# Fock State-enhanced Expressivity of Quantum Machine Learning Models

arXiv: https://arxiv.org/abs/2107.05224 · HTML: https://mlsanity.com/paper/2107.05224/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 111 references that are in the map.
- First posted on arXiv 12 Jul 2021.

## Builds on (most cited first, 25 of 25)

- [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)
- [Quantum Machine Learning](https://mlsanity.com/paper/1611.09347/) (2016)
- [A rigorous and robust quantum speed-up in supervised machine learning](https://mlsanity.com/paper/2010.02174/) (2020)
- [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)
- [Photonics for artificial intelligence and neuromorphic computing](https://mlsanity.com/paper/2011.00111/) (2020)
- [Entanglement Induced Barren Plateaus](https://mlsanity.com/paper/2010.15968/) (2020)
- [Encoding-dependent generalization bounds for parametrized quantum circuits](https://mlsanity.com/paper/2106.03880/) (2021)
- [Effect of barren plateaus on gradient-free optimization](https://mlsanity.com/paper/2011.12245/) (2020)
- [Continuous-variable quantum neural networks](https://mlsanity.com/paper/1806.06871/) (2018)
- [Universal Approximation Property of Quantum Machine Learning Models in Quantum-Enhanced Feature Spaces](https://mlsanity.com/paper/2009.00298/) (2020)
- [Towards understanding the power of quantum kernels in the NISQ era](https://mlsanity.com/paper/2103.16774/) (2021)
- [Machine learning & artificial intelligence in the quantum domain](https://mlsanity.com/paper/1709.02779/) (2017)
- [Quantum principal component analysis only achieves an exponential speedup because of its state preparation assumptions](https://mlsanity.com/paper/1811.00414/) (2018)
- [Experimental kernel-based quantum machine learning in finite feature space](https://mlsanity.com/paper/1906.04137/) (2019)
- [Generalization in Quantum Machine Learning: a Quantum Information Perspective](https://mlsanity.com/paper/2102.08991/) (2021)
- [Learning with Optimized Random Features: Exponential Speedup by Quantum Machine Learning without Sparsity and Low-Rank Assumptions](https://mlsanity.com/paper/2004.10756/) (2020)
- [Exponential Error Convergence in Data Classification with Optimized Random Features: Acceleration by Quantum Machine Learning](https://mlsanity.com/paper/2106.09028/) (2021)
- [Quantum machine learning with adaptive linear optics](https://mlsanity.com/paper/2102.04579/) (2021)

## Built on by (most cited first, 11 of 11)

- [Exponential concentration in quantum kernel methods](https://mlsanity.com/paper/2208.11060/) (2022)
- [An exponentially-growing family of universal quantum circuits](https://mlsanity.com/paper/2212.00736/) (2022)
- [Expressibility-induced Concentration of Quantum Neural Tangent Kernels](https://mlsanity.com/paper/2311.04965/) (2023)
- [Unleashing the Expressive Power of Pulse-Based Quantum Neural Networks](https://mlsanity.com/paper/2402.02880/) (2024)
- [Spectral invariance and maximality properties of the frequency spectrum of quantum neural networks](https://mlsanity.com/paper/2402.14515/) (2024)
- [Exact gradients for linear optics with single photons](https://mlsanity.com/paper/2409.16369/) (2024)
- [MerLin: A Discovery Engine for Photonic and Hybrid Quantum Machine Learning](https://mlsanity.com/paper/2602.11092/) (2026)
- [Photonic Quantum Computers](https://mlsanity.com/paper/2409.08229/) (2024)
- [Photonic Quantum Computing For Polymer Classification](https://mlsanity.com/paper/2211.12207/) (2022)
- [On the explainability of quantum neural networks based on variational quantum circuits](https://mlsanity.com/paper/2301.05549/) (2023)
- [Exploring polymer classification with a hybrid single-photon quantum approach](https://mlsanity.com/paper/2512.18125/) (2025)

## Abstract (arXiv)

The data-embedding process is one of the bottlenecks of quantum machine learning, potentially negating any quantum speedups. In light of this, more effective data-encoding strategies are necessary. We propose 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. The expressive power of the circuit can be controlled via the number of input photons. Our work shed some light on the unique advantages offers by quantum photonics on the expressive power of quantum machine learning models. By leveraging the photon-number dependent expressive power, we propose three different noisy intermediate-scale quantum-compatible binary classification methods with different scaling of required resources suitable for different supervised classification tasks.