Abstract:
A quantum signal must be routed through N nodes. The cost of transmission is not purely geometric but depends on the phase coherence between entanglement pairs and the fundamental limits of quantum mechanics.
Key Mechanics:
  1. Entanglement Phase Cost: The cost to jump from node u to v is propotional to the absolute sine of their phase different: .
  2. Quantum Tunneling: If the Euclidean distance between two nodes is a prime number (rounded), a tunnel opens. This allows a jump with a fixed cost of 0.5, but at the expense of a 20% reduction in remaining ATP.
  3. Heisenberg Uncertainly Barrier: A jump is forbidden if the product of "Position Uncertainly" () and "Phase Momentum" ( ) is less than the effective Planck constant .
  4. Trivalent Constraints: You must reach the destination before ATP reaching 0 and within a maximum of Nsteps.
Goal: Find the minimum total cost path while satisfying the uncertainty principle.
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Last Solution submitted on Mar 22, 2026

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George Berken Hoang Minh Tri

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