspectives
• Quantum Computing for Data Centric Engineering and Science
• Efficient quantum-enhanced classical simulation for patches of quantum landscapes
• Pitfalls when tackling the exponential concentration of parameterized quantum models
• Learning unitaries with quantum statistical queries
• Learning Fourier series with parametrized quantum circuits
• Building Continuous Quantum-Classical Bayesian Neural Networks for a Classical Clinical Dataset
• Artificial intelligence for representing and characterizing quantum systems
• When Quantum and Classical Models Disagree: Learning Beyond Minimum Norm Least Square
• Quantum feature-map learning with reduced resource overhead
• Gradient Scalability and Taylor Surrogation of Quantum Cost Landscapes
• Quantum Machine Learning for Climate Modelling
• Interpolation-based coordinate descent method for parameterized quantum circuits
• New perspectives on quantum kernels through the lens of entangled tensor kernels