# Hybrid Quantum Neural Networks with Amplitude Encoding: Advancing Recovery Rate Predictions

arXiv: https://arxiv.org/abs/2501.15828 · HTML: https://mlsanity.com/paper/2501.15828/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 95 references that are in the map.
- First posted on arXiv 27 Jan 2025.

## Builds on (most cited first, 16 of 16)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017)
- [XGBoost: A Scalable Tree Boosting System](https://mlsanity.com/paper/1603.02754/) (2016)
- [Spectrally-normalized margin bounds for neural networks](https://mlsanity.com/paper/1706.08498/) (2017)
- [Supervised learning with quantum enhanced feature spaces](https://mlsanity.com/paper/1804.11326/) (2018)
- [FinBERT: Financial Sentiment Analysis with Pre-trained Language Models](https://mlsanity.com/paper/1908.10063/) (2019)
- [The power of quantum neural networks](https://mlsanity.com/paper/2011.00027/) (2020)
- [Parameterized quantum circuits as machine learning models](https://mlsanity.com/paper/1906.07682/) (2019)
- [Parseval Networks: Improving Robustness to Adversarial Examples](https://mlsanity.com/paper/1704.08847/) (2017)
- [Cheap Orthogonal Constraints in Neural Networks: A Simple Parametrization of the Orthogonal and Unitary Group](https://mlsanity.com/paper/1901.08428/) (2019)
- [A Simple Way to Initialize Recurrent Networks of Rectified Linear Units](https://mlsanity.com/paper/1504.00941/) (2015)
- [Orthogonal Convolutional Neural Networks](https://mlsanity.com/paper/1911.12207/) (2019)
- [Best Subset Selection via a Modern Optimization Lens](https://mlsanity.com/paper/1507.03133/) (2015)
- [Orthogonal Deep Neural Networks](https://mlsanity.com/paper/1905.05929/) (2019)
- [Quantum Data Encoding: A Comparative Analysis of Classical-to-Quantum Mapping Techniques and Their Impact on Machine Learning Accuracy](https://mlsanity.com/paper/2311.10375/) (2023)
- [Recurrent Orthogonal Networks and Long-Memory Tasks](https://mlsanity.com/paper/1602.06662/) (2016)

## Built on by (most cited first, 2 of 2)

- [The Role of Quantum in Hybrid Quantum-Classical Neural Networks: A Realistic Assessment](https://mlsanity.com/paper/2601.04732/) (2026)
- [SAFE Quantum Machine Learning with Variational Quantum Classifiers](https://mlsanity.com/paper/2605.16067/) (2026)

## Abstract (arXiv)

Recovery rate prediction plays a pivotal role in bond investment strategies by enhancing risk assessment, optimizing portfolio allocation, improving pricing accuracy, and supporting effective credit risk management. However, accurate forecasting remains challenging due to complex nonlinear dependencies, high-dimensional feature spaces, and limited sample sizes-conditions under which classical machine learning models are prone to overfitting. We propose a hybrid Quantum Machine Learning (QML) model with Amplitude Encoding, leveraging the unitarity constraint of Parametrized Quantum Circuits (PQC) and the exponential data compression capability of qubits. We evaluate the model on a global recovery rate dataset comprising 1,725 observations and 256 features from 1996 to 2023. Our hybrid method significantly outperforms both classical neural networks and QML models using Angle Encoding, achieving a lower Root Mean Squared Error (RMSE) of 0.228, compared to 0.246 and 0.242, respectively. It also performs competitively with ensemble tree methods such as XGBoost. While practical implementation challenges remain for Noisy Intermediate-Scale Quantum (NISQ) hardware, our quantum simulation and preliminary results on noisy simulators demonstrate the promise of hybrid quantum-classical architectures in enhancing the accuracy and robustness of recovery rate forecasting. These findings illustrate the potential of quantum machine learning in shaping the future of credit risk prediction.