Quantum error correction is an essential ingredient for universal quantum computing.Despite tremendous experimental efforts in the study of quantum error correction,to date,there has been no demonstration in the realisation of universal quantum error-correcting code,with the subsequent verification of all key features including the identification of an arbitrary physical error,the capability for transversal manipulation of the logical state and state decoding.To address this challenge,we experimentally realise the[5,1,3]code,the so-called smallest perfect code that permits corrections of generic single-qubit errors.In the experiment,having optimised the encoding circuit,we employ an array of superconducting qubits to realise the[5,1,3]code for several typical logical states including the magic state,an indispensable resource for realising non-Clifford gates.The encoded states are prepared with an average fidelity of 57.1 (3)％ while with a high fidelity of 98.6(1)％ in the code space.Then,the arbitrary single-qubit errors introduced manually are identified by measuring the stabilisers.We further implement logical Pauli operations with a fidelity of 97.2(2)％ within the code space.Finally,we realise the decoding drcuit and recover the input state with an overall fidelity of 74.5(6)％,in total with 92 gates.Our work demonstrates each key aspect of the[5,1,3]code and verifies the viability of experimental realisation of quantum error-correcting codes with superconducting qubits.

Ming Gong;Xiao Yuan;Shiyu Wang;Yulin Wu;Youwei Zhao;Chen Zha;Shaowei Li;Zhen Zhang;Qi Zhao;Yunchao Liu;Futian Liang;Jin Lin;Yu Xu;Hui Beng;Hao Rong;He Lu;Simon C.Benjamin;Cheng-Zhi Peng;Xiongfeng Ma;Yu-Ao Chen;Xiaobo Zhu;Jian-Wei Pan

Hefei National Laboratory for Physical Sciences at the Microscale and Department of Modern Physics,University of Science and Technology of China,Hefei 230026,China;Shanghai Branch,CAS Center for Excellence and Synergetic Innovation Center in Quantum Information and Quantum Physics,University of Science and Technology of China,Shanghai 201315,China;Shanghai Research Center for Quantum Sciences,Shanghai 201315,China;Center for Quantum Information,Institute for Interdisciplinary Information Sciences,Tsinghua University,Beijing 100084,China;Department of Materials,University of Oxford,Oxford OX13PH,UK

国家科学评论（英文版）

[1]Ming Gong;Xiao Yuan;Shiyu Wang;Yulin Wu;Youwei Zhao;Chen Zha;Shaowei Li;Zhen Zhang;Qi Zhao;Yunchao Liu;Futian Liang;Jin Lin;Yu Xu;Hui Beng;Hao Rong;He Lu;Simon C.Benjamin;Cheng-Zhi Peng;Xiongfeng Ma;Yu-Ao Chen;Xiaobo Zhu;Jian-Wei Pan-.Experimental exploration of five-qubit quantum error-correcting code with superconducting qubits)[J].国家科学评论（英文版）,2022(01):95-101

realising,stabilisers,drcuit

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