Grover’s algorithm in a four-qubit silicon processor above the fault-tolerant threshold

Abstract

Spin qubits in silicon are strong contenders for the realization of a practical quantum computer, having demonstrated single- and two-qubit gates with fidelities above the fault-tolerant threshold, and entanglement of three qubits. However, maintaining high-fidelity operations while increasing the qubit count remains challenging and therefore only two-qubit algorithms have been executed. Here we utilize a four-qubit silicon processor with all control fidelities above the fault-tolerant threshold and demonstrate a three-qubit Grover’s search algorithm with a ~95% probability of finding the marked state. Our processor is made of three phosphorus atoms precision-patterned into isotopically pure silicon, which localise one electron. The long coherence times of the qubits enable single-qubit fidelities above 99.9% for all qubits. Moreover, the efficient single-pulse multi-qubit operations enabled by the electron–nuclear hyperfine interaction facilitate controlled-Z gates between all pairs of nuclear spins with fidelities above 99% when using the electron as an ancilla. These control fidelities, combined with high-fidelity non-demolition readout of all nuclear spins, allow the creation of a three-qubit Greenberger–Horne–Zeilinger state with 96.2% fidelity. Looking ahead, coupling neighbouring nuclear spin registers, as the one shown here, via electron–electron exchange may enable larger, fault-tolerant quantum processors. A four-qubit processor of three phosphorus nuclear spins and an electron spin in silicon enables the implementation of a three-qubit Grover’s search algorithm with 95% fidelity. The implementation is based on an advanced multi-qubit gate with single-qubit gate fidelities above 99.9% and two-qubit gate fidelities above 99%.