Overcoming limitations on gate fidelity in noisy static exchange-coupled surface qubits

Abstract Recent experiments demonstrated that the spin state of individual atoms on surfaces can be quantum-coherently controlled through all-electric electron spin resonance. By constructing interacting arrays of atoms, this results in an atomic-scale qubit platform. However, the static exchange coupling between qubits, limited lifetime, and polarization of the initial state impose significant limits on high-fidelity quantum control. We address this issue using open quantum systems simulation and quantum optimal control theory. We demonstrate the conditions under which high-fidelity operations ( $${\mathcal{F}}\,\gtrsim\, 0.9$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>F</mml:mi> <mml:mspace/> <mml:mo>≳</mml:mo> <mml:mspace/> <mml:mn>0.9</mml:mn> </mml:mrow> </mml:math> ) are feasible in this qubit platform, and show how the Krotov method of quantum optimal control theory adapts to specific noise sources to outperform the conventional Rabi drivings. Finally, we re-examine the experimental setup used in the initial demonstration of this qubit platform and propose optimized experimental designs to maximize gate fidelity in this platform.