Von Neumann Quantum Logic vs. Classical von Neumann Architecture?

TL;DR

This paper explores the conceptual connections between von Neumann's contributions to quantum mechanics and classical computer architecture, highlighting the universal role of linear algebra in diverse computational and physical theories.

Contribution

It provides a unified framework using linear algebra to describe and compare quantum logic and classical von Neumann architecture, emphasizing their interconnectedness.

Findings

Linear algebra serves as a universal language for quantum and classical models.

Quantum and classical systems can be described within a common mathematical framework.

The approach facilitates understanding of quantum computations in relation to classical architectures.

Abstract

The name of John von Neumann is common both in quantum mechanics and computer science. Are they really two absolutely unconnected areas? Many works devoted to quantum computations and communications are serious argument to suggest about existence of such a relation, but it is impossible to touch the new and active theme in a short review. In the paper are described the structures and models of linear algebra and just due to their generality it is possible to use universal description of very different areas as quantum mechanics and theory of Bayesian image analysis, associative memory, neural networks, fuzzy logic.