  Quantum manipulation protocols for quantum sensors and quantum computation
often require many single qubit rotations. However, the impact of phase noise
in the field that performs the qubit rotations is often neglected or treated
only for special cases. We present a general framework for calculating the
impact of phase noise on the state of a qubit, as described by its equivalent
Bloch vector. The analysis applies to any Bloch vector orientation, and any
rotation axis azimuthal angle for both a single pulse, and pulse sequences.
Experimental examples are presented for several special cases. We apply the
analysis to commonly used composite $\pi$-pulse sequences: CORPSE, SCROFULOUS,
and BB1, used to suppress static amplitude and detuning errors, and also to
spin echo sequences. We expect the formalism presented will help guide the
development and evaluation of future quantum manipulation protocols.
