Multi-qubit quantum logic operations with ion-implanted donor spins in silicon*

Among semiconductor qubits, the electron and nuclear spins of donors in silicon play a special role for their conceptual simplicity (a ³¹P donor in silicon is similar to hydrogen in vacuum) and their exceptional coherence times [1] and 1-qubit gate fidelities [2]. Here I will present experimental progress on multi-qubit logic operations with donor spins, which point to several credible pathways for scalability using ion-implanted donors in MOS-compatible devices. The current state of the art is a hybrid electron-nuclear 3-qubit processor [3], where two ³¹P nuclear spin qubits are coupled to the same electron. The shared electron enables a geometric nuclear two-qubit CZ gate, which we perform with 99.37% average fidelity. NMR single-qubit gates reach fidelities up to 99.95%, and state preparation and measurement are performed with 98.95% fidelity. These three metrics show how close this system is to operating at fault-tolerance thresholds. Further, we entangle the two nuclei with the electron to prepare a 3-qubit GHZ state with 92.5% fidelity. Electron-nuclear entanglement unlocks the ability to connect nuclear qubits via the electrons, for instance using exchange interactions [4]. We have operated a weakly (~10 MHz) exchange-coupled ³¹P donor pair as a 2-qubit electron system, with native CROT gates performed by resonant microwaves. Gate fidelity benchmarks are underway and will be reported at the Meeting. On the engineering side, we have demonstrated the ability to implant single donors in silicon with confidence up to 99.85% [5]. This striking result identifies ion implantation as a scalable and accurate manufacturing strategy for spin-based quantum computers in silicon.