# Can the spin-1/2 720° rotation trick apply to qubits?

The idea of a 4π rotation to return an electron to its original state instead of just a single 2π rotation exists - but can this idea apply to qubits or entangled qubits?

Are there any use cases for 360° or 720° quantum logic gates?

For a single qubit, the analogy is that 720° = $$4\pi$$ rotation is the unitary operator $$I$$, and 360° = $$2\pi$$ rotation is the unitary operator $$-I$$, while any other rotation is a unitary with $$\text{det} = 1$$, i.e. an element of the special unitary group $$SU(2)$$, which is isomorphic to the group of unit quaternions.
Even though $$-I$$ doesn't affect the state of a qubit, the controlled version Control-($$-I$$) is not the same as Control-($$I$$), which is still the identity.