We investigate the possibility of achieving a nonlocal parallel quantum computation by using hyperentangled photon pairs, quantum-dot spins, and optical-microcavities. Exploiting a pair of hyperentangled photons, the two nonlocal parties in a quantum network can perform a deterministic hyper-controlled-Z gate operation on two spins. With the parallel quantum computation operation, two identical cluster states can be built up simultaneously in a quantum computation network between non-local parties.
As the cluster state is universal substrate for one-way quantum computation, our scheme can provide a polynomial gain for the capacity and efficiency of long-distance quantum computation. For the ideal spin-cavity system, our scheme for the remote control operation between two spin-qubits is deterministic and this protocol can be well combined with the long-distance quantum repeater. We also discuss the feasibility and efficiency of our scheme, conclude that it is feasible with current technologies.