Efficient Qubit Routing for a Globally Connected Trapped Ion Quantum\n Computer

The cost of enabling connectivity in Noisy-Intermediate-Scale-Quantum devices\nis an important factor in determining computational power. We have created a\nqubit routing algorithm which enables efficient global connectivity in a\npreviously proposed trapped ion quantum computing architecture. The routing\nalgorithm was characterized by comparison against both a strict lower bound,\nand a positional swap based routing algorithm. We propose an error model which\ncan be used to estimate the achievable circuit depth and quantum volume of the\ndevice as a function of experimental parameters. We use a new metric based on\nquantum volume, but with native two qubit gates, to assess the cost of\nconnectivity relative to the upper bound of free, all to all connectivity. The\nmetric was also used to assess a square grid superconducting device. We compare\nthese two architectures and find that for the shuttling parameters used, the\ntrapped ion design has a substantially lower cost associated with connectivity.\n