Data re-uploading in Quantum Machine Learning for time series: application to traffic forecasting

TL;DR

This study investigates applying quantum machine learning, specifically data re-uploading, to traffic forecasting using high-resolution Athens traffic data. It compares two hybrid quantum-classical architectures against classical baselines: replacing a fully connected layer (Scenario A) and replacing a recurrent layer with a quantum memory via data re-uploading (Scenario B). Results show that quantum models do not outperform classical FC networks, but offer advantages in recursive, data-reuploading configurations, with performance improving as the quantum layer complexity increases; simulation-based experiments also highlight higher computational costs. Overall, the work provides one of the first empirical assessments of data re-uploading in time-series traffic forecasting, demonstrating potential gains and outlining practical considerations for scaling quantum approaches in ITS applications.

Abstract

Accurate traffic forecasting plays a crucial role in modern Intelligent Transportation Systems (ITS), as it enables real-time traffic flow management, reduces congestion, and improves the overall efficiency of urban transportation networks. With the rise of Quantum Machine Learning (QML), it has emerged a new paradigm possessing the potential to enhance predictive capabilities beyond what classical machine learning models can achieve. In the present work we pursue a heuristic approach to explore the potential of QML, and focus on a specific transport issue. In particular, as a case study we investigate a traffic forecast task for a major urban area in Athens (Greece), for which we possess high-resolution data. In this endeavor we explore the application of Quantum Neural Networks (QNN), and, notably, we present the first application of quantum data re-uploading in the context of transport forecasting. This technique allows quantum models to better capture complex patterns, such as traffic dynamics, by repeatedly encoding classical data into a quantum state. Aside from providing a prediction model, we spend considerable effort in comparing the performance of our hybrid quantum-classical neural networks with classical deep learning approaches. Our results show that hybrid models achieve competitive accuracy with state-of-the-art classical methods, especially when the number of qubits and re-uploading blocks is increased. While the classical models demonstrate lower computational demands, we provide evidence that increasing the complexity of the quantum model improves predictive accuracy. These findings indicate that QML techniques, and specifically the data re-uploading approach, hold promise for advancing traffic forecasting models and could be instrumental in addressing challenges inherent in ITS environments.

Figures (11)

• Figure 1: Location of the loop detector used in this study, relative to the center of Athens, Greece.
• Figure 2: Full extent (top) and detailed view (bottom) of the time series used in the study. The $x$-axis displays the datapoint index, while the $y$-axis shows the traffic volume in units of vehicles/hour.
• Figure 3: Schematic representation of the fully connected architecture used in the scenario described in Section \ref{['Scenario A']}. The left side of the image shows the encoding provided by the autoencoder trained as depicted in Figure \ref{['figure:autoencoder']}. The right side represents the part of the NN that acts as a regressor. In Section \ref{['Scenario A']}, we compare two approaches: a fully classic one (top right), and a hybrid one (bottom right): the difference between the two lies in the first fully connected layer. In either case, the output of the NN is a single value representing the prediction at the timestep immediately following the input sequence.
• Figure 4: The architecture of the autoencoder is used as a preprocessing step for the NNs in Figures \ref{['figure:FC']} and \ref{['figure:RNN']}. The encoder is constituted by an LSTM cell composed of 32 units and an FC layer, which shrinks the embedding space to the desired $N_q$ features; the same structure is mirrored in the decoder. The autoencoder is trained in a standard way, i.e., by matching the input sequence with the reconstructed one via minimization of the mean squared error.
• Figure 5: Example of an unfolded data re-upload scheme with $N$ re-upload blocks (blue boxes) with the same components as the ones adopted in this work. In this specific depiction, the classic input data have dimensionality 3, and the circuit is composed of 3 qubits. In each block, the grey boxes represent the rotations used to embed the classical data, and two entangling layers follow them. The first such layer is composed of rotational gates (orange boxes), each characterized by three tunable parameters ($\alpha$, $\beta$, and $\gamma$), while the second layer is composed of CNOT gates. At the output of the circuit, a measurement converts the signal back to classical data (e.g., in our work, we applied a Pauli-Z measurement to observe the state of the qubits along the Z-axis in the computational basis). In this representation, variables and parameters are indexed as $\langle . \rangle^{n}_{q}$, where $n$ is the block index, and $q$ the qubit index. In general, multiple entangling layers may be chained inside a single block to increase its complexity.