  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.
