Q-SCALE: Quantum computing-based Sensor Calibration for Advanced Learning and Efficiency

Air quality monitoring is becoming increasingly important as cities attempt to understand pollution at a much finer spatial and temporal scale. Among the pollutants that require particular attention is PM2.5, fine particulate matter capable of penetrating deep into the respiratory system. Reference-grade monitoring stations can provide accurate measurements, but their cost and maintenance requirements make it difficult to deploy them densely throughout an urban environment. Low-cost optical sensors offer a more scalable alternative, potentially enabling distributed monitoring networks with many measurement points. Their main limitation, however, is accuracy: environmental conditions and sensor characteristics can cause their measurements to deviate from those produced by professional reference instruments. The challenge therefore becomes one of calibration: can artificial intelligence learn how to transform inexpensive sensor readings into measurements that more closely approximate those of a reference station?

To investigate this question, four different learning architectures are compared. Two belong to conventional machine learning: a Feed-Forward Neural Network (FFNN) and a Long Short-Term Memory network (LSTM). Their quantum counterparts are a Variational Quantum Regressor (VQR) and a Quantum Long Short-Term Memory model (QLSTM). This comparison creates two complementary perspectives. FFNN and VQR address calibration primarily as a regression problem, while LSTM and QLSTM exploit the temporal nature of pollution measurements. The latter is particularly relevant because PM2.5 concentrations are not isolated observations: they form sequences whose evolution over time can contain information useful for correcting sensor measurements. Quantum Machine Learning introduces another dimension. Variational Quantum Circuits use parameterised quantum gates to encode and process information through quantum states. Their parameters are adjusted through classical optimisation, creating a hybrid quantum-classical learning process compatible, at least conceptually, with current NISQ computing architectures.

The experimental data were collected over seven months, from November 2022 to May 2023, using 24 low-cost PM2.5 sensors positioned close to the inlet of an official reference monitoring station in Turin. Temperature, humidity and atmospheric pressure are also measured to describe the environmental conditions surrounding the sensors. The measurements generated by the low-cost devices are aggregated at minute and hourly resolution, after which the median across the sensors is calculated to obtain representative time series. For the quantum models, part of this information also has to be transformed into a representation suitable for quantum computation. In the VQR, for example, input and output variables are scaled to ranges compatible with quantum encoding and measurement. This preprocessing stage highlights an important aspect of quantum machine learning: classical environmental information cannot simply be passed directly to a quantum circuit. It must first be encoded into quantum states before quantum operations can manipulate it.

The VQR uses angle embedding to map classical values onto rotations of qubits. Parameterised quantum operations then transform those states, while entangling layers create correlations among the qubits. Finally, quantum measurements are converted back into classical numerical predictions representing the estimated PM2.5 concentration. Both linear and nonlinear circuit structures are investigated. The nonlinear architecture repeatedly introduces data embeddings within the circuit, increasing its ability to represent more complex relationships. This approach is compared with a conventional FFNN trained on hourly PM2.5, temperature, humidity and atmospheric-pressure measurements. Extensive hyperparameter tuning and cross-validation are used to identify suitable configurations rather than comparing arbitrarily selected models. The results show that greater computational novelty does not automatically translate into better predictions. On the test set, the FFNN achieved an L1 loss of 2.92, compared with 4.81 for the VQR when evaluated using the same metric. Cross-validation reinforced this difference, with the classical network producing more reliable calibration results across the folds.

The comparison becomes more interesting when temporal models are considered. A conventional LSTM contains internal memory mechanisms that determine which information should be retained, updated or discarded as a sequence evolves. This makes it particularly suitable for environmental time series, where current pollutant concentrations can be related to previous measurements. The QLSTM preserves this sequential logic but replaces key operations inside the LSTM architecture with Variational Quantum Circuits. Separate VQCs participate in computing the forget, input and output mechanisms, as well as the candidate memory, hidden state and final output. Inside these quantum components, classical data are encoded using rotation gates, trainable quantum operations modify the resulting states, and circular CNOT connections entangle the qubits. Pauli-Z measurements then extract values that can be returned to the classical portion of the model. In this way, the model does not simply use a quantum circuit as an isolated predictor. Quantum computation becomes part of the mechanism responsible for processing temporal information.

The QLSTM produced one of the most interesting outcomes: it requires only 66 trainable weights, compared with 482 for the LSTM. Cross-validation provided a more nuanced picture. The classical LSTM achieves an average loss comparable to that of the QLSTM. Their performance is therefore extremely similar, with the quantum model performing slightly better in some folds while retaining its much smaller number of trainable parameters. This is important because the potential value of quantum machine learning does not necessarily have to appear as a dramatic improvement in predictive accuracy. It may also emerge through model efficiency: achieving comparable performance with a substantially smaller trainable parameter space.

The comparison also reveals the importance of temporal information itself. Both LSTM and QLSTM generally improve the quality of the original uncalibrated measurements, demonstrating the usefulness of learning from sequences rather than considering observations independently. Over a five-day interval, the calibrated outputs produced by the temporal models follow the reference PM2.5 measurements while smoothing some of the sharper local peaks. This behaviour is linked in part to the L1 loss used during training, which penalises large local deviations differently from MSE or RMSE. Seasonality also emerged as an important factor. Pollution levels varied across the seven-month measurement campaign, demonstrating why evaluation across multiple chronological portions of the dataset is necessary when determining whether a calibration model can generalise.

The comparison does not establish a general quantum advantage. The VQR is less effective than its classical FFNN counterpart, while QLSTM delivers performance broadly comparable to LSTM. Yet the latter achieves this result with 66 trainable parameters instead of 482, showing a potentially valuable direction for more parameter-efficient learning architectures. There is also an important limitation: the quantum circuits are simulated on classical hardware rather than executed on an actual quantum processor. Larger and more diverse datasets, broader model configurations and experiments on real quantum hardware are therefore necessary to understand whether the observed parameter efficiency can ultimately translate into a practical computational advantage. The broader direction is nevertheless clear. Low-cost sensors can make urban environmental monitoring more distributed, machine learning can transform their imperfect measurements into more reliable information, and quantum-enhanced architectures introduce a new way of exploring that calibration process. In this intersection between smart cities, environmental sensing and quantum AI, the objective is not simply to make sensors cheaper, but to make dense networks of inexpensive devices capable of producing increasingly trustworthy information about the air around us.