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

General Formalism for Evaluating the Impact of Phase Noise on Bloch Vector Rotations