# QuaCK-TSF: Quantum-Classical Kernelized Time Series Forecasting

arXiv: https://arxiv.org/abs/2408.12007 · HTML: https://mlsanity.com/paper/2408.12007/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 51 references that are in the map.
- First posted on arXiv 21 Aug 2024.

## Builds on (most cited first, 15 of 15)

- [A Tutorial on Bayesian Optimization](https://mlsanity.com/paper/1807.02811/) (2018)
- [Variational Quantum Algorithms](https://mlsanity.com/paper/2012.09265/) (2020)
- [Supervised learning with quantum enhanced feature spaces](https://mlsanity.com/paper/1804.11326/) (2018)
- [GPyTorch: Blackbox Matrix-Matrix Gaussian Process Inference with GPU Acceleration](https://mlsanity.com/paper/1809.11165/) (2018)
- [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)
- [Quantum advantage in learning from experiments](https://mlsanity.com/paper/2112.00778/) (2021)
- [Unexpected Improvements to Expected Improvement for Bayesian Optimization](https://mlsanity.com/paper/2310.20708/) (2023)
- [Bandwidth Enables Generalization in Quantum Kernel Models](https://mlsanity.com/paper/2206.06686/) (2022)
- [Importance of Kernel Bandwidth in Quantum Machine Learning](https://mlsanity.com/paper/2111.05451/) (2021)
- [Quantum algorithms applied to satellite mission planning for Earth observation](https://mlsanity.com/paper/2302.07181/) (2023)
- [Improved Financial Forecasting via Quantum Machine Learning](https://mlsanity.com/paper/2306.12965/) (2023)
- [Quantum Gaussian Process Regression for Bayesian Optimization](https://mlsanity.com/paper/2304.12923/) (2023)
- [Successive Data Injection in Conditional Quantum GAN Applied to Time Series Anomaly Detection](https://mlsanity.com/paper/2310.05307/) (2023)
- [Towards Bundle Adjustment for Satellite Imaging via Quantum Machine Learning](https://mlsanity.com/paper/2204.11133/) (2022)

## Built on by (most cited first, 5 of 5)

- [ML-Enabled Open RAN: A Comprehensive Survey of Architectures, Challenges, and Opportunities](https://mlsanity.com/paper/2604.01239/) (2026)
- [Enhancing Network Anomaly Detection with Quantum GANs and Successive Data Injection for Multivariate Time Series](https://mlsanity.com/paper/2505.11631/) (2025)
- [Quantum Fourier Transform Based Kernel for Solar Irrandiance Forecasting](https://mlsanity.com/paper/2511.17698/) (2025)
- [QFed: Parameter-Compact Quantum-Classical Federated Learning](https://mlsanity.com/paper/2601.09809/) (2026)
- [RF Spectrogram Anomaly Detection with Quantum Kitchen Sinks: Architecture, Representation, and Hardware Validation](https://mlsanity.com/paper/2607.13897/) (2026)

## Abstract (arXiv)

Forecasting in probabilistic time series is a complex endeavor that extends beyond predicting future values to also quantifying the uncertainty inherent in these predictions. Gaussian process regression stands out as a Bayesian machine learning technique adept at addressing this multifaceted challenge. This paper introduces a novel approach that blends the robustness of this Bayesian technique with the nuanced insights provided by the kernel perspective on quantum models, aimed at advancing quantum kernelized probabilistic forecasting. We incorporate a quantum feature map inspired by Ising interactions and demonstrate its effectiveness in capturing the temporal dependencies critical for precise forecasting. The optimization of our model's hyperparameters circumvents the need for computationally intensive gradient descent by employing gradient-free Bayesian optimization. Comparative benchmarks against established classical kernel models are provided, affirming that our quantum-enhanced approach achieves competitive performance.