  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.
