Neural-network-designed three-qubit gates robust against charge noise and crosstalk in silicon

Spin qubits in semiconductor quantum dots are a promising platform for quantum computing, however scaling to large systems is hampered by crosstalk and charge noise. Crosstalk here refers to the unwanted off-resonant rotation of idle qubits during the resonant rotation of the target qubit. For a three-qubit system with crosstalk and charge noise, it is difficult to analytically create gate protocols that produce three-qubit gates, such as the Toffoli gate, directly in a single shot instead of through the composition of two-qubit gates. Therefore, we numerically optimize a physics-informed neural network to produce theoretically robust shaped pulses that generate a Toffoli-equivalent gate. Additionally, robust $\frac{\pi}{2}$ $X$ and CZ gates are also presented in this work to create a universal set of gates robust against charge noise. The robust pulses maintain an infidelity of $10^{-3}$ for average quasistatic fluctuations in the voltage of up to a few mV instead of tenths of mV for non-robust pulses.