Spin amplification in an inhomogeneous system

A long-lived qubit is usually well-isolated from all other systems and the environments, and so is not easy to couple with measurement apparatus. It is sometimes difficult to implement reliable projective measurements on such a qubit. One potential solution is spin amplification with many ancillary qubits. Here, we propose a spin amplification technique, where the ancillary qubits state changes depending on the state of the target qubit. The technique works even for an inhomogeneous system. We show that fast and accurate amplification is possible even if the coupling and frequency of the ancillary qubits is inhomogeneous. Since our scheme is robust against realistic imperfections, this could provide a new mechanism for reading out a single spin that could not have been measured using the previous approaches.