Distributed Photonic Quantum Computations Assisted by Atomic Ensembles

Distributed quantum computation requires that quantum operations may be acted on remote logical qubits. We investigate the possibility of the distributed quantum computation for nonlocal photons assisted by cavity quantum electrodynamics. We first give a compact circuit for the controlled-NOT gate on a remote two-photon system. For the Toffoli gate, we introduce two circuits for a bipartite system with one photonic Einstein-Podolski-Rosen (EPR) entanglement. Two EPR pairs are required for a tripartite system. These Toffoli gates cost a half of entanglements required in the previous teleportation-based quantum computation. These elementary gates may be combined flexibly up to special decompositions of joint system in large-scale quantum applications.