Geometric phase and entanglement dynamics in trapped ion systems

Systems adopted as platforms for quantum computing typically undergo deviations from ideal dynamics due to unavoidable interactions with the environment. The hallmark of computational power is the entanglement in the system, which could suffer due to noise. Typically, gate performance is analysed and noise characterised by Quantum Process Tomography and Bell state tomography. However these methods are resource intensive, and scale exponentially with system size. In this work, we propose leveraging the geometric phase(GP) as a tool for performance assessment and noise identification in the Molmer-Sorensen (MS) gate, a commonly used entangling gate in trapped ion systems. Our findings indicate that the GP is particularly sensitive to environmental noise occurring around twice the clock pulse time. Given that GP 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.