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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.
This paper demonstrates Grover’s search algorithm on a four-qubit silicon processor with every operation above the fault-tolerant limit. This is a significant result because it showcases a successful implementation of a multi-qubit algorithm in a solid-state platform with high fidelity, paving the way for larger and more complex quantum computations.
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