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. Five nuclear spins in silicon and the [[4, 2, 2]] code are used to demonstrate a universal logical gate set and to execute a variational quantum eigensolver computation of the ground-state energy of a water molecule.

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Nature

Researchers demonstrate the first fault-tolerant logical quantum processor in silicon using five phosphorus nuclear spins and the [[4,2,2]] quantum error-detecting code. The work achieves fault-tolerant preparation of logical states with fidelities up to 97.3%, implements a universal logical gate set including single-qubit gates (X, S, T) and a two-qubit CNOT gate, and realizes the non-Clifford T gate via the gate-by-measurement method. Magic states exceeding the distillation threshold are prepared. As a practical demonstration, a variational quantum eigensolver (VQE) algorithm is executed on two logical qubits to compute the ground-state energy of the water molecule H₂O. The system exhibits strongly biased noise (phase-flip dominated), which is theoretically beneficial for lowering fault-tolerance thresholds. This marks the first realization of universal logical operations in silicon spin qubits, representing a key milestone toward scalable fault-tolerant quantum computing.

Universal logical operations in a silicon quantum processor