Numerical test of few-qubit clock protocols

TL;DR

This paper numerically evaluates the stability of various few-qubit clock protocols under realistic decoherence, identifying protocols with improved stability over traditional methods and providing insights into optimal quantum clock designs.

Contribution

It introduces a comprehensive numerical analysis of entangled qubit clock protocols, comparing their stability and identifying optimal strategies for different qubit numbers.

Findings

Squeezed states reduce clock instability compared to unentangled Ramsey protocols.

Protocols with more than 15 atoms outperform certain entangled protocols in stability.

Numerical search finds protocols with better stability than standard Ramsey spectroscopy for 2-8 qubits.

Abstract

The stability of several clock protocols based on 2 to 20 entangled atoms is evaluated numerically by a simulation that includes the effect of decoherence due to classical oscillator noise. In this context the squeezed states discussed by Andr\'{e}, S{\o}rensen and Lukin [PRL 92, 239801 (2004)] offer reduced instability compared to clocks based on Ramsey's protocol with unentangled atoms. When more than 15 atoms are simulated, the protocol of Bu\v{z}ek, Derka and Massar [PRL 82, 2207 (1999)] has lower instability. A large-scale numerical search for optimal clock protocols with two to eight qubits yields improved clock stability compared to Ramsey spectroscopy, and for two to three qubits performance matches the analytical protocols. In the simulations, a laser local oscillator decoheres due to flicker-frequency (1/f) noise. The oscillator frequency is repeatedly corrected, based on projective measurements of the qubits, which are assumed not to decohere with one another.