A major challenge in practical quantum computation is the ineludiblle 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.

CAS Key Laboratory of Quantum Information,University of Science and Technology of China,Hefei 230026,China;CAS Center for Excellence in Quantum Information and Quantum Physics,University of Science and Technology of China,Hefei 230026,China;Hefei National Laboratory,University of Science and Technology of China,Hefei 230088,China

[1]Kai Sun;Ze-Yan Hao;Yan Wang;Jia-Kun Li;Xiao-Ye Xu;Jin-Shi Xu;Yong-Jian Han;Chuan-Feng Lj;Guang-Can Guo-.Optical demonstration of quantum fault-tolerant threshold)[J].光：科学与应用（英文版）,2022(08):1834-1842

ineludiblle

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