Assessing the limits of controllability for electron spin qubits through quantum optimal control

Evaluating the most optimistic capabilities of quantum devices for specific applications is a nascent use of quantum optimal control theory, where classical numerical simulations estimate essential properties such as quantum speed limits and minimum control times as a function of system parameters and limitations. Here we estimate these quantities for nitrogen-vacancy centers in diamond, a paradigmatic example of an electron spin qubit. Our simulations are performed at high accuracy beyond the rotating wave approximation and through explicit unitary simulation of neighboring nuclear spins. Using the gradient optimization of analytic controls method we identify realistic analytical pulses for unitary control and quantify the relationship between pulse complexity, control time, and fidelity. These simulations provide insight into the throughput of quantum foundries and inform quantum device engineers about the fundamental computational and sensing rates in prospective quantum technologies.