In this paper, a multi-layer hierarchical architecture is proposed for distributing quantum computation. In a distributed quantum computing (DQC), different units or subsystems communicate by teleportation in order to transfer quantum information. Quantum teleportation requires classical and quantum resources and hence, it is essential to minimize the number of communications among these subsystems. To this end, a two-level hierarchical optimization method is proposed to distribute the qubits among different parts. In Level I, an integer linear programming model is presented to distribute a monolithic quantum system into K balanced partitions which results in the minimum number of non-local gates. When a qubit is teleported to a destination part, it can be used optimally by other gates without being teleported back to the destination part. In Level II, a data structure is proposed for quantum circuit and a recursive function is applied to minimize the number of teleportations. Experimental results show that the proposed approach outperforms the previous ones.

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