# Quantum-data-driven dynamical transition in quantum learning

arXiv: https://arxiv.org/abs/2410.01955 · HTML: https://mlsanity.com/paper/2410.01955/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 15 of its 50 references that are in the map.
- First posted on arXiv 2 Oct 2024.

## Builds on (most cited first, 15 of 15)

- [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)
- [Theory of overparametrization in quantum neural networks](https://mlsanity.com/paper/2109.11676/) (2021)
- [Continuous-variable quantum neural networks](https://mlsanity.com/paper/1806.06871/) (2018)
- [Representation Learning via Quantum Neural Tangent Kernels](https://mlsanity.com/paper/2111.04225/) (2021)
- [Subtleties in the trainability of quantum machine learning models](https://mlsanity.com/paper/2110.14753/) (2021)
- [Analytic theory for the dynamics of wide quantum neural networks](https://mlsanity.com/paper/2203.16711/) (2022)
- [Symmetric Pruning in Quantum Neural Networks](https://mlsanity.com/paper/2208.14057/) (2022)
- [Universal discriminative quantum neural networks](https://mlsanity.com/paper/1805.08654/) (2018)
- [Quantum Neural Network Classifiers: A Tutorial](https://mlsanity.com/paper/2206.02806/) (2022)
- [Laziness, Barren Plateau, and Noise in Machine Learning](https://mlsanity.com/paper/2206.09313/) (2022)
- [Analyzing Convergence in Quantum Neural Networks: Deviations from Neural Tangent Kernels](https://mlsanity.com/paper/2303.14844/) (2023)
- [Expressibility-induced Concentration of Quantum Neural Tangent Kernels](https://mlsanity.com/paper/2311.04965/) (2023)
- [Dynamical transition in controllable quantum neural networks with large depth](https://mlsanity.com/paper/2311.18144/) (2023)

## Abstract (arXiv)

Quantum neural networks, parameterized quantum circuits optimized under a specific cost function, provide a paradigm for achieving near-term quantum advantage in quantum information processing. Understanding QNN training dynamics is crucial for optimizing their performance, however, the role of quantum data in training for supervised learning such as classification and regression remains unclear. We reveal a quantum-data-driven dynamical transition where the target values and data determine the convergence of the training. Through analytical classification over the fixed points of the dynamical equation, we reveal a comprehensive `phase diagram' featuring seven distinct dynamics originating from a bifurcation with multiple codimension. Perturbative analyses identify both exponential and polynomial convergence class. We provide a non-perturbative theory to explain the transition via generalized restricted Haar ensemble. The analytical results are confirmed with numerical simulations and experimentation on IBM quantum devices. Our findings provide guidance on constructing the cost function to accelerate convergence in QNN training.