Fast and Robust Nondestructive Parity Meter for Cat-State Qubits via Reverse Engineering and Optimal Control

In this paper, a protocol for nondestructive parity meter (NPM) of two cat-state qubits is proposed. The physical model contains two cavities and an auxiliary qubit. For each cavity, the quantum information is encoded on the odd and even cat state, forming a cat-state qubit. By adjusting the strength of the driving field on the auxiliary qubit, an effective Hamiltonian for cavity-selective transition is derived. Moreover, reverse engineering based on the effective Hamiltonian is applied to find the evolution path, and the systematic-error-sensitivity nullification method is used to select proper parameters of the evolution path. In this way, robust control fields are designed to combat the influence of the systematic errors. Furthermore, the effects of random noise and decoherence on the fidelity of the protocol are considered. Numerical simulations show that the protocol is insensitive to the experimental imperfection, including systematic errors, random noise and decoherence. Therefore, the protocol is expected to expand the vision of realizing NPM.