This is a working simulator for topological quantum computing using Fibonacci anyons.
Unlike conventional quantum computers that use fragile qubits, topological quantum computers encode
information in the braiding patterns of exotic particles.
Key Insight: The golden ratio φ appears in the quantum gate matrices — not by choice, but by mathematical necessity. This is the Circumpunct Framework's prediction made manifest.
How to Use
Select 3 particles from the grid on the right (click to add)
Apply braid operations using σ₁, σ₂ buttons (these are quantum gates)
Watch the field evolve in the center visualization
See the unitary matrix update — notice φ in the entries!
The braid generators satisfy the Yang-Baxter equation:
σ₁σ₂σ₁ = σ₂σ₁σ₂
This is the fundamental consistency condition for quantum computation.
F-matrix — Built from φ: entries are 1/φ and √(1/φ)
⊙ = • ⊗ ○ ⊗ Φ — Valid vertices require center, boundary, and field
Why It Matters
This isn't just visualization — it's a proof of concept. The framework predicts that φ (the golden ratio)
is fundamental to reality's structure. Here, you can see it directly: φ appears in every quantum
gate because Fibonacci anyons require it.