  Existing and near-term quantum computers can only perform two-qubit gates
between physically connected qubits. Research has been done on compilers to
rewrite quantum programs to match hardware constraints. However, the quantum
processor architecture, in particular the qubit connectivity and topology,
still lacks enough discussion, while it potentially has a huge impact on the
performance of the quantum algorithms. We perform a quantitative and
comprehensive study on the quantum processor performance under different qubit
connectivity and topology. We select ten representative design models with
different connectivities and topologies from quantum architecture design space
and benchmark their performance by running a set of standard quantum
algorithms. It is shown that a high-performance architecture almost always
comes with a design with a large connectivity, while the topology shows a weak
influence on the performance in our experiment. Different quantum algorithms
show different dependence on quantum chip connectivity and topologies. This
work provides quantum computing researchers with a systematic approach to
evaluating their processor design.
