Implementation of a many-qubit Grover search by cavity QED

We explore the possibility of an N-qubit (N>3) Grover search in cavity QED, based on a fast operation of an N-qubit controlled phase-flip with atoms in resonance with the cavity mode. We demonstrate both analytically and numerically that our scheme can be achieved efficiently to find a marked state with high fidelity and high success probability. As an example, a ten-qubit Grover search is simulated specifically under the discussion of experimental feasibility and challenge. We argue that our scheme is applicable to the case involving an arbitrary number of qubits. As cavity decay is involved in our quantum trajectory treatment, we can analytically understand the implementation of a Grover search subject to dissipation, which will be very helpful for relevant experiments.