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

Spin qubits in silicon are strong contenders for realizing a practical quantum computer. This technology has made remarkable progress in recent years with the demonstration of single and two-qubit gates with fidelities above the fault-tolerant threshold and entanglement of up to three qubits. However, maintaining high fidelity operations while executing multi-qubit algorithms has remained elusive and only achieved for two spin qubits to date. Here, we use 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 record-breaking ~95% probability of finding the marked state. Our four-qubit processor consists of three nuclear spins hyperfine-coupled via an electron spin, providing an all-to-all connectivity in the form of efficient multi-qubit operations in which a single qubit gate on the electron spin can entangle multiple nuclear spins. Together with the long coherence times of the phosphorus nuclear spins and the electron spin, this results in all four single qubit fidelities above 99.9% and controlled-Z gates between all pairs of nuclear spins above 99% fidelity when using the electron as an ancilla qubit. These control fidelities, combined with the high-fidelity non-demolition readout of all nuclear spins, allows for the creation of a three-qubit Greenberger–Horne–Zeilinger (GHZ) state with 96.2% fidelity, the highest reported for semiconductor spin qubits so far.