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arXiv 2103.13755cs.SEquant-ph
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量子软件模型:经典和量子软件系统设计的密度矩阵

Quantum Software Models: The Density Matrix for Classical and Quantum Software Systems Design

Iaakov Exman, Alon Tsalik Shmilovich

摘要:

线性软件模型使严格的线性代数程序的模块化设计的经典软件系统。这些程序将谱方法应用于软件系统的矩阵表示-例如拉普拉斯算子。最近对量子计算机的密集研究工作增加了人们的期望,即量子计算可以在适当的时候实现为经典计算的实用替代方案。合理的做法是询问量子软件所需的特性,并为量子软件系统预先准备模块化设计过程。然而,对于模块化设计,有两个完全独立的过程是没有意义的,一个用于经典软件系统,另一个用于量子软件系统。本文认为,对于经典和量子软件系统,应该只有一个统一而严格的设计过程。我们对经典和量子软件系统的共同设计过程起点是冯·诺依曼密度算子的量子概念及其密度矩阵表示。本文阐述和证明模块化设计的投影算子从一个设计密度矩阵,并显示其等价的线性软件模型的结果的拉普拉斯矩阵谱的经典情况。经典和量子软件的设计过程在实践中的应用说明了案例研究。

英文摘要:

Linear Software Models enable rigorous linear algebraic procedures for modular design of classical software systems. These procedures apply a spectral approach to matrix representations - e.g. the Laplacian - of the software system. Recent intensive research efforts towards quantum computers have increased expectations that quantum computing could in due time materialize as a practical alternative to classical computing. It is reasonable to inquire about quantum software desirable features and prepare in advance modular design procedures for quantum software systems. However, it does not make sense to have two totally separate procedures for modular design, one for classical software systems and another for quantum software systems. This paper claims that there should be just a single unified and rigorous design procedure for both classical and quantum software systems. Our common design procedure starting point for both classical and quantum software systems is Von Neumann quantum notion of Density Operator and its Density Matrix representation. This paper formulates and demonstrates modular design in terms of projection operators obtained from a design Density Matrix and shows their equivalence to the Linear Software Models results of the Laplacian matrix spectrum for the classical case. The application in practice of the design procedure for both classical and quantum software is illustrated by case studies.

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。

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