Quantum Reservoir Computing for Realized Volatility Forecasting

Paper: arXiv 2505.13933

Authors: Qingyu Li, Chiranjib Mukhopadhyay, Abolfazl Bayat, Ali Habibnia

Abstract

Recent advances in quantum computing have demonstrated its potential to significantly enhance the analysis and forecasting of complex classical data. Among these, quantum reservoir computing has emerged as a particularly powerful approach, combining quantum computation with machine learning for modeling nonlinear temporal dependencies in high-dimensional time series. As with many data-driven disciplines, quantitative finance and econometrics can hugely benefit from emerging quantum technologies. In this work, we investigate the application of quantum reservoir computing for realized volatility forecasting. Our model employs a fully connected transverse-field Ising Hamiltonian as the reservoir with distinct input and memory qubits to capture temporal dependencies. The quantum reservoir computing approach is benchmarked against several econometric models and standard machine learning algorithms. The models are evaluated using multiple error metrics and the model confidence set procedures. To enhance interpretability and mitigate current quantum hardware limitations, we utilize wrapper-based forward selection for feature selection, identifying optimal subsets, and quantifying feature importance via Shapley values. Our results indicate that the proposed quantum reservoir approach consistently outperforms benchmark models across various metrics, highlighting its potential for financial forecasting despite existing quantum hardware constraints. This work serves as a proof-of-concept for the applicability of quantum computing in econometrics and financial analysis, paving the way for further research into quantum-enhanced predictive modeling as quantum hardware capabilities continue to advance.

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 3.0/10
• Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper is dense with advanced mathematical physics concepts, including Hamiltonians, quantum state evolution, and Shapley values for interpretability, justifying a high math score. However, it is a conceptual proof-of-concept study without explicit code, detailed backtests, or raw data disclosures; empirical results are derived from simulation/hardware limitations, resulting in low empirical rigor.

Research Flowchart

  flowchart TD
  A["Research Goal: Forecast Realized Volatility<br>using Quantum Reservoir Computing"] --> B["Data & Methodology"]
  
  B --> B1["Input: S&P 500 Realized Volatility Data"]
  B --> B2["Quantum Reservoir:<br>Transverse-Field Ising Hamiltonian"]
  B --> B3["Feature Selection:<br>Wrapper-based Forward Selection"]
  
  B1 & B2 --> C["Training & Computation"]
  B3 --> C
  
  C --> C1["Quantum Reservoir Processing"]
  C --> C2["Model Validation:<br>Model Confidence Set"]
  
  C1 & C2 --> D["Outcomes"]
  
  D --> D1["Superior Forecasting Accuracy"]
  D --> D2["Feature Importance:<br>Shapley Values"]
  D --> D3["Proof-of-Concept for<br>Quantum-Enhanced Financial Analysis"]

Cited References (135)

1. Quantum reservoir computing in Jaynes-Cummings models: Nonlinear memory and time-series prediction (2025) — link
2. Interferometric single-shot parity measurement in InAs–Al hybrid devices (2025) — link
3. LEP-QNN: Loan Eligibility Prediction Using Quantum Neural Networks (2024) — link
4. Quantum reservoir computing in atomic lattices (2024) — link
5. A Comprehensive Survey of Deep Learning for Time Series Forecasting: Architectural Diversity and Open Challenges (2024) — link
6. Quantum reservoir computing for time series processing (2024) — link
7. Memory-Augmented Hybrid Quantum Reservoir Computing (2024) — link
8. Quantum error correction below the surface code threshold (2024) — link

2 of 135 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.