The development of quantum computing architectures from early designs and current noisy devices to fully fledged quantum computers hinges on achieving fault tolerance using quantum error correction^1,2,3,4. However, these correction capabilities come with an overhead for performing the necessary fault-tolerant logical operations on logical qubits (qubits that are encoded in ensembles of physical qubits and protected by error-correction codes)^5,6,7,8. One of the most resource-efficient ways to implement logical operations is lattice surgery^9,10,11, where groups of physical qubits, arranged on lattices, can be merged and split to realize entangling gates and teleport logical information. Here we report the experimental realization of lattice surgery between two qubits protected via a topological error-correction code in a ten-qubit ion-trap quantum information processor. In this system, we can carry out the necessary quantum non-demolition measurements through a series of local and entangling gates, as well as measurements on auxiliary qubits. In particular, we demonstrate entanglement between two logical qubits and we implement logical state teleportation between them. The demonstration of these operations—fundamental building blocks for quantum computation—through lattice surgery represents a step towards the efficient realization of fault-tolerant quantum computation.

从早期设计和当前嘈杂设备到成熟的量子计算机，量子计算架构的发展取决于使用量子纠错^1,2,3,4实现容错。然而，这些校正功能伴随着对逻辑量子位（在物理量子位集合中编码并受纠错码保护的量子位）执行必要的容错逻辑操作的开销^5,6,7,8。实现逻辑运算最节省资源的方法之一是格子手术^9,10,11，其中排列在格子上的物理量子位组可以合并和拆分以实现纠缠门和传送逻辑信息。在这里，我们报告了在十量子位离子阱量子信息处理器中通过拓扑纠错码保护的两个量子位之间晶格手术的实验实现。在这个系统中，我们可以通过一系列局域和纠缠门进行必要的量子非破坏测量，以及对辅助量子比特的测量。特别是，我们展示了两个逻辑量子位之间的纠缠，并在它们之间实现了逻辑状态隐形传态。通过晶格手术对这些操作（量子计算的基本构建块）的演示代表了朝着有效实现容错量子计算迈出的一步。