范畴计算
Categorical computation
AI总结：
本文提出范畴计算方案，以（高阶）范畴间的（高阶）函子替代量子计算中的线性算子，并借助拓扑序物理给出物理实现函子的理论思路。
摘要：
在量子计算中，计算是由 Hilbert 空间内或 Hilbert 空间之间的线性算子完成的。在本工作中，我们探索一种新的计算方案，其中量子计算中的线性算子被两个（高阶）范畴之间的（高阶）函子所取代。如果说从 Turing 计算到量子计算是计算的第一次量子化，那么这一新方案可被视为计算的第二次量子化。实现这一思想的根本问题是如何在物理上实现一个（高阶）函子。我们基于拓扑序的物理学，提出了一种在物理上实现（高阶）函子的理论构想。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
