Categorical computation

Kong，Liang1,2,3; Zheng，Hao1,3,4,5,6

2023-04-01

10.1007/s11467-022-1251-5

Frontiers of Physics   Impact Factor & Quartile

2095-0462

2095-0470

In quantum computing, the computation is achieved by linear operators in or between Hilbert spaces. In this work, we explore a new computation scheme, in which the linear operators in quantum computing are replaced by (higher) functors between two (higher) categories. If from Turing computing to quantum computing is the first quantization of computation, then this new scheme can be viewed as the second quantization of computation. The fundamental problem in realizing this idea is how to realize a (higher) functor physically. We provide a theoretical idea of realizing (higher) functors physically based on the physics of topological orders.[Figure not available: see fulltext.]

categorical computation quantum computation topological order

SCI

English

First ; Corresponding

Guangdong Provincial Key Laboratory[2019B121203002] ; National Natural Science Foundation of China[11871078] ; Guangdong Basic and Applied Basic Research Foundation[2020B1515120100]

Physics

Physics, Multidisciplinary

WOS:000930137800001

HIGHER EDUCATION PRESS

2-s2.0-85148473996

Scopus

1.Shenzhen Institute for Quantum Science and Engineering,Southern University of Science and Technology,Shenzhen,518055,China
2.International Quantum Academy,Shenzhen,518048,China
3.Guangdong Provincial Key Laboratory of Quantum Science and Engineering,Southern University of Science and Technology,Shenzhen,518055,China
4.Institute for Applied Mathematics,Tsinghua University,Beijing,100084,China
5.Beijing Institute of Mathematical Sciences and Applications,Beijing,101408,China
6.Department of Mathematics,Peking University,Beijing,100871,China

Kong，Liang,Zheng，Hao. Categorical computation[J]. Frontiers of Physics,2023,18(2).

Kong，Liang,&Zheng，Hao.(2023).Categorical computation.Frontiers of Physics,18(2).

Kong，Liang,et al."Categorical computation".Frontiers of Physics 18.2(2023).