Entanglement dynamics via Geometric phases in Trapped-ions

TL;DR

This work addresses the challenge of diagnosing MS-gate performance in trapped-ion systems under environmental noise without resorting to full tomography. It introduces geometric phase (GP) analysis, using the kinematic GP framework, to monitor MS gate dynamics in both weak-field and strong-field regimes, with particular sensitivity to noise near $2T$. Key findings show that GP vanishes for ideal WF evolution but becomes nonzero with realistic parameters, and SF dynamics exhibit sharp GP features around $2T$ that correlate with entanglement decay; GP measurements also reveal signatures of non-local noise in subsystems. The approach offers a practical, tomography-free diagnostic tool that scales with system size and could be extended to multipartite gates and other qubit platforms, including considerations of non-Markovian noise.

Abstract

Trapped-ion systems are a leading platform for quantum computing. The Mølmer-Sørensen (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.

Figures (10)

• Figure 1: Energy band diagram for a two-qubit system subject to MS-interaction.
• Figure 2: Population density of energy levels during MS interaction under WF condition: $\eta = 0.1$, $\Omega = 0.1\nu$, $\delta = 0.9 \nu$, as given in ExptG38.
• Figure 3: Population density of different energy levels when MS interaction is operated in SF regime: $\omega_m = 2\pi \times2.03 \text{MHz}$, $\delta = 2\pi \times 16.7\text{kHz}$, $\eta = 0.028$, $\Omega = 2\pi \times 270\text{kHz}$ which results in $T = 66\mu s$ as given in thesis.
• Figure 4: Oscillation of entanglement measured using negativity of quantum state initially in $\ket{00}$ state during MS interaction in SF regime
• Figure 5: GP acquired by the quantum state undergoing MS-interaction under WF condition for different values of $\eta$.