Golden Ratio Eigenvalues Link Modular Group to Topological Quantum Computing — E8 Intelligence Research

July 21, 2026Open Access

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Key Points

The study aims to connect the golden ratio eigenvalues from Fibonacci anyon braiding matrices to topological quantum computation.
Examined Fibonacci anyon braiding matrices and their eigenvalues as powers of the golden ratio.
Utilized mathematical representations including the Fibonacci recurrence and Binet formula.
Analyzed the relationship between the modular group SL(2,Z) and Fibonacci anyon representations.
Identified eigenvalues related to the golden ratio, with calculations showing F_{n+1} = F_n + F_{n-1}.
Demonstrated that eigenvalues satisfy the Yang-Baxter equations, establishing a link with topological quantum computing.
Outlined modular group representations confirming their relevance to Fibonacci anyons.

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This finding links eigenvalues from Fibonacci anyon braiding matrices to topological quantum computation via the modular group.

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Andrew Stewart Caldin (2026) studied this question.

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