一种构建参数化量子线路的区块环拓扑结构
A Block-Ring Connected Topology of Parameterized Quantum Circuits
- 电子学报 2024年52卷第8期 页码：2726-2736
- 作者机构：
1.南京信息工程大学软件学院,江苏南京 210044
2.南京信息工程大学江苏省大气环境与装备技术协同创新中心,江苏南京 210044
3.数字取证教育部工程研究中心,江苏南京 210044
- 作者简介：
[ "刘文杰 男，1979年11月出生，湖北大冶人.博士.南京信息工程大学软件学院副教授、博士生导师.研究方向为量子算法、量子机器学习、量子安全多方计算、深度学习与图神经网络等.E-mail: wenjiel@163.com" ]
[ "吴青山 男，1999年5月出生，江苏扬州人.南京信息工程大学软件学院硕士研究生.主要研究方向为量子机器学习与量子算法.E-mail: qingshanw2021@163.com" ]
[ "查颖 女，1999年5月出生，江苏扬州人.南京信息工程大学软件学院硕士研究生.主要研究方向为量子机器学习与量子算法.E-mail: 3578618336@qq.com" ]
[ "王海彬 男，1980年8月出生，江苏靖江人.博士.南京信息工程大学软件学院副教授、硕士生导师.研究方向为量子机器学习、人工智能等.E-mail: 001276@nuist.edu.cn" ]
- 基金信息：国家自然科学基金(62071240);科技创新2030——“量子通信与量子计算机”重大项目(2021ZD0302901);江苏省基础研究计划（自然科学基金）项目(BK20231142)
DOI：10.12263/DZXB.20230135
中图分类号： TP391.41;收稿：2023-02-15，
修回：2023-12-30，
纸质出版：2024-08-25
- 稿件说明：
移动端阅览
刘文杰, 吴青山, 查颖, 等. 一种构建参数化量子线路的区块环拓扑结构[J]. 电子学报, 2024, 52(08): 2726-2736.
LIU Wen-jie, WU Qing-shan, ZHA Ying, et al. A Block-Ring Connected Topology of Parameterized Quantum Circuits[J]. Acta Electronica Sinica, 2024, 52(08): 2726-2736.
刘文杰, 吴青山, 查颖, 等. 一种构建参数化量子线路的区块环拓扑结构[J]. 电子学报, 2024, 52(08): 2726-2736. DOI：10.12263/DZXB.20230135
LIU Wen-jie, WU Qing-shan, ZHA Ying, et al. A Block-Ring Connected Topology of Parameterized Quantum Circuits[J]. Acta Electronica Sinica, 2024, 52(08): 2726-2736. DOI：10.12263/DZXB.20230135
摘要
在变分量子算法中，参数化量子线路拓扑结构的选择对算法性能具有重要意义.目前已有的拓扑结构存在一些问题，如全连接拓扑结构所需量子门数量较多，环型拓扑结构的表达能力与纠缠能力略有欠缺.为了解决以上问题，本文提出了一种新型的区块环（Block-Ring，BR）拓扑结构，在保障良好性能的同时减少参数规模（即量子门数量），降低线路复杂度.在BR拓扑中，
n
个量子比特被等分为多个区块，每个区块包含
m
个量子比特，区块内部所有量子比特两两连接，区块之间采用环型结构进行连接.为了构造BR拓扑结构的参数化量子线路，设计了一种多层线路生成算法，可自动生成由单量子比特门Rx、Rz和双量子比特门CRx或CRz构成的量子线路.IBM Q模拟实验表明，相较于环型拓扑结构，无论单层、双层以及三层BR拓扑结构的表达能力和纠缠能力均有不同程度的提升；相较于拥有最高表达能力与纠缠能力的全连接拓扑结构，BR拓扑结构呈现接近的性能指标，且线路复杂度显著降低，即参数数量与双量子比特门数量均从
O
（
n
2
）降低为
O
（
mn
），线路深度从
O
（
n
2
）降低为
O
（
n
/
m
+
m
2
）.
Abstract
In the variational quantum algorithm
the selection of parameterized quantum circuit topology is of great significance to the performance of the algorithm. There are some problems in the existing topology
such as the large number of quantum 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 circuit
which can automatically generate quantum circuits composed of single-qubit gate
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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 circuit complexity is significantly reduced
that is
the number of parameters and the nu
mber of double quantum gates are reduced from
O
(
n
2
) to
O
(
mn
)
and the circuit depth is reduced from
O
(
n
2
) to
O
(
n
/
m
+
m
2
).
关键词
Keywords
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