A Block-Ring Connected Topology of Parameterized Quantum Circuits
In the variational quantum algorithm,the selection of parameterized quantum circuit topology is of great signifi-cance to the performance of the algorithm.There are some problems in the existing topology,such as the large number of quan-tum gates required by the fully connected topology,and the slight lack of the expressibility and entanglement capability of the ring topology.This paper proposes a new block-ring(BR)topology to solve the problems above,which can effectively reduce the size of parameters(i.e.the number of parameterized gates)while ensuring performance.n qubits are divided into several blocks equally,each block contains m qubits.Qubits in the block are connected in pairs,and the blocks are connected by ring structure.In order to construct parameterized quantum circuits with BR topology,we designed a algorithm of generating multiple-layer cir-cuit,which can automatically generate quantum circuits composed of single-qubit gate Rx,Rz and two-qubit gate CRx or CRz.The IBM Q simulation experiment shows that compared with the ring topology,the expressibility and entanglement capability of single-layer,double-layer and triple-layer BR topology are improved in different degrees;Compared with the all-to-all connected topology with the highest expression ability and entanglement capability,BR topology presents a close performance,and the cir-cuit complexity is significantly reduced,that is,the number of parameters and the number of double quantum gates are reduced from O(n2)to O(mn),and the circuit depth is reduced from O(n2)to O(n/m+m2).