  Spin qubits in silicon are strong contenders for realizing a practical
quantum computer. This technology has made remarkable progress with the
demonstration of single and two-qubit gates 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, only
being achieved for two spin qubits to date due to the small qubit size, which
makes it difficult to control qubits without creating crosstalk errors. Here,
we use a four-qubit silicon processor with every operation above the fault
tolerant limit and demonstrate Grover's algorithm with a ~95% probability of
finding the marked state, one of the most successful implementations to date.
Our four-qubit processor is made of three phosphorus atoms and one electron
spin precision-patterned into 1.5 nm${}^2$ isotopically pure silicon. The
strong resulting confinement potential, without additional confinement gates
that can increase cross-talk, leverages the benefits of having both electron
and phosphorus nuclear spins. Significantly, the all-to-all connectivity of the
nuclear spins provided by the hyperfine interaction not only allows for
efficient multi-qubit operations, but also provides individual qubit
addressability. Together with the long coherence times of the nuclear and
electron spins, this results in all four single qubit fidelities above 99.9%
and controlled-Z gates between all pairs of nuclear spins above 99% fidelity.
The high control fidelities, combined with >99% fidelity 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. Such nuclear spin registers can be coupled via electron
exchange, establishing a path for larger scale fault-tolerant quantum
processors.
