Categorical computation

Fuente: arXiv
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Main Authors: Kong, Liang, Zheng, Hao
Format: Preprint
Published: 2021
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author Kong, Liang
Zheng, Hao
author_facet Kong, Liang
Zheng, Hao
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2102_04814
institution arXiv
publishDate 2021
record_format arxiv
spellingShingle Categorical computation
Kong, Liang
Zheng, Hao
Quantum Physics
Strongly Correlated Electrons
Category Theory
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.
title Categorical computation
topic Quantum Physics
Strongly Correlated Electrons
Category Theory
url https://arxiv.org/abs/2102.04814