Quantum Kernel-Based Long Short-term Memory for Climate Time-Series Forecasting

TL;DR

Experimental results demonstrate that QK-LSTM outperforms classical LSTM networks in AQI forecasting, showcasing its potential for environmental monitoring and resource-constrained scenarios, while highlighting the broader applicability of quantum-enhanced machine learning frameworks in tackling large-scale, high-dimensional climate datasets.

Abstract

We present the Quantum Kernel-Based Long short-memory (QK-LSTM) network, which integrates quantum kernel methods into classical LSTM architectures to enhance predictive accuracy and computational efficiency in climate time-series forecasting tasks, such as Air Quality Index (AQI) prediction. By embedding classical inputs into high-dimensional quantum feature spaces, QK-LSTM captures intricate nonlinear dependencies and temporal dynamics with fewer trainable parameters. Leveraging quantum kernel methods allows for efficient computation of inner products in quantum spaces, addressing the computational challenges faced by classical models and variational quantum circuit-based models. Designed for the Noisy Intermediate-Scale Quantum (NISQ) era, QK-LSTM supports scalable hybrid quantum-classical implementations. Experimental results demonstrate that QK-LSTM outperforms classical LSTM networks in AQI forecasting, showcasing its potential for environmental monitoring and resource-constrained scenarios, while highlighting the broader applicability of quantum-enhanced machine learning frameworks in tackling large-scale, high-dimensional climate datasets.

Figures (3)

• Figure 1: Schematic representation of a standard classical LSTM network architecture.
• Figure 2: Overview of the QK-LSTM architecture. (a) The QK-LSTM cell combines quantum kernel computations with the traditional LSTM framework, leveraging quantum-enhanced gates (forget, input, and output) to improve sequential data processing and maintain long-term temporal dependencies. (b) The QK-LSTM's sequential structure, where the cell processes input sequences $x_t$ over multiple time steps, outputs hidden states $h_t$, and maintains cell states $C_t$, enabling robust temporal modeling. (c) The unitary operator $U(x_t, w)$, representing the quantum kernel, encodes classical input data $x_t$ into a quantum feature space, while its adjoint $U^{\dagger}(x_j, w)$ computes quantum state overlaps to measure similarity. (d) The quantum circuit representation of $U(x_t, w)$ and $U^{\dagger}(x_j, w)$, illustrating the application of quantum gates to encode data and extract features for machine learning tasks. (e) The detailed implementation of the quantum kernel function within the QK-LSTM, showcasing the quantum transformations applied to integrate quantum-enhanced machine learning capabilities.
• Figure 3: Comparative analysis of air quality prediction performance using classical LSTM and QK-LSTM models. Panels (a) and (b) depict the overall predictive capabilities of the classical LSTM and QK-LSTM models, respectively, across the full dataset (2015-2020), including both training and testing phases. Panels (c) and (d) focus on the models' testing performance for 2020, with (c) highlighting the classical LSTM and (d) showcasing the QK-LSTM. The results demonstrate the models' ability to capture seasonal variations and rapid changes in air quality, with QK-LSTM exhibiting enhanced fidelity in tracking testing observations.