Collaborative quantum computation with redundant graph state

Quantum computation is a computing model based on quantum theory, which can outperform the classical computation in solving certain problems. With the increase of the complexity of quantum computing tasks, it becomes important to distribute quantum computing resources to multi-parties to cooperatively fulfill the complex tasks. Here in this paper a scheme based on the one-way quantum computing model is proposed to realize collaborative quantum computation. The standard one-way quantum computing model is based on graph states. With graph states used as resources, one can realize a universal quantum computer through using single-qubit measurements and feed-forward. In contrast to the standard one-way computation, the main resource for collaborative quantum computation is a redundant graph state (also a multi-particle highly entangled state). Unlike in the traditional graph state where each particle corresponds to a specific node, in a redundant graph state, several particles correspond to a single node, which means that each node of the graph has several redundant copies. With the help of a redundant graph state, several parties can share a graph state flexibly at will. A redundant graph state is prepared and then distributed to several parties where each of them obtains a full copy of all nodes. By communicating with each other and measuring the particles in different ways, a standard graph state is prepared and distributed among these parties. The collaborative computation then finishes through the common one-way quantum computing operations. Besides the general scheme, a concrete optical implementation of a two-party cooperative single-qubit quantum state preparation based on a six-photon redundant graph state is also put forward. Such a redundant graph state is proposed to be prepared by using the spontaneous parametric down-conversion entangled source and quantum interference. With this redundant graph state, a standard three-node graph state can be shared with the two parties in an arbitrary way. This scheme does not only make the collaborative quantum computation across several parties possible and flexible, but also guarantee the privacy of each party's operations. This feature would be particularly useful in the case where the computing resource is obtained from an outside provider. This scheme paves the way for realizing quantum computation in more general and complicated applications.