This paper researches maximally entangled Greenberger–Horne–Zeilinger (GHZ) states in a four-qubit system using Ytterbium-171 ions. A framework for a multiple instruction single data (MISD) control framework is proposed and implemented with a hyperfine ground state of Ytterbium-171 ( \(^{171}\text {Yb}^{+}\) ) ions, insensitive to noise due to magnetic field fluctuations of first order. The global entangling Molmer–Sorensen operations and single-qubit rotations apprehend the collective vibrational phonon mode ion interactions. We prove the resilience of the states by generating the pulse sequence with \(1.73 \times 10^{3}\) Hz leakage noise to mitigate errors due to laser-induced decoherence and qubit crosstalk. Results demonstrate the effective creation of GHZ states with a fidelity of 96.42% extending the operational scope of trapped-ion quantum systems towards practical quantum information processing.
