A major challenge in practical quantum computation is the ineludible errors caused by the interaction of quantum systems with their environment. Fault-tolerant schemes, in which logical qubits are encoded by several physical qubits, enable to the output of a higher probability of correct logical qubits under the presence of errors. However, strict requirements to encode qubits and operators render the implementation of a full fault-tolerant computation challenging even for the achievable noisy intermediate-scale quantum technology. Especially the threshold for fault-tolerant computation still lacks experimental verification. Here, based on an all-optical setup, we experimentally demonstrate the existence of the threshold for the fault-tolerant protocol. Four physical qubits are represented as the spatial modes of two entangled photons, which are used to encode two logical qubits. The experimental results clearly show that when the error rate is below the threshold, the probability of correct output in the circuit, formed with fault-tolerant gates, is higher than that in the corresponding non-encoded circuit. In contrast, when the error rate is above the threshold, no advantage is observed in the fault-tolerant implementation. The developed high-accuracy optical system may provide a reliable platform to investigate error propagation in more complex circuits with fault-tolerant gates.

实际量子计算的一个主要挑战是由量子系统与其环境的相互作用引起的难以消除的错误。容错方案（其中逻辑量子位由多个物理量子位编码）能够在存在错误的情况下输出更高概率的正确逻辑量子位。然而，对编码量子位和运算符的严格要求使得完全容错计算的实现具有挑战性，即使对于可实现的嘈杂中等规模量子技术也是如此。尤其是容错计算的阈值还缺乏实验验证。在这里，基于全光学设置，我们通过实验证明了容错协议阈值的存在。四个物理量子比特表示为两个纠缠光子的空间模式，用于编码两个逻辑量子位。实验结果清楚地表明，当错误率低于阈值时，由容错门形成的电路正确输出的概率高于相应的非编码电路。相反，当错误率高于阈值时，在容错实现中没有观察到优势。开发的高精度光学系统可以提供一个可靠的平台来研究具有容错门的更复杂电路中的错误传播。当错误率高于阈值时，在容错实现中没有观察到优势。开发的高精度光学系统可以提供一个可靠的平台来研究具有容错门的更复杂电路中的错误传播。当错误率高于阈值时，在容错实现中没有观察到优势。开发的高精度光学系统可以提供一个可靠的平台来研究具有容错门的更复杂电路中的错误传播。