General-purpose quantum computers can, in principle, entangle a number of noisy physical qubits to realize composite qubits protected against errors. Architectures for measurement-based quantum computing intrinsically support error-protected qubits and are the most viable approach for constructing an all-photonic quantum computer. Here we propose and demonstrate an integrated silicon photonic scheme that both entangles multiple photons, and encodes multiple physical qubits on individual photons, to produce error-protected qubits. We realize reconfigurable graph states to compare several schemes with and without error-correction encodings and implement a range of quantum information processing tasks. We observe a success rate increase from 62.5% to 95.8% when running a phase-estimation algorithm without and with error protection, respectively. Finally, we realize hypergraph states, which are a generalized class of resource states that offer protection against correlated errors. Our results show how quantum error-correction encodings can be implemented with resource-efficient photonic architectures to improve the performance of quantum algorithms.

原则上，通用量子计算机可以纠缠多个嘈杂的物理量子位，以实现防止错误的复合量子位。基于测量的量子计算架构本质上支持错误保护的量子位，并且是构建全光子量子计算机的最可行方法。在这里，我们提出并演示了一种集成的硅光子方案，该方案既可以纠缠多个光子，又可以在单个光子上编码多个物理量子位，以产生错误保护的量子位。我们实现了可重构图状态，以比较具有和不具有纠错编码的几种方案，并实现一系列量子信息处理任务。我们观察到，在没有和有错误保护的情况下运行相位估计算法时，成功率分别从 62.5% 增加到 95.8%。最后，我们实现了超图状态，它是一类通用的资源状态，可以防止相关错误。我们的结果显示了如何使用资源高效的光子架构实现量子纠错编码，以提高量子算法的性能。