Efficient Qubit Routing for a Globally Connected Trapped Ion Quantum Computer

The cost of enabling connectivity in noisy intermediate-scale quantum (NISQ) devices is an important factor in determining computational power. A qubit routing algorithm is created, which enables efficient global connectivity in a previously proposed trapped ion quantum computing architecture. The routing algorithm is characterized by comparison against both a strict lower bound, and a positional swap based routing algorithm. An error model is proposed, which can be used to estimate the achievable circuit depth and quantum volume of the device as a function of experimental parameters. A new metric based on quantum volume, but with native two-qubit gates, is used to assess the cost of connectivity relative to the upper bound of free, all to all connectivity. The metric is also used to assess a square-grid superconducting device. These two architectures are compared and it is found that for the shuttling parameters used, the trapped ion design has a substantially lower cost associated with connectivity.