High-Fidelity CNOT Gate for Donor Electron Spin Qubits in Silicon

Donor dots realized with phosphorus atoms in silicon have proven to be excellent hosts for electron spin qubits as they provide a strong confining potential that results in small wave functions and well-isolated ground states. As a promising candidate for large-scale quantum computers, such qubits have demonstrated fast, high-fidelity single-shot readout (99.8%) and extremely long coherence times (seconds) with single-qubit gates exceeding 99.94% fidelity. However, high-fidelity two-qubit gates in this platform have been elusive, with charge noise being one of the key limiting factors. Charge noise causes unwanted fluctuations in the exchange coupling between electron spins resulting in logic gate errors, a process that could be minimized if we could engineer a large enough magnetic field difference between the qubits. In this work, we show that using the donor nuclear spins as nanomagnets we can engineer a large magnetic field gradient (> 800 MHz) between the qubits thereby minimizing sensitivity to charge noise and reducing errors during two-qubit controlled-NOT (CNOT) gate operation. We develop a comprehensive theoretical framework with realistic noise sources for performing CNOT gates via controlled rotation (CROT) using multidonor dot qubits. We show that by engineering the number and location of donors within the dots we can control the hyperfine couplings to maximize the energy difference between electron spin qubits. As a result, we show that the CNOT gate error rates can be reduced by a factor of 4 when using multidonor dots as compared to single donors. Our results provide a theoretical roadmap to show how to achieve CNOT fidelities as high as 99.98% by optimizing both the local magnetic environment and the operating parameters of multidonor dot qubits.