Quantum-Driven Resource Optimization for Full-Duplex STAR-RIS-Aided NOMA-ISAC With Constraint Projection

Abstract

This paper proposes a projected quantum gradient descent (P-QGD) framework for joint beamforming and simultaneously transmitting and reflecting reconfigurable intelligent surfaces (STAR-RIS) configuration in full-duplex non-orthogonal multiple access (NOMA)-assisted integrated sensing and communication (ISAC) systems. A parameterized quantum circuit (PQC) encodes downlink beamforming vectors, STAR-RIS phase shifts, and amplitude reflection/transmission coefficients into quantum states using Pauli-$X$ rotation gates. At each iteration, measurement-based stochastic gradients are projected onto a constrained feasible set to ensure physical realizability, including unit-modulus phase constraints, amplitude normalization, and transmit power limits. A convergence guarantee is established under standard smoothness and bounded variance assumptions. The proposed P-QGD method exhibits logarithmic scaling in parameter dimensionality and achieves faster convergence compared to classical projected stochastic gradient descent (P-SGD). Extensive simulations validate that P-QGD yields higher downlink sum rate, improved sensing signal-to-interference-plus-noise ratio, and superior beamforming sharpness across varying reconfigurable intelligent surfaces (RIS) sizes, channel state information errors, and sensing–communication trade-offs. The framework also enables physical interpretability by linking quantum-optimized parameters to far-field beam pattern behavior. This work demonstrates the feasibility and advantages of quantum-native optimization in RIS-aided ISAC systems with constrained, multi-objective requirements.