Precision tomography of a three-qubit donor quantum processor in silicon

Nuclear spins were among the first physical platforms to be considered for quantum information processing(1,2), because of their exceptional quantum coherence(3) and atomic-scale footprint. However, their full potential for quantum computing has not yet been realized, owing to the lack of methods with which to link nuclear qubits within a scalable device combined with multi-qubit operations with sufficient fidelity to sustain fault-tolerant quantum computation. Here we demonstrate universal quantum logic operations using a pair of ion-implanted P-31 donor nuclei in a silicon nanoelectronic device. A nuclear two-qubit controlled-Z gate is obtained by imparting a geometric phase to a shared electron spin(4), and used to prepare entangled Bell states with fidelities up to 94.2(2.7)%. The quantum operations are precisely characterized using gate set tomography (GST)(5), yielding one-qubit average gate fidelities up to 99.95(2)%, two-qubit average gate fidelity of 99.37(11)% and two-qubit preparation/measurement fidelities of 98.95(4)%. These three metrics indicate that nuclear spins in silicon are approaching the performance demanded in fault-tolerant quantum processors(6). We then demonstrate entanglement between the two nuclei and the shared electron by producing a Greenberger-Horne-Zeilinger three-qubit state with 92.5(1.0)% fidelity. Because electron spin qubits in semiconductors can be further coupled to other electrons(7-9) or physically shuttled across different locations(10,11), these results establish a viable route for scalable quantum information processing using donor nuclear and electron spins.

Automated summary

This study demonstrates universal quantum logic operations using nuclear spins in a silicon nanoelectronic device, achieving high-fidelity entangled states. The precise characterization of quantum operations shows that nuclear spins are approaching the performance required for fault-tolerant quantum processors. Additionally, the entanglement between nuclear spins and electron spins is also demonstrated. The results establish a viable route for scalable quantum information processing using donor nuclear and electron spins.