  It is essential to select efficient topology of parameterized quantum
circuits (PQCs) in variational quantum algorithms (VQAs). However, there are
problems in current circuits, i.e. optimization difficulties caused by too many
parameters or performance is hard to guarantee. How to reduce the number of
parameters (number of single-qubit rotation gates and 2-qubit gates) in PQCs
without reducing the performance has become a new challenge. To solve this
problem, we propose a novel topology, called Block-Ring (BR) topology, to
construct the PQCs. This topology allocate all qubits to several blocks,
all-to-all mode is adopt inside each block and ring mode is applied to connect
different blocks. Compared with the pure all-to-all topology circuits which own
the best power, BR topology have similar performance and the number of
parameters and 2-qubit gate reduced from 0(n^2) to 0(mn) , m is a
hyperparameter set by ourselves. Besides, we compared BR topology with other
topology circuits in terms of expressibility and entangling capability.
Considering the effects of different 2-qubit gates on circuits, we also make a
distinction between controlled X-rotation gates and controlled Z-rotation
gates. Finally, the 1- and 2-layer configurations of PQCs are taken into
consideration as well, which shows the BR's performance improvement in the
condition of multilayer circuits.
