Quantum system reliability: A phase-encoded interference framework for interdependent and interconnected systems

Accurate reliability assessment of interconnected and interdependent systems requires explicit representation of interaction mechanisms arising from shared components, load redistribution, feedback coupling, and correlated degradation. Classical system reliability theory is formulated using real-valued probabilities and combinatorial aggregation and therefore lacks an intrinsic mathematical structure capable of encoding interaction strength, synchronization, and pathway competition. As a result, redundancy and vulnerability in highly coupled systems are often mischaracterized. This study introduces a quantum system reliability (QSR) framework that reformulates system reliability as a complex-valued field. In the proposed representation, the magnitude of each component amplitude corresponds to postevent functionality, while the phase encodes interaction induced by connectivity, redistribution, constraint release, and dependency. Because classical reliability contains no inherent phase information, this work rigorously defines reliability phase. It develops two independent extraction strategies: (1) a spectral-domain formulation based on discrete Fourier analysis of reliability fields, and (2) a quantum-field formulation derived from divergence, curl, and geometry-induced flux operators. Component reliabilities are encoded as complex amplitudes, and system reliability emerges through interference-aware aggregation rules that generalize classical series, parallel and inclusion-exclusion principles. The formulation preserves exact classical reliability under neutral-phase conditions while enabling constructive and destructive interference in the presence of dependencies. The framework is validated using benchmark networks, including cascading IEEE-118 data and interdependent graph models, demonstrating improved alignment with functional system behavior compared to classical connectivity-based metrics.