Title: A Genetic Approach to Minimising Gate and Qubit Teleportations for Multi-Processor Quantum Circuit Distribution

Abstract: Distributed Quantum Computing (DQC) provides a means for scaling available quantum computation by interconnecting multiple quantum processor units (QPUs). A key challenge in this domain is efficiently allocating logical qubits from quantum circuits to the physical qubits within QPUs, a task known to be NP-hard. Traditional approaches, primarily focused on graph partitioning strategies, have sought to reduce the number of required Bell pairs for executing non-local CNOT operations, a form of gate teleportation. However, these methods have limitations in terms of efficiency and scalability. Addressing this, our work jointly considers gate and qubit teleportations introducing a novel meta-heuristic algorithm to minimise the network cost of executing a quantum circuit. By allowing dynamic reallocation of qubits along with gate teleportations during circuit execution, our method significantly enhances the overall efficacy and potential scalability of DQC frameworks. In our numerical analysis, we demonstrate that integrating qubit teleportations into our genetic algorithm for optimising circuit blocking reduces the required resources, specifically the number of EPR pairs, compared to traditional graph partitioning methods. Our results, derived from both benchmark and randomly generated circuits, show that as circuit complexity increases - demanding more qubit teleportations - our approach effectively optimises these teleportations throughout the execution, thereby enhancing performance through strategic circuit partitioning. This is a step forward in the pursuit of a global quantum compiler which will ultimately enable the efficient use of a 'quantum data center' in the future.