Trapped ion (TI) qubits are a leading quantum computing platform. Current TI systems have less than 60 qubits, but a modular architecture known as the Quantum Charge-Coupled Device (QCCD) is a promising path to scale up devices. There is a large gap between the error rates of near-term systems ($10^{-3}$ to $10^{-4}$) and the requirements of practical applications (below $10^{-9}$). To bridge this gap, we require Quantum Error Correction (QEC) to build \emph{logical qubits} that are composed of multiple physical qubits. While logical qubits have been demonstrated on TI qubits, these demonstrations are restricted to small codes and systems. There is no clarity on how QCCD systems should be designed to implement practical-scale QEC. This paper studies how surface codes, a standard QEC scheme, can be implemented efficiently on QCCD-based systems. To examine how architectural parameters of a QCCD system can be tuned for surface codes, we develop a near-optimal topology-aware compilation method that outperforms existing QCCD compilers by an average of 3.8X in terms of logical clock speed. We use this compiler to examine how hardware trap capacity, connectivity and electrode wiring choices can be optimised for surface code implementation. In particular, we demonstrate that small traps of two ions are surprisingly ideal from both a performance-optimal and hardware-efficiency standpoint. This result runs counter to prior intuition that larger traps (20-30 ions) would be preferable, and has the potential to inform design choices for upcoming systems.

翻译：囚禁离子（TI）量子比特是一种主流的量子计算平台。当前TI系统的量子比特数少于60个，但一种称为量子电荷耦合器件（QCCD）的模块化架构为扩展系统规模提供了可行路径。近期系统的错误率（$10^{-3}$至$10^{-4}$）与实际应用需求（低于$10^{-9}$）之间存在巨大差距。为弥合这一差距，我们需要通过量子纠错（QEC）构建由多个物理量子比特组成的逻辑量子比特。尽管已在TI量子比特上演示了逻辑量子比特的实现，但这些演示仅限于小型编码和系统。目前尚不清楚应如何设计QCCD系统以实现实用规模的量子纠错。本文研究了如何基于QCCD系统高效实现表面码这一标准量子纠错方案。为探究如何针对表面码调整QCCD系统的架构参数，我们开发了一种近似最优的拓扑感知编译方法，其逻辑时钟速度平均达到现有QCCD编译器的3.8倍。利用该编译器，我们分析了如何针对表面码实现优化硬件囚禁阱容量、连接性和电极布线选择。特别地，我们证明从性能最优和硬件效率的角度来看，仅囚禁两个离子的小型阱具有出人意料的理想特性。这一结果与先前认为较大囚禁阱（20-30个离子）更优的直觉认知相悖，可能为未来系统的设计选择提供重要参考。