Global State Resilience: A Turing-Inspired Analysis of Grover’s Algorithm Under Decoherence

This study investigates Grover’s quantum search algorithm under decoherence using a global state evolution approach, implemented via an R-based simulator with Monte Carlo averaging. By introducing Gaussian and uniform noise perturbations during iterations, we demonstrate that the algorithm’s full probability distribution maintains structural stability despite decoherence, deviating only slightly from the ideal uniform distribution. Our findings suggest that global state analysis enhances noise resilience compared to single-measurement models, supporting the potential of Turing-quantum hybrid computing for high-performance applications. Future work will explore multi-qubit extensions and error correction integration.