Entanglement dynamics via Geometric phases in Trapped-ions

Trapped-ion systems are a leading platform for quantum computing. The M{\o}lmer-S{\o}rensen (MS) gate is a widely used method for implementing controlled interactions in multipartite systems. However, due to unavoidable interactions with the environment, quantum states undergo non-unitary evolution, leading to significant deviations from ideal dynamics. Common techniques such as Quantum Process Tomography (QPT) and Bell State Tomography (BST) are typically employed to evaluate MS gate performance and to characterize noise in the system. In this letter, we propose leveraging the geometric phase as a tool for performance assessment and noise identification in the MS gate. Our findings indicate that the geometric phase is particularly sensitive to environmental noise occurring around twice the clock pulse time. Given that geometric phase measurements do not require full-state tomography, this approach offers a practical and experimentally feasible method to detect entanglement and classify the nature of noise affecting the system.
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