Initial Partitioning-Aware Optimization of Communication Cost in the Distributed Quantum Computing

Due to the complexities of making quantum computers, to have a large quantum computer, a viable solution is to build a network of quantum computers of finite size that are interconnected through a quantum or classical channel and can handle the whole behavior of the quantum system. In other words, the quantum computing circuit model can be extended to distributed quantum computing, where each subsystem transmits its data to other parts on demand via a communication channel. A reliable mechanism for such communication is distributed using the concept of quantum telecommunication between nodes of a quantum system. Minimizing the number of quantum telecommunications between nodes of a distributed quantum computer is considered as a measure of its productivity. In a previous work, a method for optimizing the number of quantum telecommunications between two parts of a distributed quantum system is presented. It starts with a quantum circuit that is initially divided into two parts. Then, using a proposed algorithm, it optimizes the communication cost (number of quantum telecommunications) between the two parts of this distributed quantum circuit. Obviously, changing the initial configuration can lead to other solutions. In this paper, the quantum circuit is mapped to a weighted graph and is divided into three partitions by three graph partitioning methods, namely KL, FM and genetic algorithms. On each partition, a continuation algorithm of the previous method to optimize the communication cost is implemented and finally the output with the minimum number of communication costs is reported. The results of the test on the test circuits show that the proposed method reduces the communication cost by 12.51% on average