Minimal Time Robust Control for Superconducting Qubit Devices*

Fault tolerant quantum computing requires quantum gates with high delity. Given limitations
on the lifetime of the qubits two-qubit gate delities can be coherence limited if the gate times are
too long, but decreasing the operation time of two-qubit gates is a non-trivial exercise. Optimal
control techniques can be used to decrease the operation time in theory, but generally do not take
into account the realistic nature of uncertainty within the system when doing so. We apply robust
optimal control techniques to demonstrate that it is feasible to reduce the operation time of the
cross-resonance gate in superconducting systems to under 100 ns with two-qubit gate delities of
F > 0:999, where this gate delity will not be coherence limited and would thus be achievable in
experimental operation. This is while ensuring the pulse is robust to some uncertainty in the system,
and having chosen a parameterization that aides in experimental feasibility.