量子计算的表象无关性探讨

大因数分解和数据检索量子算法的提出带来了量子计算与量子信息的研究高潮。由于量子计算具有并行性、不可克隆性及量子态的不可测性,使得量子信息及量子计算在某些方面具有传统计算所无法比拟的优势。量子的态空间作为一个完备的Hilbert空间,在定义了内积和范数并赋予相应的物理意义后,就构成了理论意义上的量子计算系统。该文抽象了量子系统的本质,描述了量子计算及遵循的计算规则以及如何实现量子信息表示和进行信息的处理与测量,从理论上阐述了量子态系统迁移的线性同构和等距同构,说明了量子计算与量子信息的研究与具体的量子表象空间无关。

Discussion on Independence of Representative Space of Quantum Computing

Quantum algorithms of prime factors of an integer and data retrieval have aroused great interest in the research of quantum information and quantum computing.The parallelism of quantum computing and the non-cloning and immeasurability properties of quantum states make quantum computing and quantum information incomparable with classical computing and information.As a complete Hilbert space with inner product and norm being defined with proper physical meanings,quantum state space can be regarded as a quantum computing system physically.This paper explains what the quantum system really is,the laws quantum computing should obey,and how quantum information is represented,processed and measured.Quantum state space evolution is a mapping from one Hilbert space to another,and all these spaces are linear isomorphism and equidistant isomorphism.The paper concludes that quantum computing and quantum information have nothing to do with the selected representative space.