Szegedy quantum walks with memory on regular graphs

被引：5

作者：

Li, Dan ^{[1
,2
,3
]}

Liu, Ying ^{[1
]}

Yang, Yu-Guang ^{[4
]}

Xu, Juan ^{[1
]}

Yuan, Jia-Bin ^{[1
]}

机构：

[1] Nanjing Univ Aeronaut & Astronaut, Coll Comp Sci & Technol, Nanjing, Peoples R China

[2] State Key Lab Cryptol, POB 5159, Beijing 100878, Peoples R China

[3] Collaborat Innovat Ctr Novel Software Technol & I, Nanjing, Peoples R China

[4] Beijing Univ Technol, Fac Informat Technol, Beijing, Peoples R China

来源：

QUANTUM INFORMATION PROCESSING | 2020年 / 19卷 / 01期

基金：

北京市自然科学基金; 中国博士后科学基金;

关键词：

Quantum walks; Quantum walks with memory; Szegedy quantum walks with memory; Line digraph; ALGORITHMS;

D O I：

10.1007/s11128-019-2534-9

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

Quantum walks with memory (QWM) are types of modified quantum walks that record the walker's latest path. The general model of coined QWM is presented in Li et al. (Phys Rev A 93:042323, 2016). In this paper, we present the general Szegedy QWM model and we describe its relationship with the coined QWM model. A coined QWM can be transformed into a Szegedy QWM, while a Szegedy QWM can be transformed into a coined QWM with any partition. These results may help in the analysis of the coined QWM. By transforming a coined QWM into a Szegedy QWM, the essential structure of the coined QWM is revealed. We give an example and we prove that two known QWMs are equal when they have a proper position-dependent coin operator.

引用

页数：12

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