QuaCK-TSF: Quantum-Classical Kernelized Time Series Forecasting

TL;DR

This paper presents QuaCK-TSF, a quantum-classical kernelized approach for probabilistic time series forecasting that leverages quantum feature maps and Bayesian optimization to improve prediction accuracy and uncertainty quantification.

Contribution

It introduces a novel quantum kernel method for time series forecasting, combining quantum feature maps with Bayesian hyperparameter optimization, and demonstrates competitive performance against classical models.

Findings

Quantum kernel approach achieves competitive accuracy.

Quantum feature map captures temporal dependencies effectively.

Bayesian optimization efficiently tunes hyperparameters.

Abstract

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.