Optimal robust control of cat-state qubits against parameter imperfections

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 where 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 high-fidelity state transfer 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 bit flipping. Numerical simulations demonstrate that the bit flipping can be robust against systematic errors in our protocol. Even when the parameter imperfection rate for bit-flip control is 20<i>%</i>, the final population of the target state can still reach ≥ 99<i>%</i>. The optimally robust control provides a feasible method for fault-tolerant and scalable quantum computation.