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Potential and limitations of random Fourier features for dequantizing quantum machine learning

arXiv 2309.11647 ↗First posted 20 Sep 2023quant-ph cs.LGcited by 22

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Abstract (arXiv)

Quantum machine learning is arguably one of the most explored applications of near-term quantum devices. Much focus has been put on notions of variational quantum machine learning where parameterized quantum circuits (PQCs) are used as learning models. These PQC models have a rich structure which suggests that they might be amenable to efficient dequantization via random Fourier features (RFF). In this work, we establish necessary and sufficient conditions under which RFF does indeed provide an efficient dequantization of variational quantum machine learning for regression. We build on these insights to make concrete suggestions for PQC architecture design, and to identify structures which are necessary for a regression problem to admit a potential quantum advantage via PQC based optimization.

Key facts. Cited by 22 papers in the map (data through 14 Oct 2026). Builds on 16 of its 42 references that are in the map. First posted on arXiv 20 Sep 2023.

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16 of 42 references.

References · 16

  1. 2020Variational Quantum Algorithmscited by 692
  2. 2020The effect of data encoding on the expressive power of variational quantum machine learning modelscited by 333
  3. 2019Parameterized quantum circuits as machine learning modelscited by 332
  4. 2021Supervised quantum machine learning models are kernel methodscited by 200
  5. 2016Generalization Properties of Learning with Random Featurescited by 164
  6. 2021Quantum machine learning beyond kernel methodscited by 92
  7. 2021Encoding-dependent generalization bounds for parametrized quantum circuitscited by 82
  8. 2015On the Error of Random Fourier Featurescited by 76
  9. 2022Exploiting symmetry in variational quantum machine learningcited by 69
  10. 2022Group-Invariant Quantum Machine Learningcited by 56
  11. 2019Expressive power of tensor-network factorizations for probabilistic modeling, with applications from hidden Markov models to quantum machine learningcited by 55
  12. 2022Classical surrogates for quantum learning modelscited by 39
4 more
  1. 2015Optimal Rates for Random Fourier Featurescited by 38
  2. 2019Input Redundancy for Parameterized Quantum Circuitscited by 33
  3. 2023Shadows of quantum machine learningcited by 31
  4. 2021Lower and Upper Bounds on the VC-Dimension of Tensor Network Modelscited by 1

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2023: 3; 2024: 5; 2025: 9; 2026: 5.

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  1. 2023Does provable absence of barren plateaus imply classical simulability?cited by 80
  2. 2024On the relation between trainability and dequantization of variational quantum learning modelscited by 25
  3. 2023On fundamental aspects of quantum extreme learning machinescited by 18
  4. 2023On the expressivity of embedding quantum kernelscited by 17
  5. 2024A Comparative Analysis of Adversarial Robustness for Quantum and Classical Machine Learning Modelscited by 12
  6. 2025A Primer on Quantum Machine Learningcited by 12
  7. 2025Artificial intelligence for representing and characterizing quantum systemscited by 10
  8. 2025Double descent in quantum kernel methodscited by 9
  9. 2024Efficient Learning for Linear Properties of Bounded-Gate Quantum Circuitscited by 7
  10. 2024Opportunities and limitations of explaining quantum machine learningcited by 7
  11. 2025Spectral Bias in Variational Quantum Machine Learningcited by 5
  12. 2025Prospects for quantum advantage in machine learning from the representability of functionscited by 4
10 more
  1. 2026Spectral methods: crucial for machine learning, natural for quantum computers?cited by 4
  2. 2024Prospects of Privacy Advantage in Quantum Machine Learningcited by 3
  3. 2025On the similarity of bandwidth-tuned quantum kernels and classical kernelscited by 3
  4. 2025Demonstration of Efficient Predictive Surrogates for Large-scale Quantum Processorscited by 3
  5. 2026Non-variational supervised quantum kernel methods: a reviewcited by 2
  6. 2025Enhancing the Scalability of Classical Surrogates for Real-World Quantum Machine Learning Applicationscited by 1
  7. 2026Theory and interpretability of Quantum Extreme Learning Machines: a Pauli-transfer matrix approachcited by 1
  8. 2026Optimal algorithmic complexity of inference in quantum kernel methodscited by 1
  9. 2025Connecting phases of matter to the flatness of the loss landscape in analog variational quantum algorithmscited by 0
  10. 2026Mitigating Bias in Low-SNR Financial Reinforcement Learning via Quantum Representationscited by 0

Similar, not cited

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  1. 2026A Quantum-Inspired Dequantization Method for Diagonally Weighted Matrix Functions: Application to Learning with Optimized Random Features
  2. 2024Discrete Randomized Smoothing Meets Quantum Computing
  3. 2026Comparing Classical and Quantum Variational Classifiers on the XOR Problem
  4. 2025Quantum Data Encoding and Variational Algorithms: A Framework for Hybrid Quantum Classical Machine Learning
  5. 2025Quantum Long Short-term Memory with Differentiable Architecture Search
  6. 2021Variational Quantum Classifiers Through the Lens of the Hessian
  7. 2023Robust Dequantization of the Quantum Singular value Transformation and Quantum Machine Learning Algorithms
  8. 2026Towards Surrogate Based Dequantization of Quantum Reinforcement Learning