# Exploring Channel Distinguishability in Local Neighborhoods of the Model Space in Quantum Neural Networks

arXiv: https://arxiv.org/abs/2410.09470 · HTML: https://mlsanity.com/paper/2410.09470/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 30 of its 72 references that are in the map.
- First posted on arXiv 12 Oct 2024.

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

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Variational Quantum Algorithms](https://mlsanity.com/paper/2012.09265/) (2020)
- [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)
- [The effect of data encoding on the expressive power of variational quantum machine learning models](https://mlsanity.com/paper/2008.08605/) (2020)
- [On the Expressive Power of Deep Neural Networks](https://mlsanity.com/paper/1606.05336/) (2016)
- [Supervised quantum machine learning models are kernel methods](https://mlsanity.com/paper/2101.11020/) (2021)
- [Noise-Induced Barren Plateaus in Variational Quantum Algorithms](https://mlsanity.com/paper/2007.14384/) (2020)
- [Connecting ansatz expressibility to gradient magnitudes and barren plateaus](https://mlsanity.com/paper/2101.02138/) (2021)
- [Flipout: Efficient Pseudo-Independent Weight Perturbations on Mini-Batches](https://mlsanity.com/paper/1803.04386/) (2018)
- [Barren Plateaus in Variational Quantum Computing](https://mlsanity.com/paper/2405.00781/) (2024)
- [Parametric Noise Injection: Trainable Randomness to Improve Deep Neural Network Robustness against Adversarial Attack](https://mlsanity.com/paper/1811.09310/) (2018)
- [Entanglement Induced Barren Plateaus](https://mlsanity.com/paper/2010.15968/) (2020)
- [Theory of overparametrization in quantum neural networks](https://mlsanity.com/paper/2109.11676/) (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)
- [Backdooring Convolutional Neural Networks via Targeted Weight Perturbations](https://mlsanity.com/paper/1812.03128/) (2018)
- [Group-Invariant Quantum Machine Learning](https://mlsanity.com/paper/2205.02261/) (2022)
- [Equivalence of quantum barren plateaus to cost concentration and narrow gorges](https://mlsanity.com/paper/2104.05868/) (2021)
- [Representation Theory for Geometric Quantum Machine Learning](https://mlsanity.com/paper/2210.07980/) (2022)
- [Don't Lie to Me! Robust and Efficient Explainability with Verified Perturbation Analysis](https://mlsanity.com/paper/2202.07728/) (2022)
- [On the relation between trainability and dequantization of variational quantum learning models](https://mlsanity.com/paper/2406.07072/) (2024)
- [BEINIT: Avoiding Barren Plateaus in Variational Quantum Algorithms](https://mlsanity.com/paper/2204.13751/) (2022)
- [A semi-agnostic ansatz with variable structure for quantum machine learning](https://mlsanity.com/paper/2103.06712/) (2021)
- [NeuralSens: Sensitivity Analysis of Neural Networks](https://mlsanity.com/paper/2002.11423/) (2020)
- [Variational quantum simulation: a case study for understanding warm starts](https://mlsanity.com/paper/2404.10044/) (2024)
- [Stability of Graph Convolutional Neural Networks through the lens of small perturbation analysis](https://mlsanity.com/paper/2312.12934/) (2023)
- [Symmetry breaking in geometric quantum machine learning in the presence of noise](https://mlsanity.com/paper/2401.10293/) (2024)
- [Unleashing the Expressive Power of Pulse-Based Quantum Neural Networks](https://mlsanity.com/paper/2402.02880/) (2024)
- [On Optimizing Hyperparameters for Quantum Neural Networks](https://mlsanity.com/paper/2403.18579/) (2024)

## Abstract (arXiv)

With the increasing interest in Quantum Machine Learning, Quantum Neural Networks (QNNs) have emerged and gained significant attention. These models have, however, been shown to be notoriously difficult to train, which we hypothesize is partially due to the architectures, called ansatzes, that are hardly studied at this point. Therefore, in this paper, we take a step back and analyze ansatzes. We initially consider their expressivity, i.e., the space of operations they are able to express, and show that the closeness to being a 2-design, the primarily used measure, fails at capturing this property. Hence, we look for alternative ways to characterize ansatzes by considering the local neighborhood of the model space, in particular, analyzing model distinguishability upon small perturbation of parameters. We derive an upper bound on their distinguishability, showcasing that QNNs with few parameters are hardly discriminable upon update. Our numerical experiments support our bounds and further indicate that there is a significant degree of variability, which stresses the need for warm-starting or clever initialization. Altogether, our work provides an ansatz-centric perspective on training dynamics and difficulties in QNNs, ultimately suggesting that iterative training of small quantum models may not be effective, which contrasts their initial motivation.