Modelling noise in global Molmer-Sorensen interactions applied to quantum approximate optimization

TL;DR

This paper develops a comprehensive physical noise model for many-qubit Mølmer-Sørensen interactions in trapped ions, validated against experiments, and used to predict and improve quantum approximate optimization algorithm performance.

Contribution

The paper introduces a parameterized noise model for many-qubit MS interactions based on simple measurements, validated with experiments, and applied to optimize QAOA performance predictions.

Findings

Model shows reasonable agreement with experiments (χ²_red ≈ 2).

Predicted QAOA approximation ratios are close to experimental values.

Improvements in measurement and trap stability could increase ratios to 99% of optimal.

Abstract

Many-qubit M{\o}lmer-S{\o}rensen (MS) interactions applied to trapped ions offer unique capabilities for quantum information processing, with applications including quantum simulation and the quantum approximate optimization algorithm (QAOA). Here, we develop a physical model to describe many-qubit MS interactions under four sources of experimental noise: vibrational mode frequency fluctuations, laser power fluctuations, thermal initial vibrational states, and state preparation and measurement errors. The model parameterizes these errors from simple experimental measurements, without free parameters. We validate the model in comparison with experiments that implement sequences of MS interactions on two $^{171}$Yb$^+$ ions. The model shows reasonable agreement after several MS interactions as quantified by the reduced chi-squared statistic $\chi^2_\mathrm{red} \approx 2$. As an application we examine MaxCut QAOA experiments on three and six ions. The experimental performance is quantified by approximation ratios that are $91\%$ and $83\%$ of the optimal theoretical values. Our model predicts $0.93^{+0.03}_{-0.02}$ and $0.95^{+0.04}_{-0.03}$, respectively, with disagreement in the latter value attributable to secondary noise sources beyond those considered in our analysis. With realistic experimental improvements to reduce measurement error and radial trap frequency variations the model achieves approximation ratios that are 99$\%$ of the optimal. Incorporating these improvements into future experiments is expected to reveal new aspects of noise for future modeling and experimental improvements.