One-step parity measurement of N cat-state qubits via reverse engineering and optimal control

In this paper, a one-step protocol is proposed for the parity measurement of N cat-state qubits which are encoded on the cat states of the modes in superconducting Kerr-nonlinear cavities. The parity measurement is performed with the help of an auxiliary qutrit. Especially, the auxiliary qutrit can (cannot) be excited to the higher-energy levels when the cat-state qubits are in the even- (odd-) parity state. By designing the Rabi frequency of the classical fields via reverse engineering and optimal control, the qutrit is driven to an excited dressed state in the even-parity case, which is robust to the systematic errors of the qutrit-cavity coupling strengths. Accordingly, the parity of the cat-state qubits can be distinguished with high accuracy by measuring the final population of the ground state of the auxiliary qutrit. Numerical simulations also show that the protocol is insensitive to the systematic errors of the classical fields, the inhomogeneity of the coupling strengths, intercavity cross talk, unwanted qutrit transitions, and decoherence. Therefore, the protocol may provide an effective approach for parity measurement of multiple cat-state qubits.