  In holonomic quantum computation, single-qubit gates are performed using
driving protocols that trace out closed loops on the Bloch sphere, making them
robust to certain pulse errors. However, dephasing noise that is transverse to
the drive, which is significant in many qubit platforms, lies outside the
family of correctable errors. Here, we present a general procedure that
combines two types of geometry -- holonomy loops on the Bloch sphere and
geometric space curves in three dimensions -- to design gates that
simultaneously suppress pulse errors and transverse noise errors. We
demonstrate this doubly geometric control technique by designing explicit
examples of such dynamically corrected holonomic gates.
