Date of Award

Spring 5-20-2024

Document Type

Undergraduate Honors Thesis

Degree Name

Bachelor of Science in Physics

Advisor

Dr. Marin Mossman

Abstract

Integrated Information Theory (IIT) provides a rigorous mathematical framework for consciousness, defining it by a system’s intrinsic causal power, quantified by the integrated information (Φ). A central obstacle to testing IIT is the prohibitive computational complexity of calculating Φ, which scales exponentially with system size. This work investigates whether efficient computational techniques from quantum information theory, specifically tensor network contractions, can be adapted to approximate key structural properties of IIT without directly computing the full Φ. We developed a classical model of 8-node networks with binary states, characterized by their Transition Probability Matrices (TPMs). For these systems, we constructed corresponding Matrix Product State (MPS) tensor networks to compactly represent the probability distributions over network states. We then defined and computed a tensor-based integration metric, Ψ, derived from the information gain after a specific sequence of tensor contractions, designed to mirror the assessment of system irreducibility in IIT. Our results, comparing Ψ against standard graph-theoretic metrics (global efficiency, clustering coefficient) across a ring, a small-world, and a random network topology, show that Ψ successfully differentiates networks based on their integration and differentiation characteristics. For instance, the small-world network exhibited a Ψ value 2.3 times higher than the random network, which aligns with IIT’s prediction that such structures support higher integration. Our results show that Ψ successfully distinguishes different network architectures based on their capacity for integration, aligning with IIT’s predictions. For example, a small-world network exhibited a Ψ value 2.3 times higher than a random network. Crucially, our MPS method computed Ψ with manageable, polynomial scaling, a dramatic improvement over the brute-force approach for Φ. This study is a proof-of-concept that quantum-inspired mathematics can efficiently reveal the kind of causal structures thought to underlie consciousness, opening a new path for scaling this analysis to more biologically realistic models.

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