# Unleashing the Expressive Power of Pulse-Based Quantum Neural Networks

arXiv: https://arxiv.org/abs/2402.02880 · HTML: https://mlsanity.com/paper/2402.02880/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 49 references that are in the map.
- First posted on arXiv 5 Feb 2024.

## Builds on (most cited first, 17 of 17)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [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)
- [The effect of data encoding on the expressive power of variational quantum machine learning models](https://mlsanity.com/paper/2008.08605/) (2020)
- [Supervised quantum machine learning models are kernel methods](https://mlsanity.com/paper/2101.11020/) (2021)
- [Quantum advantage in learning from experiments](https://mlsanity.com/paper/2112.00778/) (2021)
- [Universal Approximation Property of Quantum Machine Learning Models in Quantum-Enhanced Feature Spaces](https://mlsanity.com/paper/2009.00298/) (2020)
- [Pseudo-dimension of quantum circuits](https://mlsanity.com/paper/2002.01490/) (2020)
- [On the statistical complexity of quantum circuits](https://mlsanity.com/paper/2101.06154/) (2021)
- [Power and limitations of single-qubit native quantum neural networks](https://mlsanity.com/paper/2205.07848/) (2022)
- [Universal discriminative quantum neural networks](https://mlsanity.com/paper/1805.08654/) (2018)
- [Fock State-enhanced Expressivity of Quantum Machine Learning Models](https://mlsanity.com/paper/2107.05224/) (2021)
- [Optimized Quantum Compilation for Near-Term Algorithms with OpenPulse](https://mlsanity.com/paper/2004.11205/) (2020)
- [Hybrid Gate-Pulse Model for Variational Quantum Algorithms](https://mlsanity.com/paper/2212.00661/) (2022)
- [Ensemble Control on Lie Groups](https://mlsanity.com/paper/2008.03243/) (2020)

## Built on by (most cited first, 4 of 4)

- [Barren Plateaus in Variational Quantum Computing](https://mlsanity.com/paper/2405.00781/) (2024)
- [Exploring Channel Distinguishability in Local Neighborhoods of the Model Space in Quantum Neural Networks](https://mlsanity.com/paper/2410.09470/) (2024)
- [On the Design of Expressive and Trainable Pulse-based Quantum Machine Learning Models](https://mlsanity.com/paper/2508.05559/) (2025)
- [Quantum SEDONet: Spectrally-Embedded Quantum Deep Operator Networks for Partial Differential Equations](https://mlsanity.com/paper/2608.27626/) (2026)

## Abstract (arXiv)

Quantum machine learning (QML) based on Noisy Intermediate-Scale Quantum (NISQ) devices hinges on the optimal utilization of limited quantum resources. While gate-based QML models are user-friendly for software engineers, their expressivity is restricted by the permissible circuit depth within a finite coherence time. In contrast, pulse-based models enable the construction of "infinitely" deep quantum neural networks within the same time, which may unleash greater expressive power for complex learning tasks. In this paper, this potential is investigated from the perspective of quantum control theory. We first indicate that the nonlinearity of pulse-based models comes from the encoding process that can be viewed as the continuous limit of data-reuploading in gate-based models. Subsequently, we prove that the pulse-based model can approximate arbitrary nonlinear functions when the underlying physical system is ensemble controllable. Under this condition, numerical simulations demonstrate the enhanced expressivity by either increasing the pulse length or the number of qubits. As anticipated, we show through numerical examples that the pulse-based model can unleash more expressive power compared to the gate-based model. These findings lay a theoretical foundation for understanding and designing expressive QML models using NISQ devices.