Bryan Gard

Many-qubit Mølmer-Sørensen (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 $χ^2_\mathrm{red} \approx 2$. 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.

We present methods for constructing any target coupling graph using limited global controls in an Ising-like quantum spin system. Our approach is motivated by implementing the quantum approximate optimization algorithm (QAOA) on trapped ion quantum hardware to find approximate solutions to Max-Cut. We present a mathematical description of the problem and provide approximately optimal algorithmic constructions that generate arbitrary unweighted coupling graphs with $n$ nodes in $O(n)$ global entangling operations and weighted graphs with $m$ edges in $O(m)$ operations. These upper bounds are not tight in general, and we formulate a mixed-integer program to solve the graph coupling problem to optimality. We perform numeric experiments on small graphs with $n\le8$ and show that optimal sequences, which use fewer operations, can be found using mixed-integer programs. Noisy simulations of Max-Cut QAOA show that our implementation is less susceptible to noise than the standard gate-based compilation.