Exploring operation parallelism vs. ion movement in ion-trapped QCCD architectures

Ion-trapped Quantum Charge-Coupled Device (QCCD) architectures have emerged as a promising alternative to scale single-trap devices by interconnecting multiple traps through ion shuttling, enabling the execution of parallel operations across different traps. While this parallelism enhances computational throughput, it introduces additional operations, raising the following question: do the benefits of parallelism outweigh the potential loss of fidelity due to increased ion movements? This paper answers this question by exploring the trade-off between the parallelism of operations and fidelity loss due to movement overhead, comparing sequential execution in single-trap devices with parallel execution in QCCD architectures. We first analyze the fidelity impact of both methods, establishing the optimal number of ion movements for the worst-case scenario. Next, we evaluate several quantum algorithms on QCCD architectures by exploiting parallelism through ion distribution across multiple traps. This analysis identifies the algorithms that benefit the most from parallel executions, explores the underlying reasons, and determines the optimal balance between movement overhead and fidelity loss for each algorithm.