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

Paper: arXiv 2501.15828

Abstract

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.

Complexity vs Empirical Score

• Math Complexity: 7.5/10
• Empirical Rigor: 8.0/10
• Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper employs advanced quantum mechanics and linear algebra (e.g., amplitude encoding, unitary constraints, Hilbert space), justifying a high math score; it also provides concrete empirical results with a specific dataset (1,725 observations, 256 features), comparative RMSE metrics against classical baselines (Neural Networks, XGBoost), and discussions on noisy simulators, making it highly backtest-ready.

Research Flowchart

  flowchart TD
  A["Research Goal<br>Predict Bond Recovery Rates<br>Improving Credit Risk Accuracy"] --> B["Dataset & Encoding<br>1,725 Observations<br>256 Features (1996-2023)<br>Amplitude Encoding"]
  
  B --> C{"Model Architecture"}
  
  C --> D["Hybrid QML<br>PQC Unitarity Constraint<br>Exponential Compression"]
  C --> E["Classical Neural Network<br>Standard Deep Learning"]
  C --> F["QML Angle Encoding<br>Baseline Quantum"]
  
  D --> G["Simulation & Validation"]
  E --> G
  F --> G
  
  G --> H["Key Findings"]
  
  H --> I["Hybrid QML (Amplitude)<br>RMSE: 0.228"]
  H --> J["Classical NN<br>RMSE: 0.246"]
  H --> K["QML (Angle)<br>RMSE: 0.242"]
  
  I --> L["Outcome<br>Outperforms Classical Models<br>Competes with XGBoost<br>Promising for NISQ Hardware"]

Cited References (179)

1. Generalization in quantum machine learning: A quantum information standpoint (2021)
2. Improving training of deep neural networks via singular value bounding (2017)
3. Train faster, generalize better: Stability of stochastic gradient descent (2016)
4. A CB (corporate bond) pricing probabilities and recovery rates model for deriving default probabilities and recovery rates (2012)
5. The determinants of recovery rates in the US corporate bond market (2014)
6. Empirical Asset Pricing with Probability Forecasts (2024)
7. Is machine learning a necessity? A regression-based approach for stock return prediction (2025)
8. Machine learning goes global: Cross-sectional return predictability in international stock markets (2023)

3 of 179 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.