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<p>Quantum errors induced by environmental noise are unavoidable and preclude the direct implementation of practical quantum computation. Fault-tolerant quantum computation offers one of the viable paths, necessitating the encoding and processing of information within logical qubits to curb such errors. Although substantial progress has been achieved recently in building silicon quantum computers, logical operations still haven’t been realized in silicon. Here we demonstrate a logical quantum processor using a phosphorus donor cluster in silicon. By implementing the [[4, 2, 2]] code, we realize the essential components for logical operations, which include fault-tolerant preparation of logical states and the characterization of a universal gate set comprising logical single-qubit and two-qubit gates. In particular, the logical <i>T</i> gate is achieved using the gate-by-measurement method, and magic states based on this gate are prepared. Furthermore, we execute the variational quantum eigensolver algorithm using two logical qubits and simulate the ground state of the electronic structure of the water molecule H<sub>2</sub>O. This work represents a key step towards scalable, fault-tolerant quantum computation in silicon spin qubits.</p>

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Universal logical operations in a silicon quantum processor

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年3月23日

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  • Chunhui Zhang,
  • Feng Xu,
  • Shihang Zhang,
  • Mingchao Duan,
  • Dupeng Zhong,
  • Xuesong Bai,
  • Hao Wang,
  • Chao Huang,
  • Yi Deng,
  • Miao Gao,
  • Yu-Ning Zhang,
  • Jiaze Liu,
  • Chunhui Li,
  • Yan Jiang,
  • Baolong Zhao,
  • Huan Shu,
  • Kunrong Wu,
  • Keji Shi,
  • Qiming Ding,
  • Zhen Tian,
  • Guanyong Wang,
  • Xiao Yuan,
  • Tao Xin,
  • Guangchong Hu,
  • Song Liu,
  • Tianluo Pan,
  • Peihao Huang,
  • Yu He,
  • Dapeng Yu

摘要

Quantum errors induced by environmental noise are unavoidable and preclude the direct implementation of practical quantum computation. Fault-tolerant quantum computation offers one of the viable paths, necessitating the encoding and processing of information within logical qubits to curb such errors. Although substantial progress has been achieved recently in building silicon quantum computers, logical operations still haven’t been realized in silicon. Here we demonstrate a logical quantum processor using a phosphorus donor cluster in silicon. By implementing the [[4, 2, 2]] code, we realize the essential components for logical operations, which include fault-tolerant preparation of logical states and the characterization of a universal gate set comprising logical single-qubit and two-qubit gates. In particular, the logical T gate is achieved using the gate-by-measurement method, and magic states based on this gate are prepared. Furthermore, we execute the variational quantum eigensolver algorithm using two logical qubits and simulate the ground state of the electronic structure of the water molecule H2O. This work represents a key step towards scalable, fault-tolerant quantum computation in silicon spin qubits.