Title  Sectional curvatures distribution of complexity geometry 
Author  
Corresponding Author  Wu, QiFeng 
Publication Years  20220819

DOI  
Source Title  
ISSN  10298479

Issue  8 
Abstract  In the geometric approach to defining complexity, operator complexity is defined as the distance in the operator space. In this paper, based on the analogy with the circuit complexity, the operator size is adopted as the metric of the operator space where the path length is the complexity. The typical sectional curvatures of this complexity geometry are positive. It is further proved that the typical sectional curvatures are always positive if the metric is an arbitrary function of operator size, while complexity geometry is usually expected to be defined on negatively curved manifolds. By analyzing the sectional curvatures distribution for the Nqubit system, it is shown that surfaces generated by Hamiltonians of size smaller than the typical size can have negative curvatures. In the large N limit, the form of complexity metric is uniquely constrained up to constant corrections if we require sectional curvatures are of order 1/N2. With the knowledge of states, the operator size should be modified due to the redundant action of operators, and thus is generalized to be statedependent. Then we use this statedependent operator size as the metric of the Hilbert space to define state complexity. It can also be shown that in the Hilbert space, 2surfaces generated by operators of size much smaller than the typical size acting on typical states also have negative curvatures. 
Keywords  
URL  [Source Record] 
Indexed By  
Language  English

Important Publications  NI Journal Papers

SUSTech Authorship  Corresponding

WOS Research Area  Physics

WOS Subject  Physics, Particles & Fields

WOS Accession No  WOS:000842157900016

Publisher  
ESI Research Field  PHYSICS

Data Source  Web of Science

Citation statistics 
Cited Times [WOS]:1

Document Type  Journal Article 
Identifier  http://kc.sustech.edu.cn/handle/2SGJ60CL/382589 
Department  Institute for Quantum Science and Engineering 理学院_物理系 
Affiliation  1.Fudan Univ, Dept Phys, 220 Handan Rd, Shanghai 200433, Peoples R China 2.Fudan Univ, Ctr Field Theory & Particle Phys, 220 Handan Rd, Shanghai 200433, Peoples R China 3.Southern Univ Sci & Technol, Dept Phys, 1088 Xueyuan Ave, Shenzhen 518055, Peoples R China 4.Southern Univ Sci & Technol, Inst Quantum Sci & Engn, 1088 Xueyuan Ave, Shenzhen 518055, Peoples R China 
First Author Affilication  Department of Physics; Institute for Quantum Science and Engineering 
Corresponding Author Affilication  Department of Physics; Institute for Quantum Science and Engineering 
Recommended Citation GB/T 7714 
Wu, QiFeng. Sectional curvatures distribution of complexity geometry[J]. JOURNAL OF HIGH ENERGY PHYSICS,2022(8).

APA 
Wu, QiFeng.(2022).Sectional curvatures distribution of complexity geometry.JOURNAL OF HIGH ENERGY PHYSICS(8).

MLA 
Wu, QiFeng."Sectional curvatures distribution of complexity geometry".JOURNAL OF HIGH ENERGY PHYSICS .8(2022).

Files in This Item:  
There are no files associated with this item. 
Items in the repository are protected by copyright, with all rights reserved, unless otherwise indicated.
Edit Comment