General formalism for evaluating the impact of phase noise on Bloch vector rotations

摘要

Quantum manipulation protocols for quantum sensors and quantum computation often require many singlequbitnrotations. However, the impact of phase noise in the field that performs the qubit rotations is oftennneglected or treated only for special cases. We present a general framework for calculating the impact ofnphase noise on the state of a qubit, as described by its equivalent Bloch vector. The analysis applies to anynBloch vector orientation and any rotation axis azimuthal angle for both a single pulse and pulse sequences.nExperimental examples are presented for several special cases.We apply the analysis to commonly used compositenπ pulse sequences for suppression of static amplitude or detuning errors and also to spin-echo sequences. Wenexpect the formalism presented will help guide the development and evaluation of future quantum manipulationnprotocols.