Abstract
We study the influence of multi-photon processes on the geometric quantum computation in the systems of superconducting qubits based on the displacement-like and the general squeezed operator methods. As an example, we focus on the question about how to implement a two-qubit geometric phase gate using superconducting circuit quantum electrodynamics with both single- and two-photon interaction between the qubits and the cavity modes. We find that the multiphoton processes are not only controllable but also improve the gating speed. The comparison with other physical systems and experimental feasibility are discussed in detail.
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