# Why don't qubits continuously rotate in the $z$ direction due to free time evolution?

If we have a physical qubit with energy eigenstates $$|0\rangle$$ and $$|1\rangle$$ with energy separation $$\Delta E$$ its Hamiltonian in the absence of any interaction is

$$H=\hbar\frac{\Delta E}{2}\sigma_z$$

the time evolution operator is $$U=e^{-iHt/\hbar}$$, so why doesn't a qubit left to itself not just continuously rotate in the $$z$$ direction? And if it does, how is this not a problem? It seems to me that after some time $$t$$, a $$\sigma_z$$ gate will be applied whether we want it or not!

It does, unless you have a way to tune your Hamiltonian such that $$\Delta$$ becomes zero. Since a tunable Hamiltonian is something you usually want in a quantum computer implementation, this should not be a problem.