# How to implement a $\frac{\theta}{2}$ rotation from $\theta$ rotation?

Is there a way to create a rotation gate which has half the angle of some implementable gate?

I am looking to implement a gate on Quirk which allows for standard time-dependent rotations

$$R_x(\theta=t)=e^{iXt}$$

but I'd like to construct the same gate but with $$\theta=\frac{t}{2}$$ so I can have two different oscillation frequencies.

Is there some standard way to do this?

It's not possible to have proper half-speed time-dependent rotations in Quirk. Behind the scenes there is actually a value $$t$$ that is varying from 0 to 1 and then cycling. If you managed to find a construction to cut the angle in half, your rotation would jump from 180 degrees to 0 degrees when $$t$$ went from 1 to 0.
An alternative trade-off do is define double-speed rotations by using pairs of time-dependent rotation gates, and then work in units of $$2t$$ instead of $$t$$. You can use custom circuit gates to fuse them into a single block. If custom gates annoy you (they are by far the weakest part of the UX), the time-dependent gradient gate gives you a series of faster and faster rotations: