Time evolution of complexity: a critique of three methods

被引:91
作者
Ali, Tibra [1 ]
Bhattacharyya, Arpan [2 ]
Haque, S. Shajidul [3 ]
Kim, Eugene H. [3 ]
Moynihan, Nathan [4 ]
机构
[1] Perimeter Inst, 31 Caroline St North, Waterloo, ON N2L 2Y5, Canada
[2] Kyoto Univ, Yukawa Inst Theoret Phys YITP, Ctr Gravitat Phys, Sakyo Ku, Kitashirakawa Oiwakecho, Kyoto 6068502, Japan
[3] Univ Windsor, Dept Phys, 401 Sunset Ave, Windsor, ON N9B 3P4, Canada
[4] Univ Cape Town, Dept Math & Appl Math, Lab Quantum Grav & Strings, ZA-7701 Rondebosch, South Africa
基金
新加坡国家研究基金会;
关键词
Effective Field Theories; Lattice Quantum Field Theory; AdS-CFT Correspondence; Black Holes in String Theory; QUANTUM; ENTANGLEMENT;
D O I
10.1007/JHEP04(2019)087
中图分类号
O412 [相对论、场论]; O572.2 [粒子物理学];
学科分类号
摘要
In this work, we propose a testing procedure to distinguish between the different approaches for computing complexity. Our test does not require a direct comparison between the approaches and thus avoids the issue of choice of gates, basis, etc. The proposed testing procedure employs the information-theoretic measures Loschmidt echo and Fidelity; the idea is to investigate the sensitivity of the complexity (derived from the different approaches) to the evolution of states. We discover that only circuit complexity obtained directly from the wave function is sensitive to time evolution, leaving us to claim that it surpasses the other approaches. We also demonstrate that circuit complexity displays a universal behaviour - the complexity is proportional to the number of distinct Hamiltonian evolutions that act on a reference state. Due to this fact, for a given number of Hamiltonians, we can always find the combination of states that provides the maximum complexity; consequently, other combinations involving a smaller number of evolutions will have less than maximum complexity and, hence, will have resources. Finally, we explore the evolution of complexity in non-local theories; we demonstrate the growth of complexity is sustained over a longer period of time as compared to a local theory.
引用
收藏
页数:43
相关论文
共 112 条
[1]  
Aaronson S, 2015, ACM S THEORY COMPUT, P307, DOI [10.1145/2746539.2746547, 10.1137/15M1050902]
[2]  
Aaronson S, 2010, ACM S THEORY COMPUT, P141
[3]   Holographic subregion complexity from kinematic space [J].
Abt, Raimond ;
Erdmenger, Johanna ;
Gerbershagen, Marius ;
Melby-Thompson, Charles M. ;
Northe, Christian .
JOURNAL OF HIGH ENERGY PHYSICS, 2019, 2019 (01)
[4]   Topological Complexity in AdS3/CFT2 [J].
Abt, Raimond ;
Erdmenger, Johanna ;
Hinrichsen, Haye ;
Melby-Thompson, Charles M. ;
Meyer, Rene ;
Northe, Christian ;
Reyes, Ignacio A. .
FORTSCHRITTE DER PHYSIK-PROGRESS OF PHYSICS, 2018, 66 (06)
[5]   Subsystem complexity and holography [J].
Agon, Cesar A. ;
Headrick, Matthew ;
Swingle, Brian .
JOURNAL OF HIGH ENERGY PHYSICS, 2019, 2019 (02)
[6]  
Ali T., ARXIV181105985
[7]  
Ali T., COMPLEXITY VS ENTANG
[8]  
Alishahiha M., ARXIV180906031
[9]   Holographic fidelity susceptibility [J].
Alishahiha, Mohsen ;
Astaneh, Amin Faraji .
PHYSICAL REVIEW D, 2017, 96 (08)
[10]   Holographic complexity [J].
Alishahiha, Mohsen .
PHYSICAL REVIEW D, 2015, 92 (12)