Quantum Neural Network Architectures for Multivariate Time-Series Forecasting

TL;DR

The paper tackles multivariate time-series forecasting with quantum machine learning by extending variational quantum circuits to multi-channel data and introducing the iQTransformer, which embeds a quantum self-attention mechanism into an iTransformer-like backbone. It systematically benchmarks several VQC-based and hybrid architectures (independent-channel VQCs, VQC+MLP, dense embedding, encoder–decoder, and data re-uploading) and pairs them with a novel quantum Transformer variant, the iQTransformer, that uses QSANN for cross-channel attention. Empirical results on synthetic Lorenz data and real ITER wind-turbine data show that quantum-based models can achieve competitive or superior forecasting accuracy with fewer trainable parameters and faster convergence than several classical and quantum baselines, especially in short-term predictions; the iQTransformer often delivers the best performance with notable parameter efficiency. Overall, the work demonstrates the potential of quantum-enhanced architectures as efficient, scalable tools for multivariate forecasting and highlights hybrid quantum-classical designs as a promising path toward practical applicability.

Abstract

In this paper, we address the challenge of multivariate time-series forecasting using quantum machine learning techniques. We introduce adaptation strategies that extend variational quantum circuit models, traditionally limited to univariate data, toward the multivariate setting, exploring both purely quantum and hybrid quantum-classical formulations. First, we extend and benchmark several VQC-based and hybrid architectures to systematically evaluate their capacity to model cross-variable dependencies. Second, building upon these foundations, we introduce the iQTransformer, a novel quantum transformer architecture that integrates a quantum self-attention mechanism within the iTransformer framework, enabling a quantum-native representation of inter-variable relationships. Third, we provide a comprehensive empirical evaluation on both synthetic and real-world datasets, showing that quantum-based models may achieve competitive or superior forecasting accuracy with fewer trainable parameters and faster convergence than state-of-the-art classical and quantum baselines in some cases. These contributions highlight the potential of quantum-enhanced architectures as efficient and scalable tools for advancing multivariate time-series forecasting.

Figures (8)

• Figure 1: Different VQC-based architectures: (a) Naive baseline: independent VQC per channel, each modeled by the same univariate circuit without cross-channel interaction. (b) Hybrid baseline: independent VQCs per channel followed by a shallow MLP aggregating the quantum outputs to capture cross-channel correlations. (c) Dense Embedding: employs a dense rotational encoding embedding up to three input channels per qubit, capturing correlations directly at the quantum level. Two output variants are considered: (i) single-qubit with Pauli $\{X, Y, Z\}$ measurements, and (ii) three-qubit with Pauli-$Z$ measurements per channel. (d) Encoder–decoder: an encoder maps the input time series to the quantum space, a VQC processes the embedded features, and a decoder projects the outputs back to the forecasting space. (e) Data re-uploading: each time step is sequentially encoded through alternating encoding and variational layers.
• Figure 2: Variational quantum circuit used as a generic VQC ansatz. Each layer consists of single-qubit $R_y$ rotations followed by a ring of CNOT gates. $\theta$ correspond to trainable parameters. This block is repeated $p$ times to enhance expressivity.
• Figure 3: Schematic of the iTransformer/iQTransformer forecasting pipeline. Each variate is tokenized, processed through $L$ stacked Transformer blocks with self-attention across variates and feed-forward networks across time, and finally projected to the prediction horizon. In the iTransformer the Self-Attention block corresponds to the classical mechanism, whereas in the iQTransformer it is replaced by a Quantum Self-Attention Layer (QSAL).
• Figure 4: Schematic of a quantum self-attention layer (QSAL). Classical inputs are encoded into quantum states, processed by variational circuits representing query, key, and value, and then combined via Gaussian-projected self-attention coefficients.
• Figure 5: Variational quantum ansatz used in QSANN. Layers of single-qubit rotations and entangling CNOT gates are repeated $p$ times to enhance expressivity.