Impact of qubit connectivity on quantum algorithm performance

Quantum computing hardware is undergoing rapid development from proof-of-principle devices to scalable machines that could eventually challenge classical supercomputers on specific tasks. On platforms with local connectivity, the transition from one- to two-dimensional arrays of qubits is seen as a natural technological step to increase the density of computing power and to reduce the routing cost of limited connectivity. Here we map and schedule representative algorithmic workloads - the Quantum Fourier Transform (QFT) relevant to factoring, the Grover diffusion operator relevant to quantum search, and Jordan-Wigner parity rotations relevant to simulations of quantum chemistry and materials science - to qubit arrays with varying connectivity. In particular we investigate the impact of restricting the ideal all-to-all connectivity to a square grid, a ladder and a linear array of qubits. Our schedule for the QFT on a ladder results in running time close to that of a system with all-to-all connectivity. Our results suggest that some common quantum algorithm primitives can be optimized to have execution times on systems with limited connectivities, such as a ladder and linear array, that are competitive with systems that have all-to-all connectivity