Evolving Hybrid Quantum-Classical GRU Architectures for Multivariate Time Series

Predicting what happens next in a time series becomes considerably more challenging when several variables evolve simultaneously. Energy systems, meteorological measurements and environmental monitoring are typical examples: temperature may interact with humidity, solar radiation with atmospheric conditions, and electrical measurements with multiple operational variables. Recurrent neural networks are particularly suitable for these problems because they can preserve information from previous observations while processing new data. LSTM networks are widely used for this purpose, but their relatively complex internal architecture can increase the computational burden. GRUs provide a more streamlined alternative, using only reset and update gates while maintaining the ability to capture temporal dependencies. The idea explored here is to take this simpler recurrent architecture one step further by integrating quantum computation directly into its internal mechanisms.

The resulting architecture is a Quantum Gated Recurrent Unit, or QGRU: a hybrid model in which classical neural-network components work together with Variational Quantum Circuits (VQCs). Rather than replacing the entire recurrent network with a quantum system, the approach modifies specific operations inside the GRU. The reset, update and output mechanisms are implemented through three VQCs, while classical fully connected layers manage the interface between conventional data and the quantum circuits. The parameters of the quantum and classical components can then be trained together. This structure is particularly relevant for current NISQ devices, where quantum resources remain limited. Instead of requiring a fully quantum neural network, computation is divided between the two paradigms, allowing each to perform a specific role.

For a hybrid architecture to work, ordinary numerical data must first be transformed into quantum states. Here, angle encoding is used to associate input variables with rotations of individual qubits. After encoding, the information passes through a trainable quantum structure based on Basic Entangler layers. Parameterized rotation gates manipulate individual qubits, while CNOT gates introduce interactions between them. The quantum state is eventually measured, converting the result back into numerical information that can continue through the classical part of the network. This creates a recurring cycle: classical information is prepared for the quantum circuit, transformed through quantum operations, measured and returned to the classical architecture.

The architecture is evaluated on four multivariate time-series datasets representing different forecasting conditions. These include electricity transformer measurements, solar and meteorological observations from Elizabeth City and Sacramento, and environmental measurements from New York City. The forecasting targets therefore range from electrical behaviour to solar radiation and Earth skin temperature. The New York dataset, for example, combines Earth skin temperature with wind speed, specific humidity and surface pressure, while the solar datasets combine total solar radiation with ambient temperature and relative humidity. All datasets are divided into 80% training and 20% testing samples and normalized before training. This variety is important because the objective is not simply to demonstrate that a quantum recurrent model can learn one specific signal. It is to determine whether the same architecture can handle different kinds of multidimensional temporal relationships.

The QGRU is compared against several alternatives: classical GRU, LSTM and bidirectional LSTM architectures, as well as a Quantum LSTM. A naïve predictor is also included as a baseline. The quantum models are configured with five qubits and two variational layers, while all recurrent architectures used the same hidden dimension of five. The comparison therefore examines not only whether quantum computation can participate in recurrent forecasting, but whether a simpler quantum recurrent structure can remain competitive with both established classical networks and a more complex quantum LSTM.

One of the central characteristics of the QGRU comes directly from its structure. A QLSTM requires four VQCs, while the QGRU uses three. Consequently, the QGRU requires 25% fewer quantum parameters than the QLSTM. This reduction is particularly relevant for near-term quantum computing. Every additional trainable quantum component increases the complexity of optimization and the amount of computation required during training and inference. The proposed architecture therefore attempts to preserve recurrent memory while reducing the quantum resources needed to implement it. This simpler design is approximately 25% faster during training and inference than the quantum LSTM configuration considered, reinforcing the idea that quantum recurrent architectures do not necessarily need to become larger to become more effective.

The experimental results show that the QGRU performs particularly well across the different forecasting tasks. On the Elizabeth City dataset, it achieves an MSE improvement of at least 8% compared with the classical architectures considered, while on the Sacramento dataset the improvement is at least 7%. At the same time, it uses approximately 28% fewer parameters than the classical GRU, 46% fewer than the LSTM and 73% fewer than the Bi-LSTM. The results are not identical for every dataset. For the TEMP3 temperature dataset, the Bi-LSTM obtaines the lowest MSE, although the QGRU achieves a similar MSE and a lower MAE while maintaining a much smaller parameter count. On ETTH1, the QGRU produces the strongest results among the recurrent architectures evaluated.

The significance of this approach lies not only in prediction accuracy, but in the relationship between performance and architectural complexity. Quantum machine learning is still constrained by limited qubit counts, hardware noise and the practical difficulties of executing large quantum circuits. Designing smaller hybrid architectures is therefore an important part of making quantum-enhanced machine learning more compatible with available hardware. By replacing selected GRU operations with variational quantum circuits, the QGRU creates a compact bridge between recurrent deep learning and quantum computation. The experiments indicate that this architecture can model complex multivariate temporal relationships while using fewer parameters than several classical and quantum alternatives. The next important step is moving beyond simulation. Validation on actual quantum hardware would make it possible to evaluate not only forecasting accuracy and parameter efficiency, but also the real computational costs introduced by quantum execution. For now, the results point toward a broader principle for quantum AI: progress may come not from replacing classical intelligence entirely, but from carefully inserting quantum computation where it can make an existing architecture more compact and efficient.