  It has been known since the early days of quantum mechanics that hyperbolic
secant pulses possess the unique property that they can perform cyclic
evolution on two-level quantum systems independently of the pulse detuning.
More recently, it was realized that they induce detuning- controlled phases
without changing state populations. Here, we experimentally demonstrate the
properties of hyperbolic secant pulses on superconducting transmon qubits and
contrast them with the more commonly used Gaussian and square waves. We further
show that these properties can be exploited to implement phase gates, nominally
without exiting the computational subspace. This enables us to demonstrate the
first microwave-driven Z-gates with a single control parameter, the detuning.
