# Subtleties in the trainability of quantum machine learning models

@article{Thanasilp2021SubtletiesIT, title={Subtleties in the trainability of quantum machine learning models}, author={Supanut Thanasilp and Samson Wang and Nhat A. Nghiem and Patrick J. Coles and Mar{\'i}a Cerezo}, journal={ArXiv}, year={2021}, volume={abs/2110.14753} }

A new paradigm for data science has emerged, with quantum data, quantum models, and quantum computational devices. This ﬁeld, called Quantum Machine Learning (QML), aims to achieve a speedup over traditional machine learning for data analysis. However, its success usually hinges on eﬃciently training the parameters in quantum neural networks, and the ﬁeld of QML is still lacking theoretical scaling results for their trainability. Some trainability results have been proven for a closely related…

## 13 Citations

### Exponential concentration and untrainability in quantum kernel methods

- Computer ScienceArXiv
- 2022

This work shows that, under certain conditions, values of quantum kernels over diﬀerent input data can be exponentially concentrated towards some value, leading to an exponential scaling of the number of measurements required for successful training.

### Theoretical Guarantees for Permutation-Equivariant Quantum Neural Networks

- Computer ScienceArXiv
- 2022

This work provides the first theoretical guarantees for equivariant QNNs, thus indicating the extreme power and potential of GQML.

### Challenges and opportunities in quantum machine learning

- Computer Science, PhysicsNature Computational Science
- 2022

Current methods and applications for quantum machine learning are reviewed, including differences between quantum and classical machine learning, with a focus on quantum neural networks and quantum deep learning.

### Optimisation-free Classification and Density Estimation with Quantum Circuits

- Computer Science, PhysicsQuantum Mach. Intell.
- 2022

A variational quantum circuit approach that could leverage quantum advantage for the implementation of a novel machine learning framework for probability density estimation and classiﬁcation using quantum circuits is discussed.

### Fock state-enhanced expressivity of quantum machine learning models

- Computer Science, Physics2021 Conference on Lasers and Electro-Optics (CLEO)
- 2021

A photonic-based bosonic data-encoding scheme that embeds classical data points using fewer encoding layers and circumventing the need for nonlinear optical components by mapping the data points into the high-dimensional Fock space is proposed.

### Exponential data encoding for quantum supervised learning

- Computer SciencePhysical Review A
- 2023

It is numerically demonstrated that even exponential-data-encoding circuits with single-layer training modules can generally express functions that lie outside the classically-expressible region, thereby supporting the practical beneﬁts of such a resource advantage.

### Quantum Mixed State Compiling

- Computer Science
- 2022

This work presents a variational quantum algorithm (VQA) to learn mixed states which is suitable for near-term hardware and investigates the e-cacy of the algorithm through extensive numerical implementations, showing that typical random states and thermal states of many body systems may be learnt this way.

### Diagnosing Barren Plateaus with Tools from Quantum Optimal Control

- MathematicsQuantum
- 2022

Variational Quantum Algorithms (VQAs) have received considerable attention due to their potential for achieving near-term quantum advantage. However, more work is needed to understand their…

### Generalization in quantum machine learning from few training data

- Computer ScienceNature Communications
- 2022

This work provides a comprehensive study of generalization performance in QML after training on a limited number N of training data points, and reports rigorous bounds on the generalisation error in variational QML, confirming how known implementable models generalize well from an efficient amount ofTraining data.

### Equivalence of quantum barren plateaus to cost concentration and narrow gorges

- PhysicsQuantum Science and Technology
- 2022

This work analytically proves the connection between three different landscape features that have been observed for PQCs: exponentially vanishing gradients, exponential cost concentration about the mean, and the exponential narrowness of minina.

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