Estimating Quantum Steerability of Qubit-Pair States with Quantum Neural Networks

Quantum steering has attracted increasing research attention due to its fundamental importance and applications in quantum information science. Conventionally, determining the maximum quantum steerability of qubit-pair states involves extensive iterative Semidefinite Programming (SDP) tests over incompatible measurements, a process that is computationally demanding.Here, we propose a novel Quantum Neural Network (QNN) model to address this challenge. Our QNN integrates trainable parameters in a quantum circuit with classical neural network optimization. Specifically, the model employs a parameterized quantum circuit (PQC) where each qubit is initialized with a trainable U3 (θ,Φ,λ) gate, allowing for arbitrary single-qubit rotations. Entangling gates, such as CNOT,are utilized to establish quantum correlations. The circuit output is obtained by measuring the expectation value of the Pauli-Ζ operator (〈σZ〉). The trainable parameters are iteratively updated using neural network backpropagation.Once trained, this QNN model efficiently predicts the maximum quantum differentiability of arbitrary quantum bit pair states.The model's performance was evaluated using testing data and a special quantum state (Werner s tate), compared against an ANN. Results demonstrate strong competitiveness against ANNs. We further explored how the QNN's Featurema, Ansatz, and Measurement architectures influence model performance, facilitating easier QNN design in future work.