Categorical computation  

作　　者：Liang Kong Hao Zheng 

机构地区：[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

出　　处：《Frontiers of physics》2023年第2期181-187,共7页物理学前沿（英文版）

基　　金：We are supported by Guangdong Provincial Key Laboratory(Grant No.2019B121203002);L.K.is also supported by the National Natural Science Foundation of China under Grant No.11971219;Guangdong Basic and Applied Basic Research Foundation under Grant No.2020B1515120100;H.Z.is also supported by the National Natural Science Foundation of China under Grant No.11871078.

摘　　要：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.

关 键 词：quantum computation categorical computation topological order 

分 类 号：O15[理学—数学]