High-rate quantum low-density parity-check (qLDPC) codes are a leading candidate for fault-tolerant quantum computing. They feature higher encoding rates than planar alternatives such as the surface code, but their implementation often entails significant hardware hurdles like the need for long-range couplers. We leverage the flexibility of a trapped-ion quantum computer to demonstrate nine quantum error-correcting codes with starkly different qubit connectivity requirements on a single device without any hardware reconfiguration. These experiments span three families of quantum error-correcting codes: qLDPC codes, topological codes, and concatenated codes. With a qLDPC code encoding 4 logical qubits into 18 physical qubits, we achieve a logical error rate up to $9\times$ better than a previous demonstration of a similar code on superconducting solid-state qubits. Moreover, our implementation exhibits breakeven performance, with some instances achieving qubit lifetimes comparable to or slightly exceeding that of our trapped-ion qubits. We use a novel implementation of the optical-metastable-ground (OMG) architecture for addressable mid-circuit measurement and reset, which enables us to perform these experiments without any ion transport or dedicated coolant ions, requirements that typically consume a large fraction of the runtime or ion count of trapped-ion quantum computers.

翻译：高编码率的量子低密度奇偶校验码（qLDPC codes）是容错量子计算的主要候选方案。与平面替代方案（如表面码）相比，它们具有更高的编码率，但其实现通常面临显著的硬件挑战，例如需要远程耦合器。我们利用离子阱量子计算机的灵活性，在无需任何硬件重构的情况下，在同一设备上演示了九种具有截然不同量子比特连接需求的量子纠错码。这些实验涵盖三类量子纠错码：qLDPC码、拓扑码和级联码。使用一种将4个逻辑量子比特编码到18个物理量子比特中的qLDPC码，我们实现的逻辑错误率比此前在超导固态量子比特上同类码的演示结果最高提升9倍。此外，我们的实现展现出盈亏平衡性能，某些实例中量子比特寿命达到或略微超过离子阱量子比特的寿命。我们采用一种新型光学亚稳态-基态（OMG）架构实现可寻址的电路中间测量与重置，这使得我们无需任何离子传输或专用冷却离子即可完成这些实验——这两项需求通常会消耗离子阱量子计算机运行时或离子数的很大比例。