Exchange-Only Silicon Based Spin Qubits: Charge Noise, PINN Optimised Pulse Sequences,and Gate-Level Fidelity

Abstract: Exchange-only (EO) spin qubits in silicon realise all-electrical qubit control through pairwise Heisenberg exchange interactions, making them attractive for scalable quantum computation. Their principal vulnerability is charge noise, which couples multiplicatively to the exchange coupling and degrades gate fidelity. We present a \emph{two-stage} Physics-Informed Neural Network (PINN) framework for per-gate pulse optimisation. In \textbf{Stage~I} (iterations~1--100) the PINN maximises the noise-averaged gate fidelity toward a threshold of $\Fth=0.99$; the pulse duration is held fixed at its nominal hardware value. Once the threshold is crossed, \textbf{Stage~II} (iterations~101--250) progressively compresses the total pulse time while maintaining $F\geq\Fth$ via continuous fine-tuning of the pulse-shape parameters. The cost function is a Monte-Carlo ensemble mean-squared error (MSE) averaged over $N_{\rm real}=2000$ quasi-static Gaussian noise realisations drawn fresh at every iteration. We benchmark the framework on the single-qubit gate set ${X,Y,Z,H}$ and the two-qubit set ${X,Y,Z,H,\mathrm{CX}}$ at noise levels $\sigmaJ/J\in{1\%,5\%,10\%}$. All single-qubit gates cross $\Fth$ within the first 100 iterations across all noise levels; Stage~II then reduces pulse durations by 20--40\% from their nominal values. The two-qubit gates follow the same two-phase behaviour, with the CX gate compressing from its nominal \SI{31}{\nano\second} to $\approx\SI{22}{\nano\second}$ at 1\% noise.