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Table of Contents
Abstract
1. Introduction
2. Vector Space Models in AI and Quantum Physics
2.1 Vector Models in AI
2.2 Why Quantum Theory?
2.3 Formal Quantum Mechanics
2.4 Waves as Vectors
Summary
The paper discusses the common mathematical areas shared by artificial intelligence (AI) and quantum computing, focusing on vector space models. It highlights the historical roots of vectors, their use in AI for information retrieval and deep learning, and their relation to quantum mechanics. The paper explores the utilization of quantum mathematics in AI, emphasizing the potential benefits and applications. It delves into formal quantum mechanics, explaining the mathematical formulation of quantum theory using standard linear algebra. The concept of waves as vectors is also discussed, showcasing how waves can be represented as functions and how Fourier series play a crucial role in wave representations.