Non-adiabatic holonomic manipulation of the polariton qubit in circuit QED

As a qubit usually has a limited lifetime, its manipulation should be as fast as possible, and thus non-adiabatic operation is more preferable. Moreover, as a qubit inevitably interacts with its surrounding environment, robust operations are of great significance. Here, we propose a scheme for quantum manipulation of the polariton qubit in circuit QED using non-adiabatic holonomy, which is inherently fast and robust. In particularly, the polariton qubit is shown to be robust against arbitrary low-frequency noise due to its near symmetric spectrum, which can also be convenient manipulated by external microwave driven fields in a holonomic way. Therefore, our scheme presents a promising way of manipulating polariton qubits for on-chip solid-state quantum computation.