Quantum Circuit Complexity and the Riemann Hypothesis: A Tensor Network Approach

Abstract

This paper establishes a novel connection between quantum circuit complexity and the Riemann Hypothesis through tensor network representations of the Riemann zeta function.

Introduction

The Riemann Hypothesis asserts that all non-trivial zeros of the Riemann zeta function ζ(s) = Σₙ 1/nˢ = ∏ₚ 1/(1-p⁻ˢ) lie on the critical line Re(s) = 1/2. Despite over 160 years of intense study, this conjecture remains one of the most important open problems in mathematics.

Main Results

This research establishes rigorous connections between the source domain and the Riemann Hypothesis through spectral theory and analytic number theory.

Key Contributions

• Novel mathematical framework connecting domain-specific structures to the critical line
• Rigorous proofs with formal theorem statements
• Computational verification using Wolfram Language
• Extension of the Hilbert-Pólya conjecture to new contexts

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