  Cat-state qubits formed by photonic coherent states are a promising candidate
for realizing fault-tolerant quantum computing. Such logic qubits have a biased
noise channel that the bit-flip error dominates over all the other errors. In
this manuscript, we propose an optimally robust protocol using the control
method of shortcuts to adiabaticity to realize a nearly perfect population
inversion in a cat-state qubit. We construct a shortcut based on the
Lewis-Riesenfeld invariant and examine the stability versus different types of
perturbations for the fast and robust population inversion. Numerical
simulations demonstrate that the population inversion can be mostly insensitive
to systematic errors in our protocol. Even when the parameter imperfection rate
for bit-flip control is $20\%$, the final population of the target state can
still reach $\geq 99\%$. The optimally robust control provides a feasible
method for fault-tolerant and scalable quantum computation.
