# Beyond Classical AI: Detecting Fake News with Hybrid Quantum Neural Networks
## 2 Materials and Methods
### Proposed Model: HQDNN
#### 2.3.2 Details of the Quantum Layer  
The quantum circuit in the proposed architecture is designed to transform the two-dimensional output of the classical layer within a parameterized quantum system. Each qubit is sequentially processed through three quantum gates: RX, RY, and RZ. In the first stage, each component of the input vector is encoded onto its corresponding qubit via RX rotation, which enables the injection of classical data into the quantum circuit through angular rotation, a widely adopted strategy in variational quantum algorithms. Following this, RY and RZ gates are applied, each parameterized by trainable weights, allowing for the quantum state to be adjusted during training through learned transformations. This three-gate sequence on each qubit enables the formation of multi-dimensional decision boundaries within a Hilbert space [29]. Figure 1: Hybrid Quantum–Deep Neural Network (HQDNN) architecture. At the end of the circuit, Pauli-Z measurement (\(\langle Z\rangle\)) is performed on each qubit, yielding a classical output vector that reflects the final quantum state of the system. These expectation values serve as the output of the quantum layer and are passed to the subsequent classical output layer of the model. This configuration allows for the modeling of high-order nonlinear transformations with a limited number of parameters, offering a compact, yet expressive representational capacity compared to the traditional learning methods. The quantum circuit used in the proposed HQDNN model is implemented using the PennyLane library [30] and executed with the default.qubit simulator device. The entire circuit is optimized within a hybrid training loop, enabling the model to jointly learn from both classical and quantum representations in a coherent manner and demonstrating that even a shallow quantum layer with only two qubits can contribute meaningfully to complex NLP tasks such as fake news classification. The selected gate configuration (RX \(\rightarrow\) CNOT \(\rightarrow\) RY/RZ) is commonly adopted in variational quantum classifiers, enabling both data encoding and quantum entanglement with minimal circuit depth. Specifically, RX gates inject classical input features into quantum states via angular rotation, while the CNOT gate entangles qubits, allowing for complex correlations to be captured. Trainable RY and RZ gates introduce additional nonlinearity and expressive power during optimization. Prior empirical studies [15; 16] have demonstrated that such shallow quantum circuits can effectively model nonlinear decision boundaries in low-dimensional embedding spaces. These findings support the use of this compact quantum layer in our HQDNN, particularly given the resource-constrained simulation environment and the short-length, sparse nature of the LIAR dataset. All quantum simulations were conducted using the default.qubit backend of PennyLane (v0.40.0). The experiments were performed using a local machine equipped with an Intel64 (12-core) processor and 32 GB of RAM. All quantum computations were run in classical simulation mode using PennyLane's built-in simulator, ensuring full reproducibility and transparency. The use of a two-qubit quantum circuit was motivated by the need to maintain low computational cost during simulation, as increasing the qubit count significantly extends the simulation time. Given that the simulations were conducted on classical hardware, the two-qubit configuration provided an optimal balance between feasibility and expressive capacity for the task. As such, the two-qubit configuration strikes a practical trade-off between representational power and efficiency [29]. While this study focused on a minimal two-qubit configuration to ensure efficiency and reproducibility, future experiments will explore deeper circuits and higher qubit counts to analyze how increased quantum capacity affects the performance in NLP tasks. Figure 2 illustrates the architecture and functioning of the quantum layer in greater detail. Figure 2: Detailed architecture of quantum layer.