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

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.

arXiv comment12 pages, 6 figures, submitted to PRA

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• Sensitivity of quantum gate fidelity to laser phase and intensity noise
• A low phase noise microwave source for atomic spin squeezing experiments in 87Rb
• The effect of fast noise on the fidelity of trapped-ions quantum gates
• Observation of Microwave Shielding of Ultracold Molecules
• Dynamical low-noise microwave source for cold-atom experiments
• High-power, low-phase-noise, frequency-agile laser system for delivering fiber-noise-cancelled pulses for Strontium clock atom interferometry
• A High-Power Clock Laser Spectrally Tailored for High-Fidelity Quantum State Engineering
• High-fidelity two-qubit gates via dynamical decoupling of local 1/f noise at optimal point
• Reducing Collective Quantum State Rotation Errors with Reversible Dephasing
• Opportunities and Limitations in Broadband Sensing