Topological–Cyclotomic Resonance in Ring-Entangled Quantum Circuits

Kevin Miller

Published Jan 14, 2026• 1 citation

Abstract

We report the discovery of Topological Cyclotomic Resonance (TCR), a phenomenon where quantum circuits on ring topologies exhibit optimal fidelity at a rotation parameter λ* = sin(π/11). Using IBM Quantum hardware (ibm_fez, ibm_torino) with 960,000 total shots and rigorous ABBA drift-cancellation protocols, we observe the predicted resonance with 8.4σ significance (p < 10⁻¹⁶). The constant generalizes to λ*_V = sin(π/(2V+1)) for V-qubit rings, connecting quantum computing to cyclotomic field theory. All data, code, and preregistration documents are publicly available.

DOI: 10.5281/zenodo.18250271

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