$N$-Qubit State Protection Against Amplitude Damping by Quantum Feed-Forward Control and its Reversal

Abstract

We propose a state protection scheme of quantum feed-forward control and its reversal (QFFCR) by quantum weak measurement and quantum control to protect the arbitrary N -qubit state in amplitude-damping channel (ADC). Before the state enters the ADC, a weak measurement and an offsetting operation are made to make the state almost immune to the effect of ADC. After the state passes the ADC, the reversed offsetting operation and a correction rotation are applied to recover the state. Unlike most previous state protection schemes, ours does not use weak measurement reversal, but a correction rotation to bring back the state to its initial amount. Our protection scheme can also protect entangled states even for heavy damping probabilities effectively. Fidelity and success probability are used to evaluate the effect of the proposed scheme. The general formula for complete recovery and the total success probability of N -qubit system are derived. The effectiveness of our control scheme is demonstrated by simulation results.