Quantum Fibrations:Quantum Computation on an Arbitrary Topological Space  

作　　者：Kazuki IKEDA 

机构地区：[1]Co-design Center for Quantum Advantage(C2QA)&Center For Nuclear Theory,Department of Physics and Astronomy,Stony Brook University,Stony Brook,USA [2]Department of Mathematics and Statistics&Centre for Quantum Topology and Its Applications(quanTA),University of Saskatchewan,Saskatoon,Canada

出　　处：《Acta Mathematica Sinica,English Series》2024年第11期2693-2718,共26页数学学报（英文版）

基　　金：supported by Pacific Institute for the Mathematical Science(PIMS)postdoctoral fellowship award and by the U.S.Department of Energy,Office of Science,National Quantum Information Science Research Centers,Co-design Center for Quantum Advantage(C2QA)under Contract No.DESC0012704。

摘　　要：Using operator algebras,we extend the theory of quantum computation on a graph to a theory of computation on an arbitrary topological space.Quantum computation is usually implemented on finite discrete sets,and the purpose of this study is to extend this to theories on arbitrary sets.The conventional theory of quantum computers can be viewed as a simplified algebraic geometry theory in which the action of SU(2)is defined on each point of a discrete set.In this study,we extend this in general as a theory of quantum fibrations in which the action of the von Neumann algebra is defined on an arbitrary topological space.The quantum channel is then naturally extended as a net of von Neumann algebras.This allows for a more mathematically rigorous discussion of general theories,including physics and chemistry,which are defined on sets that are not necessarily discrete,from the perspective of quantum computer science.

关 键 词：Quantum computation operator algebra von Neumann algebra FIBRATION quantum computational chemistry complexity theory 

分 类 号：O413[理学—理论物理] TP38[理学—物理]