# Classical surrogates for quantum learning models

arXiv: https://arxiv.org/abs/2206.11740 · HTML: https://mlsanity.com/paper/2206.11740/

## Key facts

- Cited by 39 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 12 references that are in the map.
- First posted on arXiv 23 Jun 2022.

## Builds on (most cited first, 6 of 6)

- [Quantum Machine Learning](https://mlsanity.com/paper/1611.09347/) (2016)
- [A rigorous and robust quantum speed-up in supervised machine learning](https://mlsanity.com/paper/2010.02174/) (2020)
- [Encoding-dependent generalization bounds for parametrized quantum circuits](https://mlsanity.com/paper/2106.03880/) (2021)
- [On the Quantum versus Classical Learnability of Discrete Distributions](https://mlsanity.com/paper/2007.14451/) (2020)
- [Machine learning & artificial intelligence in the quantum domain](https://mlsanity.com/paper/1709.02779/) (2017)
- [Input Redundancy for Parameterized Quantum Circuits](https://mlsanity.com/paper/1901.11434/) (2019)

## Built on by (most cited first, 30 of 39)

- [Better than classical? The subtle art of benchmarking quantum machine learning models](https://mlsanity.com/paper/2403.07059/) (2024)
- [Does provable absence of barren plateaus imply classical simulability?](https://mlsanity.com/paper/2312.09121/) (2023)
- [Quantum Convolutional Neural Networks are Effectively Classically Simulable](https://mlsanity.com/paper/2408.12739/) (2024)
- [Learning to predict arbitrary quantum processes](https://mlsanity.com/paper/2210.14894/) (2022)
- [Shadows of quantum machine learning](https://mlsanity.com/paper/2306.00061/) (2023)
- [On the relation between trainability and dequantization of variational quantum learning models](https://mlsanity.com/paper/2406.07072/) (2024)
- [Potential and limitations of random Fourier features for dequantizing quantum machine learning](https://mlsanity.com/paper/2309.11647/) (2023)
- [Problem-Dependent Power of Quantum Neural Networks on Multi-Class Classification](https://mlsanity.com/paper/2301.01597/) (2022)
- [On fundamental aspects of quantum extreme learning machines](https://mlsanity.com/paper/2312.15124/) (2023)
- [On the expressivity of embedding quantum kernels](https://mlsanity.com/paper/2309.14419/) (2023)
- [A Comparative Analysis of Adversarial Robustness for Quantum and Classical Machine Learning Models](https://mlsanity.com/paper/2404.16154/) (2024)
- [Artificial intelligence for representing and characterizing quantum systems](https://mlsanity.com/paper/2509.04923/) (2025)
- [Efficient Learning for Linear Properties of Bounded-Gate Quantum Circuits](https://mlsanity.com/paper/2408.12199/) (2024)
- [Quantum computing and artificial intelligence: status and perspectives](https://mlsanity.com/paper/2505.23860/) (2025)
- [Learning unitaries with quantum statistical queries](https://mlsanity.com/paper/2310.02254/) (2023)
- [Building Continuous Quantum-Classical Bayesian Neural Networks for a Classical Clinical Dataset](https://mlsanity.com/paper/2406.06307/) (2024)
- [Prospects for quantum advantage in machine learning from the representability of functions](https://mlsanity.com/paper/2512.15661/) (2025)
- [Spectral methods: crucial for machine learning, natural for quantum computers?](https://mlsanity.com/paper/2603.24654/) (2026)
- [Post-variational quantum neural networks](https://mlsanity.com/paper/2307.10560/) (2023)
- [Prospects of Privacy Advantage in Quantum Machine Learning](https://mlsanity.com/paper/2405.08801/) (2024)
- [Exploiting the equivalence between quantum neural networks and perceptrons](https://mlsanity.com/paper/2407.04371/) (2024)
- [Quantum Supervised Learning](https://mlsanity.com/paper/2407.17161/) (2024)
- [Concept learning of parameterized quantum models from limited measurements](https://mlsanity.com/paper/2408.05116/) (2024)
- [Demonstration of Efficient Predictive Surrogates for Large-scale Quantum Processors](https://mlsanity.com/paper/2507.17470/) (2025)
- [Multiple Embeddings for Quantum Machine Learning](https://mlsanity.com/paper/2503.22758/) (2025)
- [A PAC-Bayesian approach to generalization for quantum models](https://mlsanity.com/paper/2603.22964/) (2026)
- [Enhancing the Scalability of Classical Surrogates for Real-World Quantum Machine Learning Applications](https://mlsanity.com/paper/2508.06131/) (2025)
- [Quantum feature-map learning with reduced resource overhead](https://mlsanity.com/paper/2510.03389/) (2025)
- [Limits of quantum generative models with classical sampling hardness](https://mlsanity.com/paper/2512.24801/) (2025)
- [Theory and interpretability of Quantum Extreme Learning Machines: a Pauli-transfer matrix approach](https://mlsanity.com/paper/2602.18377/) (2026)

## Abstract (arXiv)

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.