Quantum Cognitive Internet of Things Framework for Energy Consumption Prediction and Optimization in Smart Home

Household electricity consumption constitutes a significant portion of total energy usage across various countries. In Algeria, the residential sector was the largest consumer of electricity, accounting for 38% of the final electricity consumption in 2023 [1]. Similarly, in the European Union, households represented 25.8% of final energy consumption in 2022 [2]. thus, the adoption of solutions to minimize electric power consumption has attached significant research interest.

The rapid adoption of Internet of Things (IoT) technologies has revolutionized the concept of smart homes, enabling real-time monitoring and control of energy consumption through interconnected devices such as sensors, smart meters, and actuators [3].

Phung et al. [4] presented an IoT-based dependable control system for managing solar energy in microgrids. Advanced systems like the one proposed by Sampaio et al. [5] utilize autonomic management and context-awareness to dynamically optimize energy consumption, demonstrating the versatility and effectiveness of IoT in energy management. Furthermore, Dutta et al. [6] developed a system utilizing Wi-Fi smart plugs and MQTT protocol for real-time monitoring and control of electricity consumption in buildings. In the realm of smart homes, Salma et al. [7] combined IoT and blockchain technologies to create a secure framework for controlling light consumption in smart city buildings. Recently Saadawi et al. [8] implemented an IoT-based energy management system employing the Harmony Search Optimization Technique to optimize energy usage, Integrating renewable energy sources.

While these works have improved the efficiency of energy management systems, they face several limitations. Classical IoT-based solutions often struggle with scalability, latency, and the inability to adapt effectively in real-time to dynamic environments with heterogeneous data sources [9].

To address these challenges, Recurrent Neural Networks (RNNs) and Long Short-Term Memory (LSTM) networks have been applied to energy prediction tasks [10, 11]. Among these, encoder-decoder architectures have gained attention for their ability to capture long-range dependencies and are well-suited for sequence-to-sequence modeling in energy forecasting [12].

Classical machine/deep learning models, though powerful, require large volumes of training data, and their performance degrades significantly in the presence of noise and non-stationary patterns, which are common in energy consumption time series. These models also exhibit limited ability to capture long-term dependencies in complex sequences, often leading to suboptimal forecasting accuracy.

The integration of machine/deep learning with IoT has given rise to the Cognitive Internet of Things (CIoT) paradigm. CIoT frameworks have improved adaptability and decision-making in energy systems by incorporating intelligent algorithms. For example, Liu et al. [13] presented a green CIoT system that integrates energy harvesting with joint optimization strategies to balance spectrum sensing and energy harvesting tasks effectively, an AI-based load optimization model within CIoT networks was developed to enhance energy efficiency through intelligent algorithms. Similarly, Kalinga et al. [14] implemented a CIoT framework utilizing linear regression models to monitor and control energy consumption of various devices, achieving notable savings. Rahmani and Arefi [15] presented a self-organizing CIoT framework employing learning automata to adaptively manage transmission power, resulting in improved energy efficiency. However, these systems still struggle to generalize in data-scarce environments, and cannot efficiently explore complex solution spaces due to the inherent limitations of classical processors.

To overcome these barriers, quantum machine learning (QML) has emerged as a promising direction. QML models exploit the principles of quantum parallelism and entanglement, enabling richer data representations in high-dimensional Hilbert spaces [16]. Hybrid models such as the Quantum LSTM (QLSTM) integrate parameterized quantum circuits within classical LSTM layers, offering superior expressiveness and robustness to noise [17].

Recent advancements in quantum machine learning have shown promise in improving energy consumption forecasting. Sagingalieva et al. [18] developed hybrid quantum neural networks that significantly improved photovoltaic power forecasting accuracy. Nutakki et al. [19] proposed Quantum Support Vector Machines (QSVMs) to enhance load forecasting in Home Energy Management Systems (HEMS), demonstrating superior accuracy in handling complex consumption patterns. Similarly, hybrid quantum neural networks have been applied to photovoltaic power forecasting, achieving significant improvements in prediction accuracy, especially in data-scarce scenarios. In the realm of energy efficiency, Quantum Reinforcement Learning (QRL) has been explored for optimizing energy usage in various applications. These approaches leverage quantum algorithms to learn optimal policies for energy management tasks [20].

In this paper, we propose a novel Quantum Cognitive Internet of Things (QCIoT) framework for smart home energy forecasting, which integrates IoT data acquisition, deep learning, and quantum computing. Our main technical contributions are as follows:

(1) We design a Quantum LSTM Encoder-Decoder architecture that leverages quantum circuits to enhance sequence modeling,  improving the system's ability to learn long-term dependencies and generalize in noisy or low-data regimes.

(2) We demonstrate how quantum parallelism can significantly improve the computational efficiency of the forecasting model in dynamic smart home environments.

(3) Through extensive experiments on real-world energy consumption data, we show that our QCIoT framework outperforms classical LSTM and deep learning models in terms of accuracy, energy savings, and adaptability, especially under noisy and data-limited conditions.

This study proposes a Quantum Cognitive IoT Framework for optimizing residential energy consumption through intelligent forecasting and decision-making. The methodology integrates hybrid quantum-classical machine learning with IoT infrastructure, comprising five systematic key phases: (1) data acquisition and preprocessing, (2) hybrid Quantum Long Short-Term Memory (QLSTM) model design, (3) classical baseline implementation, (4) training and optimization, and (5) evaluation metrics used to demonstrate the effectiveness of our proposed model.

3.1 Data collection and preprocessing

3.1.1 Dataset

The UCI Household Power Consumption Dataset [24] was selected for its high-resolution recordings of energy usage (1-minute intervals) from a single household over four years (2006–2010). The dataset includes:

(1) Global_active_power: Total household power consumption (kW).

(2) Sub-metering: Granular measurements for appliances (e.g., kitchen, heating…).

(3) Voltage, Global_intensity, and reactive power measurements.

3.1.2 Preprocessing pipeline

Our preprocessing pipeline employed rigorous techniques to ensure data quality and model compatibility:

Data cleaning.  Gaps (marked as "?") were replaced with NaN, then addressed through temporal imputation. Recognizing the strong diurnal patterns in residential energy use, we implemented a day-lag filling approach.

Resampling and aggregation (daily granularity). To balance computational efficiency with temporal resolution, minute-level observations were aggregated to daily totals through summation. This transformation: Reduces high-frequency noise, maintains meaningful consumption patterns and enables longer forecast horizons.

Normalization and windowing. The processed dataset was enhanced through:

-Min-Max normalization to [-1, 1] range,

-Creation of Temporal Windowing (7-days input/output windows) for sequence prediction,

-Stratified temporal splitting (70% training, 15% validation, 15% test)

Feature Selection. Our study initially utilizes the Global_active_power variable from the UCI dataset, then we expanded our investigation to multivariate prediction, incorporating additional relevant features to capture more complex interdependencies in the energy consumption patterns.

3.2 Hybrid quantum-classical model design

In our work, we propose a hybrid quantum-classical sequence-to-sequence model designed to predict short-term power consumption based on past energy usage. The model is structured using an encoder-decoder architecture, with both modules leveraging a custom-built Quantum-enhanced Long Short-Term Memory cell (QLSTMCell). The design seamlessly integrates classical neural operations with parameterized quantum circuits (PQCs), allowing us to investigate potential benefits of quantum computation in sequential learning tasks.

3.2.1 Parameterized quantum circuits

Figure 2 show the parametrized quantum circuit used to implement our quantum neural network layer (encoder and decoder) for our QLSTM. The circuit is composed of 4 qubits, initialized to 0>, and is divided into three main stages:

2.png

Figure 2. Architecture of the parameterized quantum circuit

Quantum data encoding layer. We Use angle embedding to map classical input data $x \in \mathrm{R}^n$ to quantum state $|\psi(\mathrm{x})\rangle$ through Rx rotations. Each feature $\mathrm{x}_{\mathrm{i}}$ is mapped to a rotation angle $\theta_{\mathrm{i}}=\pi \mathrm{x}_{\mathrm{i}}$, see Eq. (1).

$|\psi(x)\rangle=\bigotimes_{i=1}^n R_{X\left(\theta_i\right)}|0\rangle^{\{\otimes n\}}, R_{X\left(\theta_i\right)}=e^{-i \theta X / 2}$                   (1)

Each RX($\theta_i$) rotates $|0\rangle$ around the X-axis by $\theta_i$, placing the qubit at ($\pi$/2,$\theta_i$) in spherical coordinates (latitude $\pi$/2, longitude $\theta_i$).

Variational Quantum Circuit (Ansatz). The trainable circuit consists of:

- Single-Qubit Rotations (RX-RY-RZ): Each qubit i in the circuit undergoes three rotations as shown in Eq. (2) and Eq. (3).

$U_i\left(\alpha_i, \beta_i, \gamma_i\right)=\bigotimes_{i=0}^{n-1} R_X\left(\alpha_i\right) R_Y\left(\beta_i\right) R_Z\left(\gamma_i\right)$                  (2)

where,

$R_{X(\alpha)}=e^{-i \alpha X / 2}, R_{y(\beta)}=e^{-i \beta Y / 2}, R_{z(\gamma)}=e^{-i \gamma Z / 2}$                    (3)

- Entanglement via CNOT: that link the qubits in a closed linear entangling pattern designed to maximize entanglement. Each CNOT gate “$\mathrm{CNOT}_{i,j}$’’ is a 2-qubit unitary operation with the form depicted in Eq. (4):

$U_{\text {ent }}=\prod_{i=0}^{n-1}$ CNOT $_{i,(i+1) \bmod n}$                     (4)

The full unitary for the variational part of our proposed circuit is presented in the Eq. (5).

$U_{\text {circuit }}=\binom{\left[\prod_{i=0}^{n-1} C N O T_{i,(i+1) \bmod n}\right]}{\cdot\left[\bigotimes_{i=0}^{n-1} R_Z\left(\gamma_i\right) R_Y\left(\beta_i\right) R_X\left(\alpha_i\right)\right]}$                     (5)

Each qubit is both a control and a target in the entanglement structure, allowing strong correlations.

Pauli-z measurements. The measurements produce classical output data, which can then be used in our quantum-classical hybrid model (make prediction). Eq. (6) shows the final state measured via Pauli-Z operators on m output qubits:

$y_t=W *\left\langle\psi\left(x_t\right)\right| Z^{\otimes m}\left|\psi\left(x_t\right)\right\rangle+b, \mathrm{Z}=\left(\begin{array}{cc}1 & 0 \\ 0 & -1\end{array}\right)$                  (6)

3.2.2 Quantum LSTM cell (QLSTMCell)

At the core of both the encoder and decoder is a modified LSTM cell where the traditional gates (forget, input, candidate/update, and output) are replaced by parameterized quantum circuits. Each gate follows the same hybrid pattern:

(1) First, classical input vectors (from the current input and previous hidden state) are projected through fully connected layers to match the dimension of the quantum circuit.

(2) The resulting vectors are summed and passed into the dedicated Parameterized/Variational Quantum Circuit (VQC).

(3) The quantum circuit outputs the expectation values of Pauli-Z measurements on all qubits, which are then processed by a classical linear layer.

(4) Finally, classical nonlinearities (sigmoid or tanh) are applied to produce gate activations.

3.png

Figure 3. Architecture of the QLSTMCell [25]

This structure allows each gate to learn nonlinear transformations in a hybrid quantum-classical parameter space. Figure 3 illustrates the QLSTM Cell’s architecture.

The dynamics of information propagation within a Quantum LSTM cell are governed by the following mathematical expressions:

- Forget Gate: $\mathrm{f}_{\mathrm{t}}=\sigma\left(\langle Z\rangle_{\mathrm{f}}\right)$

- Input Gate: $i_t=\sigma\left(\langle Z\rangle_I\right)$

- Candidate gate: $\tilde{c}_t=\tanh \left(\langle Z\rangle_c\right)$

- Cell State Update: $\mathrm{c}_{\mathrm{t}}=\mathrm{f}_{\mathrm{t}} . \mathrm{c}_{\mathrm{t}-1}+\mathrm{i}_{\mathrm{t}} . \tilde{\mathrm{c}}_{\mathrm{t}}$

- Output Gate: $\mathrm{o}_{\mathrm{t}}=\sigma\left(\langle\mathrm{Z}\rangle_{\mathrm{o}}\right)$

- Hidden State Update: $\mathrm{h}_{\mathrm{t}}=\mathrm{o}_{\mathrm{t}} .\tanh \left(\mathrm{c}_{\mathrm{t}}\right)$

3.2.3 Encoder module

The encoder receives a univariate or multivariate time series sequence of shape [batch_size, sequence_length, input_size]. It processes the input sequentially, time step by time step, using a single shared QLSTM cell. The encoder maintains and updates two internal states, the hidden state h(t) and the cell state c(t), initialized to zero. At the end of the input sequence, the final hidden and cell states are passed to the decoder as a summary of the input history. Figure 4 is a detailed schematic description that illustrate the architecture of our hybrid quantum encoder.

4.png

Figure 4. Architecture of the encoder

3.2.4 Decoder module

The decoder is designed to autoregressively generate a sequence of future values, given the encoded states. It reuses the QLSTM architecture. At each step, the decoder updates its hidden state using the quantum cell and generates the next prediction via a classical linear layer applied to the hidden state. This output becomes the input for the next time step. The decoder iterates for a fixed number of steps equal to the prediction horizon (7 days in our work), and the outputs are concatenated into a final prediction vector of shape [batch_size, sequence_length, input_size]. Figure 5 illustrates the architecture of our hybrid quantum decoder.

5.png

Figure 5. Architecture of the decoder

3.3 Comparative baseline

We compare our proposed QLSTM model with a classical LSTM model that use an identical architecture to the QLSTM model but with classical LSTM cells.

3.4 Model training and hyperparameters

To evaluate quantum enhancements of our proposed model, we compared it against a classical encoder-decoder LSTM. To ensure a fair Comparison between the classical LSTM and QLSTM we use the same training hyperparameters. This controlled comparison isolates the effects of quantum components.

3.4.1 Model architecture hyper parameters

Number of lstm layers. We use the same number of layers

(1 layer for the encoder and decoder).

Hidden Units per Layer. We use the same number of hidden units (64 hidden units for each model).

Input Sequence Length. We use the same sequence length (7 time steps for input/output sequence length).

3.4.2 Training hyperparameters

Optimization. Adam optimizer with learning rate Lr = 0.01.

Batch Size. We use the same batch size (batch size =32).

Number of Epochs. We use the same number of epochs (num_epochs =100 Epochs).

Loss Function. MSE Loss Function.

3.4.3 Regularization hyperparameters

Early Stopping. Employed early stopping with patience=5 to prevent overfitting.

3.4.4 Quantum-Specific hyperparameters

Number of Qubits. This is a new hyperparameter specific to the QLSTM. (n-qubits=4).

Quantum Circuit Depth. The depth of the quantum circuit can impact performance (n-Layers=1).

The choice of using 4 qubits and a single-layer depth in the parameterized quantum circuit was not arbitrary, but rather the result of a series of systematic experiments.

3.5 Evaluation metrics

Performance assessment incorporates multiple quantitative metrics as shown in Table 2.

Table 2. Evaluation metrics

3.6 Implementation

The experiments were conducted on the Anaconda3 which provides an environment for classical and quantum computing.  The classical LSTM and QLSTM models were implemented using PyTorch and PennyLane. Quantum simulations were performed using PennyLane’s “default.qubit”simulator (CPU).

The experimental results demonstrate the advantages of integrating quantum computing principles into deep learning models for time series forecasting of smart home energy consumption. This section explores the theoretical underpinnings of these performances, focusing on how quantum computing principles, such as superposition, entanglement, and quantum parallelism, enhance the capacity of LSTMs to capture complex temporal dependencies.

5.1 Quantum parallelism and enhanced feature representation

Classical LSTMs process sequential data through deterministic weight updates, which can struggle with high-dimensional or noisy time-series data due to limited representational capacity. In contrast, QLSTMs leverage quantum parallelism, enabling them to explore multiple states simultaneously during training. This property allows QLSTMs to:

(1) Efficiently encode temporal patterns in a high-dimensional Hilbert space, capturing nonlinear relationships that classical LSTMs may miss.

(2) Mitigate the curse of dimensionality in multivariate settings (as seen in MultivQLSTM’s superior RMSE of 392.58 vs. MultivLSTM’s 590.87), where quantum state superposition helps model interactions between variables more effectively.

The improved R² scores of QLSTMs (UnivQLSTM: 0.3323, MultivQLSTM: 0.3819 vs. negative values for classical LSTMs) suggest that quantum enhancements provide a better fit to the underlying data distribution, likely due to richer feature embeddings.

5.2 Entanglement and long-term dependency learning

A key challenge in classical LSTMs is their reliance on gating mechanisms (input, forget, and output gates) to manage long-term dependencies, which can fail when gradients vanish or explode. Quantum entanglement, a phenomenon where qubits remain correlated even when separated, offers a theoretical advantage:

(1) Entangled quantum gates in QLSTMs may strengthen memory retention across time steps, explaining their lower validation loss STD (UnivQLSTM: 0.0036 vs. UnivLSTM: 0.0074).

(2) This aligns with the smoother convergence observed in QLSTMs, where entanglement could stabilize gradient flow during backpropagation.

5.3 Quantum noise resistance and generalization

Classical LSTMs are sensitive to noise and overfitting, as evidenced by the higher train/val loss STD of MultivLSTM (0.0137/0.0066) compared to MultivQLSTM (0.0081/0.0065). Quantum models inherently exploit noise resilience through:

(1) Probabilistic state measurements, which may act as a natural regularizer, reducing overfitting.

(2) Quantum interference effects, which can cancel out spurious correlations in training data, leading to better generalization (lower generalization mean/median in QLSTMs; Table 7).

5.4 Convergence dynamics: Quality vs. speed trade-off

While QLSTMs required more epochs to converge (UnivQLSTM: epoch 81; MultivQLSTM: epoch 100) than classical LSTMs (MultivLSTM: epoch 31), their final performance was superior. Slower convergence often yields globally optimal solutions. Theoretically, this suggests:

(1) Quantum optimization explores the loss landscape more thoroughly, avoiding shallow local minima that trap classical models.

(2) The lower final test loss of MultivQLSTM (0.0270 vs. MultivLSTM’s 0.0362) supports this hypothesis.

5.5 Implications

These results highlight the potential of quantum deep learning for energy forecasting tasks. By leveraging the computational richness of quantum circuits, the QLSTM model is able to capture more nuanced temporal relationships, leading to more accurate and efficient predictions. This has practical implications for smart home energy management systems, enabling more adaptive and data-driven control strategies.

5.6 Limitations and future work

While the results are promising, they are constrained by the use of quantum simulation rather than real quantum hardware. Current quantum processors still face limitations such as decoherence (loss of quantum state stability) and gate errors (imperfect operations), which degrade QLSTM performance. These issues limit circuit depth and scalability. Possible solutions include error mitigation techniques (e.g., dynamical decoupling), hybrid quantum-classical architectures to reduce circuit complexity, and fault-tolerant designs leveraging quantum error correction. Advances in qubit coherence times and high-fidelity gates are critical for practical deployment. Future work will focus on:

5.6.1 Deployment on real quantum hardware

The present study relied on quantum simulations due to the current limitations of available quantum devices. Future work should involve testing the QLSTM architecture on real quantum hardware to evaluate the model’s resilience to noise, gate fidelity issues, and decoherence effects.

5.6.2 Ansatz optimization 

While the proposed hybrid quantum-classical LSTM model has demonstrated improved performance in terms of RMSE and other evaluation metrics, the current quantum circuit architecture may not represent the optimal configuration. Future research should explore alternative quantum circuit designs, including variations in the number of qubits, depth, and types of parameterized gates. Additionally, testing different circuit layer configurations could reveal architectures that are better suited for learning temporal patterns in energy consumption data. Such exploration would not only enhance the predictive capability of the model but also contribute to a deeper understanding of the interplay between quantum circuit complexity and learning performance in hybrid frameworks.

5.6.3 Extension to multihousehold datasets

Our experiments were conducted on a single-household dataset. A lo6gical next step is to scale the model to handle larger, multivariate datasets that reflect the diversity and heterogeneity of energy usage across different households and regions.

5.6.4 Exploration of alternative quantum circuits

Further investigation into the design and optimization of variational quantum circuits may reveal circuit architectures better suited to sequential data. Techniques such as quantum convolution and quantum attention mechanisms could be explored in future implementations.

5.6.5 Real-time integration and edge deployment

With the growing ubiquity of edge devices and IoT frameworks, integrating QLSTM models into real-time systems for dynamic load forecasting and energy management presents a valuable research trajectory. This will require careful consideration of computational efficiency and latency in edge environments.

5.6.6 Robustness and interpretability studies

As quantum models gain traction, ensuring their robustness to data anomalies and their interpretability from a decision-making standpoint becomes increasingly important. Investigating explainability methods tailored to hybrid quantum-classical models would be a valuable contribution.