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

TL;DR

This paper introduces a comprehensive framework to evaluate how phase noise affects qubit state rotations, applicable to various pulse sequences and orientations, aiding the design of more robust quantum control protocols.

Contribution

It provides a general formalism for quantifying phase noise impact on Bloch vector rotations, applicable to any orientation and pulse sequence, including composite and echo sequences.

Findings

Applied to composite π-pulse sequences like CORPSE, SCROFULOUS, and BB1.

Analyzed phase noise effects on spin echo sequences.

Framework helps optimize quantum manipulation protocols.

Abstract

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.