# On the relation between trainability and dequantization of variational quantum learning models

arXiv: https://arxiv.org/abs/2406.07072 · HTML: https://mlsanity.com/paper/2406.07072/

## Key facts

- Cited by 25 papers in the map (data through 14 Oct 2026).
- Builds on 40 of its 88 references that are in the map.
- First posted on arXiv 11 Jun 2024.

## Builds on (most cited first, 30 of 40)

- [Variational Quantum Algorithms](https://mlsanity.com/paper/2012.09265/) (2020)
- [Supervised learning with quantum enhanced feature spaces](https://mlsanity.com/paper/1804.11326/) (2018)
- [Barren plateaus in quantum neural network training landscapes](https://mlsanity.com/paper/1803.11173/) (2018)
- [The power of quantum neural networks](https://mlsanity.com/paper/2011.00027/) (2020)
- [Power of data in quantum machine learning](https://mlsanity.com/paper/2011.01938/) (2020)
- [The effect of data encoding on the expressive power of variational quantum machine learning models](https://mlsanity.com/paper/2008.08605/) (2020)
- [Parameterized quantum circuits as machine learning models](https://mlsanity.com/paper/1906.07682/) (2019)
- [A rigorous and robust quantum speed-up in supervised machine learning](https://mlsanity.com/paper/2010.02174/) (2020)
- [Predicting Many Properties of a Quantum System from Very Few Measurements](https://mlsanity.com/paper/2002.08953/) (2020)
- [Generalization in quantum machine learning from few training data](https://mlsanity.com/paper/2111.05292/) (2021)
- [Supervised quantum machine learning models are kernel methods](https://mlsanity.com/paper/2101.11020/) (2021)
- [Barren Plateaus in Variational Quantum Computing](https://mlsanity.com/paper/2405.00781/) (2024)
- [Absence of Barren Plateaus in Quantum Convolutional Neural Networks](https://mlsanity.com/paper/2011.02966/) (2020)
- [The Inductive Bias of Quantum Kernels](https://mlsanity.com/paper/2106.03747/) (2021)
- [Encoding-dependent generalization bounds for parametrized quantum circuits](https://mlsanity.com/paper/2106.03880/) (2021)
- [Does provable absence of barren plateaus imply classical simulability?](https://mlsanity.com/paper/2312.09121/) (2023)
- [A quantum-inspired classical algorithm for recommendation systems](https://mlsanity.com/paper/1807.04271/) (2018)
- [Training Quantum Embedding Kernels on Near-Term Quantum Computers](https://mlsanity.com/paper/2105.02276/) (2021)
- [On the Quantum versus Classical Learnability of Discrete Distributions](https://mlsanity.com/paper/2007.14451/) (2020)
- [Equivalence of quantum barren plateaus to cost concentration and narrow gorges](https://mlsanity.com/paper/2104.05868/) (2021)
- [Theoretical Guarantees for Permutation-Equivariant Quantum Neural Networks](https://mlsanity.com/paper/2210.09974/) (2022)
- [Understanding quantum machine learning also requires rethinking generalization](https://mlsanity.com/paper/2306.13461/) (2023)
- [Escaping from the Barren Plateau via Gaussian Initializations in Deep Variational Quantum Circuits](https://mlsanity.com/paper/2203.09376/) (2022)
- [Classical surrogates for quantum learning models](https://mlsanity.com/paper/2206.11740/) (2022)
- [Subtleties in the trainability of quantum machine learning models](https://mlsanity.com/paper/2110.14753/) (2021)
- [Shadows of quantum machine learning](https://mlsanity.com/paper/2306.00061/) (2023)
- [Pseudo-dimension of quantum circuits](https://mlsanity.com/paper/2002.01490/) (2020)
- [Exponential separations between classical and quantum learners](https://mlsanity.com/paper/2306.16028/) (2023)
- [Structural risk minimization for quantum linear classifiers](https://mlsanity.com/paper/2105.05566/) (2021)
- [Exponentially Many Local Minima in Quantum Neural Networks](https://mlsanity.com/paper/2110.02479/) (2021)

## Built on by (most cited first, 25 of 25)

- [Quantum Convolutional Neural Networks are Effectively Classically Simulable](https://mlsanity.com/paper/2408.12739/) (2024)
- [A Primer on Quantum Machine Learning](https://mlsanity.com/paper/2511.15969/) (2025)
- [Exponential quantum advantage in processing massive classical data](https://mlsanity.com/paper/2604.07639/) (2026)
- [Artificial intelligence for representing and characterizing quantum systems](https://mlsanity.com/paper/2509.04923/) (2025)
- [Double descent in quantum kernel methods](https://mlsanity.com/paper/2501.10077/) (2025)
- [Opportunities and limitations of explaining quantum machine learning](https://mlsanity.com/paper/2412.14753/) (2024)
- [Quantum computing and artificial intelligence: status and perspectives](https://mlsanity.com/paper/2505.23860/) (2025)
- [Entanglement-induced provable and robust quantum learning advantages](https://mlsanity.com/paper/2410.03094/) (2024)
- [Prospects for quantum advantage in machine learning from the representability of functions](https://mlsanity.com/paper/2512.15661/) (2025)
- [On the similarity of bandwidth-tuned quantum kernels and classical kernels](https://mlsanity.com/paper/2503.05602/) (2025)
- [TQml Simulator: optimized simulation of quantum machine learning](https://mlsanity.com/paper/2506.04891/) (2025)
- [Iterative Quantum Feature Maps](https://mlsanity.com/paper/2506.19461/) (2025)
- [How to find expressible and trainable parameterized quantum circuits?](https://mlsanity.com/paper/2603.14451/) (2026)
- [A PAC-Bayesian approach to generalization for quantum models](https://mlsanity.com/paper/2603.22964/) (2026)
- [Quantum Curriculum Learning](https://mlsanity.com/paper/2407.02419/) (2024)
- [Enhancing the Scalability of Classical Surrogates for Real-World Quantum Machine Learning Applications](https://mlsanity.com/paper/2508.06131/) (2025)
- [Limits of quantum generative models with classical sampling hardness](https://mlsanity.com/paper/2512.24801/) (2025)
- [Optimal algorithmic complexity of inference in quantum kernel methods](https://mlsanity.com/paper/2604.15214/) (2026)
- [Exploring Channel Distinguishability in Local Neighborhoods of the Model Space in Quantum Neural Networks](https://mlsanity.com/paper/2410.09470/) (2024)
- [The role of data-induced randomness in quantum machine learning classification tasks](https://mlsanity.com/paper/2411.19281/) (2024)
- [Variational decision diagrams for quantum-inspired machine learning applications](https://mlsanity.com/paper/2502.04271/) (2025)
- [Differential equation quantum solvers: engineering measurements to reduce cost](https://mlsanity.com/paper/2503.22656/) (2025)
- [Detecting underdetermination in parameterized quantum circuits](https://mlsanity.com/paper/2504.03315/) (2025)
- [Universality of Many-body Projected Ensemble for Learning Quantum Data Distribution](https://mlsanity.com/paper/2601.18637/) (2026)
- [QuPID: Quantum Parameter-Efficient Input-Dependent Retrieval Adaptation for Medical RAG](https://mlsanity.com/paper/2609.33351/) (2026)

## Abstract (arXiv)

The quest for successful variational quantum machine learning (QML) relies on the design of suitable parametrized quantum circuits (PQCs), as analogues to neural networks in classical machine learning. Successful QML models must fulfill the properties of trainability and non-dequantization, among others. Recent works have highlighted an intricate interplay between trainability and dequantization of such models, which is still unresolved. In this work we contribute to this debate from the perspective of machine learning, proving a number of results identifying, among others when trainability and non-dequantization are not mutually exclusive. We begin by providing a number of new somewhat broader definitions of the relevant concepts, compared to what is found in other literature, which are operationally motivated, and consistent with prior art. With these precise definitions given and motivated, we then study the relation between trainability and dequantization of variational QML. Next, we also discuss the degrees of "variationalness" of QML models, where we distinguish between models like the hardware efficient ansatz and quantum kernel methods. Finally, we introduce recipes for building PQC-based QML models which are both trainable and nondequantizable, and corresponding to different degrees of variationalness. We do not address the practical utility for such models. Our work however does point toward a way forward for finding more general constructions, for which finding applications may become feasible.