Queuing Theory Models for (Fault-Tolerant) Quantum Circuits: Analysis and Optimization

The surface code is one of the preferred quantum error correction codes for implementing fault-tolerant quantum computations and lattice surgery is considered being the most resource-efficient method to implement surface code computations. We discuss how to apply queuing theory models for the efficient compilation of lattice surgery quantum circuits. We use queuing theory to optimize the footprint of quantum addition circuits and the depths of quantum multiplication circuits.