Error-corrected simultaneous control at the quantum speed limit

Simultaneous control of two or more Qubits has typically been done by addressing the two qubits separately in frequency space or sequentially by having them make multiple revolutions. While effective, these approaches require relatively long pulses; executing state transitions as quickly as possible is a virtue in many quantum information applications.
Here we present an analytic result for simultaneous trajectories at the quantum speed limit. We demonstrate these pulses on a xenon-129 spin ensemble and further demonstrate error correction for this type of pulse as well. Our approach provides a way to achieve two key "wants" in quantum information that are often in tension: the ability to perform gates both quickly and robustly to errors.