Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quantum Software Models: The Density Matrix for Classical and Quantum
  Software Systems Design   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.

32
The categories of this paper are: atom-ph
37
The categories of this paper are: supr-con
3
The categories of this paper are: physics
6
The categories of this paper are: astro-ph
11
The categories of this paper are: hep-lat
17
The categories of this paper are: q-fin
24
The categories of this paper are: dg-ga
7
The categories of this paper are: hep-th
29
The categories of this paper are: funct-an
16
The categories of this paper are: stat
20
The categories of this paper are: acc-phys
31
The categories of this paper are: ao-sci
10
The categories of this paper are: q-bio
26
The categories of this paper are: bayes-an
33
The categories of this paper are: plasm-ph
22
The categories of this paper are: chao-dyn