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. Single- and two-qubit gates have shown fidelities above the fault-tolerant threshold, and entanglement of three qubits has been achieved. Furthermore, high-fidelity operation of two-qubit algorithms is possible. Here we implement a four-qubit silicon processor with all control fidelities above the fault-tolerant threshold. We demonstrate a three-qubit Grover’s search algorithm with a ~95% probability of finding the marked state. To this end, we fabricate the processor from three phosphorus atoms precision-patterned into isotopically pure silicon. We define three phosphorus nuclear spin qubits and one electron spin qubit. The long coherence times of the qubits enable single-qubit fidelities above 99.9% for all qubits. Moreover, the efficient single-pulse multi-qubit operation enabled by the electron–nuclear hyperfine interaction facilitates controlled-Z gates with above 99% fidelity between all pairs of nuclear spins when using the electron as an ancilla. These control fidelities, combined with high-fidelity non-demolition readout of all nuclear spins, allows 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, yet fault-tolerant, quantum processors.