Categorical computation

doi:10.1007/s11467-022-1251-5

Frontiers of Physics

2023, Vol. 18

Issue (2): 21302 https://doi.org/10.1007/s11467-022-1251-5

本期目录

Categorical computation

Liang Kong^1,^2,³(

), Hao Zheng^1,^3,^4,^5,⁶(

)

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

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Abstract：

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.

Key words： quantum computation categorical computation topological order

收稿日期: 2022-11-07 出版日期: 2023-01-17

Corresponding Author(s): Liang Kong,Hao Zheng

引用本文:

. [J]. Frontiers of Physics, 2023, 18(2): 21302.
Liang Kong, Hao Zheng. Categorical computation. Front. Phys. , 2023, 18(2): 21302.

链接本文:

https://academic.hep.com.cn/fop/CN/10.1007/s11467-022-1251-5
https://academic.hep.com.cn/fop/CN/Y2023/V18/I2/21302

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