当前位置: X-MOL 学术Phys. Rev. Lett. › 论文详情
How fast do quantum walks mix?
Physical Review Letters ( IF 9.227 ) Pub Date : 
Shantanav Chakraborty, Kyle Luh, and Jérémie Roland

The fundamental problem of sampling from the limiting distribution of quantum walks on networks, known as mixing, finds widespread applications in several areas of quantum information and computation. Of particular interest in most of these applications, is the minimum time beyond which the instantaneous probability distribution of the quantum walk remains close to this limiting distribution, known as the quantum mixing time. However this quantity is only known for a handful of specific networks. In this letter, we prove an upper bound on the quantum mixing time for almost all networks, i.e. the fraction of networks for which our bound holds, goes to one in the asymptotic limit. To this end, using several results in random matrix theory, we find the quantum mixing time of Erd"os-Renyi random networks: networks of n nodes where each edge exists with probability p independently. For example for dense random networks, where p is a constant, we show that the quantum mixing time is $\Oo(n^{3/2 + o(1)})$. Besides opening avenues for the analytical study of quantum dynamics on random networks, our work could find applications beyond quantum information processing. Owing to the universality of Wigner random matrices, our results on the spectral properties of random graphs hold for general classes of random matrices that are ubiquitous in several areas of physics. In particular, our results could lead to novel insights into the equilibration times of isolated quantum systems defined by random Hamiltonians, a foundational problem in quantum statistical mechanics.
更新日期:2020-01-14

 

全部期刊列表>>
限时免费阅读临床医学内容
ACS材料视界
科学报告最新纳米科学与技术研究
清华大学化学系段昊泓
自然科研论文编辑服务
中国科学院大学楚甲祥
中国科学院微生物研究所潘国辉
中国科学院化学研究所
课题组网站
X-MOL
北京大学分子工程苏南研究院
华东师范大学分子机器及功能材料
中山大学化学工程与技术学院
试剂库存
天合科研
down
wechat
bug