Quantum optimal control in a generalized rotating frame

With superconducting-qubit gate operations now routinely approaching their speed limits, strategies for mitigating the impact of coherent errors are increasingly important. In this talk, we introduce a method for quantum optimal control in an extended Hilbert space, where the quantum dynamics becomes exactly differentiable without needing rotating-wave approximations. Our representation exploits an expansion of the quantum controls in a physically motivated basis, which conveniently leads to waveforms with a bounded frequency spectrum. We perform numerical simulations using our optimal-control method and demonstrate improved two-qubit gate fidelities for typical transmon- and fluxonium-qubit architectures. We show, for instance, that our numerical technique rediscovers known pulse schedules for minimizing leakage, e.g., DRAG for single qubits, and generalizes such a strategy to larger systems. We extend our optimal-control approach to Liouville space and discuss the impact of dissipation and finite amplitude and frequency resolution on the two-qubit gate fidelities.