Quantum Software Models: Software Density Matrix is a Perfect Direct Sum of Module Matrices
Iaakov Exman, Alexey V. Nechaev · Proceedings/Proceedings of the ... International Conference on Software Engineering and Knowledge Engineering · 2022
Quantum Software Models is a theoretical framework to systematically design and analyze any software system -be it quantum, classical or hybrid -representing it by a design Density Matrix.Recently, we have demonstrated a top-down approach, to decompose a whole software system Density Matrix into modules, using basis vector projectors of the Matrix.However, it would be even more natural to have a systematic bottom-up procedure, to compose a whole software system Density Matrix, given a set of well-designed software module matrices, taken as sub-systems.This is exactly the paper's purpose.The result obtained: the whole software system Density Matrix is a perfect Direct Sum of module density matrices.This result yields clear software design benefits: it is bidirectional, one can traverse the software system hierarchy top-down or bottom-up, in particular, gradually building up the whole system from verified correct modules, assured by spectral decoupling techniques.The claim is formally validated and is illustrated by software system studies.