  We propose a quantum speedup method for adiabatic generation of cat states in
bosonic Josephson junctions via shortcuts to adiabaticity. We apply
approximated counter-diabatic driving to a bosonic Josephson junction using the
Holstein-Primakoff transformation. In order to avoid the problem of divergence
in counter-diabatic driving, we take finite-size corrections into account. The
resulting counter-diabatic driving is well-defined over whole processes.
Schedules of the counter-diabatic driving consist of three steps; the
counter-diabatic driving in the disordered phase, smoothly and slowly
approaching the critical point, and the counter-diabatic driving in the ordered
phase. Using the counter-diabatic driving, adiabatic generation of cat states
is successfully accelerated. The enough large quantum Fisher information
ensures that generated cat states are highly entangled.
